UNIVERSIT`A DEGLI STUDI DI TORINO Chemical ... - iBrarian [PDF]

` DEGLI STUDI DI TORINO UNIVERSITA DIPARTIMENTO DI FISICA GENERALE

DOTTORATO DI RICERCA IN FISICA XV I o Ciclo

Chemical Enrichment of the Intergalactic Medium by Galactic Winds

Tesi presentata da Serena Bertone

Relatori: Dott. Antonaldo Diaferio Prof. Simon D.M. White

Coordinatore del Ciclo: Prof. Ezio Menichetti

Anni Accademici 2000–2001 2001–2002 2002–2003

“Mars causes accidents and burns and things like that, and when it makes an angle to Saturn, like now” she drew a right angle in the air above her “that means that people need to be extra careful when handling hot things...” “That,” said Firenze calmly, “is human nonsense.”

Abstract In this thesis, we present a new implementation of the physics of galactic winds within the semi–analytic galaxy formation model of Springel et al. (2001a), and we apply it to a set of high resolution N–body simulations of structure formation in a ΛCDM universe (Stoehr 2003). The evolution of winds is investigated by following the expansion of supernova driven supershells around the several hundred thousand galaxies that form in an approximately spherical region of space with diameter 52h −1 Mpc and mean density close to the mean density of the Universe. We focus our attention on the impact of winds on the diffuse intergalactic medium. Initial conditions for mass loss at the base of winds are taken from Shu, Mo & Mao (2003). These parameterise the mass loss and the initial velocity of winds as a function of the star formation rate of the galaxy. We follow the evolution of galactic winds throughout most of the history of the universe and we outline their impact on the IGM by estimating the volume filling factor of winds and the fraction of IGM mass in shells. Their dependence on the model parameters is carefully investigated. We find that a high volume filling factor does not necessarily correspond to a high mass fraction in wind cavities and shells, implying that even very spatially extended galactic winds may not leave detectable imprints on the Lyα forest. Low mass galaxies play a major role in seeding the IGM with metals at high redshift in models where winds sweep up little gas from the IGM and supernova ejecta constitute most of the mass in shells. The formation of winds in low mass galaxies is instead suppressed in models in which the mass of IGM entrained in winds is significant. In these models, the IGM is enriched at later times. We present our metodology to extract artificial spectra from our simulated region and we discuss some preliminary results about feedback signatures in the Lyα forest. A more accurate analysis will be left for future investigations. We search for wind signatures by looking at the spectral optical depth and at the transmitted flux in the surroundings of wind–blowing galaxies. We find that galactic winds evacuate cavities in the IGM, in which the transmitted flux of UV photons may be significantly enhanced, as observed by Adelberger et al. (2003). The matter accumulated in shells may produce observable absorption features in the spectra, if the temperature

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Abstract

of the gas is low enough to allow at least part of the gas to return neutral. In our spectra we don not observe absorption by shells between z ∼ 3 and z ∼ 2, because the gas is at temperatures higher than 10 6 K and is completely ionised. The thesis is organised as follow. In chapter 1 we outline the basics of modern cosmology, with particular emphasis on the current knowledge of the intergalactic medium and galactic winds. In chapter 2 we give an overview about different simulation techniques and describe in detail our numerical implementation of the physics of galactic winds in the semi–analytic code of Springel et al. (2001a). In chapter 3 we describe briefly our main results for the evolution of winds and we outline some of their global properties as a function of our model parameters. Chapter 4 presents the volume filling factor of winds and the fraction of mass in shells. In chapter 5 we show our results about the ejection of metals in the IGM by galactic winds and we briefly discuss the two possible scenarios of chemical enrichment which arise from our models. In chapter 6 we describe our method to extract synthetic spectra from our simulated region and show our preliminary results about feedback effects on the Lyα forest. We finally draw our conclusions and discuss future developments.

Contents Abstract 1 The Theoretical Framework 1.1 The Foundation of Modern Cosmology . . . . . . . . 1.2 The Large Scale Structure of the Universe . . . . . . 1.2.1 Inflation and Primordial Density Fluctuations 1.2.2 Galaxy and Cluster Surveys . . . . . . . . . . 1.3 (Dark) Matter and Energy Content of the Universe . 1.3.1 The Dark Energy . . . . . . . . . . . . . . . . 1.3.2 The Dark Matter . . . . . . . . . . . . . . . . 1.3.3 An alternative to the Dark Stuff: MOND . . 1.4 Galaxy Formation in a ΛCDM Universe . . . . . . . 1.4.1 The Power Spectrum of Density Fluctuations 1.4.2 The Formation of Cosmic Structures . . . . . 1.4.3 Problems of the CDM Paradigm . . . . . . . 1.5 The Intergalactic Medium . . . . . . . . . . . . . . . 1.5.1 Cosmological Reionisation . . . . . . . . . . . 1.5.2 The UV Ionising Background Radiation . . . 1.5.3 The Equation of State of the IGM . . . . . . 1.5.4 The Lyα Forest . . . . . . . . . . . . . . . . . 1.5.5 Damped Lyα Systems . . . . . . . . . . . . . 1.5.6 Lyman Break Galaxies . . . . . . . . . . . . . 1.5.7 SCUBA Galaxies . . . . . . . . . . . . . . . . 1.6 Element Abundances . . . . . . . . . . . . . . . . . . 1.6.1 Metals in the Lyα Forest . . . . . . . . . . . 1.6.2 Other Reservoirs of Metals . . . . . . . . . . 1.6.3 Sources of Metal Enrichment . . . . . . . . . 1.7 Galactic Winds . . . . . . . . . . . . . . . . . . . . . 1.7.1 Phenomenology and Energetics . . . . . . . . 1.7.2 Winds in Local Starbursts . . . . . . . . . . . 1.7.3 Galactic Winds in the High Redshift Universe

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2 Numerical Simulations of Structure Formation 2.1 An Overview of Simulation Techniques . . . . . . . . 2.2 The Physics of Cosmological Simulations . . . . . . . 2.2.1 Collisionless Dynamics . . . . . . . . . . . . . 2.2.2 Gasdynamics . . . . . . . . . . . . . . . . . . 2.2.3 Smoothed Particle Hydrodynamics . . . . . . 2.2.4 Our Set of Cosmological N–body Simulations 2.2.5 The Mass Refinement Technique . . . . . . . 2.3 Semi–Analytic Models for Galaxy Formation . . . . 2.3.1 Merging Trees and Galaxy Populations . . . 2.3.2 The NFW Halo Density Profile . . . . . . . . 2.3.3 Gas Cooling . . . . . . . . . . . . . . . . . . . 2.3.4 Star formation . . . . . . . . . . . . . . . . . 2.3.5 Feedback . . . . . . . . . . . . . . . . . . . . 2.3.6 Galaxy Merging . . . . . . . . . . . . . . . . 2.3.7 Spectrophotometric evolution . . . . . . . . . 2.3.8 Morphological evolution . . . . . . . . . . . . 2.4 New Feedback Recipes for Galactic Winds . . . . . . 2.4.1 The Thin Shell Approximation . . . . . . . . 2.4.2 Wind Velocity and Mass Loss Rate . . . . . . 2.4.3 The Wind Environment . . . . . . . . . . . . 2.4.4 Shell Merging . . . . . . . . . . . . . . . . . . 2.4.5 Metals in Winds . . . . . . . . . . . . . . . .

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3 Evolution of Winds 3.1 Solution for a Single Galaxy . . . . . . . . . . . . . . . . 3.1.1 General Trends . . . . . . . . . . . . . . . . . . . 3.2 Properties of the Shell Population . . . . . . . . . . . . 3.2.1 Properties as a Function of z . . . . . . . . . . . 3.2.2 Properties at z = 3 as a Function of Parameters 3.2.3 The Fraction of Wind–Blowing Galaxies . . . . . 4 Filling Factor 4.1 Volume Filling Factor . . . . . . . . . . 4.1.1 Connections with the Lyα Forest 4.1.2 Definition . . . . . . . . . . . . . 4.1.3 Graphic Visualisations . . . . . . 4.1.4 Evolution with Time . . . . . . . 4.1.5 Clustering and Overlapping . . . 4.2 The Wind Mass Budget . . . . . . . . .

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CONTENTS 5 Metals in Winds 5.1 Metal Ejection and Galaxies at z ∼ 3 . . . . 5.2 Metals in Shells at z ∼ 3 . . . . . . . . . . . 5.3 Shell Metallicity . . . . . . . . . . . . . . . 5.4 Missing Metals? . . . . . . . . . . . . . . . . 5.5 The Role of Galaxies with Different Masses

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6 Artificial Spectra 6.1 Feedback and the Lyα Forest . . . . . . . . . . . . . . . . . 6.2 The Ingredients for the Spectra . . . . . . . . . . . . . . . . 6.2.1 Particle Densities . . . . . . . . . . . . . . . . . . . . 6.2.2 Particle Temperatures . . . . . . . . . . . . . . . . . 6.2.3 Hydrogen Ionisation State . . . . . . . . . . . . . . . 6.3 Construction of Spectra . . . . . . . . . . . . . . . . . . . . 6.3.1 Identification of a Random LoS . . . . . . . . . . . . 6.3.2 The Integration along the LoS . . . . . . . . . . . . 6.3.3 From the Optical Depth to the Spectrum . . . . . . 6.3.4 The Voigt Line Profile . . . . . . . . . . . . . . . . . 6.3.5 Normalisation of Spectra . . . . . . . . . . . . . . . 6.3.6 Some Examples of Unperturbed Spectra . . . . . . . 6.4 Shell Contributions to the Optical Depth . . . . . . . . . . 6.4.1 Shell Optical Depth . . . . . . . . . . . . . . . . . . 6.4.2 Surface Number Density and Temperature of Shells 6.4.3 Shell Cooling Time . . . . . . . . . . . . . . . . . . . 6.5 Wind Signatures in Spectra . . . . . . . . . . . . . . . . . . 6.5.1 Wind Cavities . . . . . . . . . . . . . . . . . . . . . 6.5.2 Shell Signatures . . . . . . . . . . . . . . . . . . . . 6.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Future Prospects . . . . . . . . . . . . . . . . . . . .

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Conclusions

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Bibliography

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References

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Acknowledgements

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List of Figures 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

The 2dFGRS Galaxy Distribution . . The Lyα Forest in a QSO Spectrum . The Lyα Mean H I Opacity . . . . . . The Lyman Break Technique . . . . . Column Density Distribution of C IV . Element Abundances at z = 3 . . . . . Metals and Baryons at z ∼ 2.5 . . . . The Local Starburst Galaxy M82 . . . ES1: A Galactic Wind at z=5.19 . . .

2.1 2.2 2.3 2.4

DM Density Evolution of M3 . . . . . . . . . . . . . Mass Resolution Effects in the M Simulations . . . . Zoom–in on the DM Density Distribution of M3 at z Wind Initial Conditions . . . . . . . . . . . . . . . .

3.1 3.2 3.3 3.4 3.5

Example of Wind Evolution . . . . . . . . . . . . . . . . Radii and Masses of Shells in Time . . . . . . . . . . . . Radii and Masses of Shells with Parameters . . . . . . . Fraction of Wind–Blowing Galaxies . . . . . . . . . . . . Differential Fraction of Wind–Blowing Galaxies at z = 3

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Wind–Filled Region I . . . . Wind–Filled Region II . . . . Volume Filling Factor . . . . Overlapping and Clustering of Fraction of Mass in Shells . .

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Cumulative Distribution of Metals at z = 3 Cumulative Distribution of Stars at z = 3 . Metals in Shells . . . . . . . . . . . . . . . . Metallicity of Shells . . . . . . . . . . . . . Effect of Mass Resolution . . . . . . . . . .

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IGM Temperature at ρ = ρ¯ . . . . . . . . . . . . . . . . . . . 109

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LIST OF FIGURES

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Gas Temperatures at z = 3 . . . . . . . . A Line of Sight Construction at z = 3 . . Examples of Spectra at z = 3 . . . . . . . Wind Signatures in the LoS Construction Wind Signatures in Spectra at z = 3 . . . Wind Signatures in Spectra at z = 2 . . .

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“So,” he said. “Have you been practicing?” “Yes,” Harry lied, looking carefully at one of the legs of Snape’s desk. “Well, we’ll soon find out, won’t we?”

Chapter 1

The Theoretical Framework In this chapter we review the main theoretical and observational paradigms of present day cosmology. We start from the dark components of the matter and energy content of the Universe and we subsequently focus on its baryonic components. The properties of the intergalactic medium are presented together with the ones of the populations of high redshift galaxies responsible for the physical and chemical state of the IGM.

1.1

The Foundation of Modern Cosmology

The first self–consistent theory of the Universe as a whole was proposed by Albert Einstein back in 1915, immediately after the set up of the definitive version of the General Theory of Relativity. Einstein’s field equations describe how a four–dimensional space–time is distorted by the presence of matter and how, in turn, matter moves along trajectories in bent space–time. Several solutions to the equations were soon derived to describe our Universe, which at that time was believed to be stationary. Einstein (1917) was able to find stable static solutions only by introducing what is now known as the cosmological constant Λ, but shortly afterwards Willem de Sitter demonstrated that the equations can be solved also in the case of an empty Universe. In 1922 Aleksander Friedmann published the two famous papers in which he discovered both static and expanding solutions, actually before it was realised that the Universe is nonstationary. His achievements were not fully appreciated until 1929, when Edwin Hubble realised that the Universe is expanding by discovering that the galaxies, which at that time were believed to be extragalactic nebulae, are all moving away from the Milky Way with a recessional velocity proportional to their distance from our Galaxy. Friedmann’s solutions to Einstein’s field equations satisfyingly describe a uniformly expanding Universe without recurring to the cosmological constant. Einstein regarded the introduction of Λ as “the biggest blunder of

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The Theoretical Framework

my life” (Gamow 1970), but, as Zeldovich remarked, “the genie is out of the bottle and, once he is out, he is very difficult to put back in again”. Zeldovich prediction became true in recent years, when the cosmological constant was resumed from oblivion thanks to new observations of distant supernovae of type Ia (SNIa) and of the Cosmic Microwave Background radiation (CMB) and to new results from numerical simulations of structure formation, as we will see in the following. After the Second World war, George Gamow realised that, if the Universe is expanding, the very early stages of its formation must have been very hot and the dynamics of the expansion must have been dominated by the energy density of thermal radiation, rather than by the mass content of the Universe. Gamow attempted to explain the origin of the chemical elements by primordial nucleosynthesis, but his theory was unable to synthesise elements heavier than helium. By 1964, it was clear that heavy elements could not have a primordial origin. Though, observations of a mass fraction of helium as high as 24% suggested that most of it must have been created by primordial nucleosynthesis in the early Universe, since it could not have been produced entirely by stars. Detailed calculations by Fred Hoyle, Roger Tayler and collaborators confirmed that about 23 to 25% of helium in mass is produced by primordial nucleosynthesis, together with few other light isotopes, namely 3 He, 7 Li and deuterium D, which are difficult to account for by stellar nucleosynthesis. The idea that a background of black–body radiation with a temperature of about 5 K might have been left behind as a cooled remnant by the hot early phases of the expansion of the Universe was first proposed by two collaborators of Gamow, Ralph Alpher and Robert Herman. The predicted remnant of the Big Bang, the CMB, was discovered accidentally by Arno Penzias and Robert Wilson (1965), when the sensitivity of receivers at centimeter wavelengths improved. In the last fourty years our knowledge of the Universe has made an impressive progress and a wealth of details has been added to the theory of the hot Big Bang. However, the basic picture of its origin and evolution still relies on the same four simple independent pieces of evidence: the expansion of the distribution of galaxies discovered by Hubble; the black body spectrum and the isotropy of the CMB; the primordial abundance of elements; the fact that the age of the oldest stars and the age of the Earth, as measured by nucleocosmochronology, are of the same order as the expansion age of the Universe.

1.2

The Large Scale Structure of the Universe

The isotropy and homogeneity of Friedmann’s world models does not account for the enormous diversity of structures we observe in the Universe

1.2 The Large Scale Structure of the Universe

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today. The next step in developing a more realistic model is therefore to include tiny density perturbations, originated as quantum zero–point fluctuations during the period of inflationary expansion, into the homogeneous model and to study their development under the influence of gravity. To first order, the density perturbations are characterised by a single function P (k, z), the power spectrum, which gives the variance of the fluctuations as a function of wavenumber k and redshift z. The power spectrum depends on three factors: the seed fluctuations created in the early Universe, the galaxy formation process and the cosmic matter budget.

1.2.1

Inflation and Primordial Density Fluctuations

The Gaussianity of the distribution of primordial fluctuations is a key assumption of modern cosmology, motivated by simple models of inflation. An epoch of accelerated expansion in the early Universe, inflation, dynamically resolves cosmological puzzles such as homogeneity, isotropy and flatness of the Universe (Guth 1981, Linde 1982). The majority of inflation models predicts Gaussian, adiabatic, nearly scale–invariant primordial fluctuations (Peiris et al. 2003). Since the statistical properties of the primordial fluctuations are closely related to those of the CMB radiation anisotropy, a detection or a non–detection of non–Gaussianity of the CMB is a direct test of the inflation paradigm and can shed light on the physics of the early Universe. Recently, the Wilkinson Microwave Anisotropy Probe satellite (WMAP, Bennett et al. 2003a, [10]) demonstrated that the CMB anisotropy obeys Gaussian statistics within a 95% confidence level (Komatsu et al. 2003, Bennett et al. 2003b, Spergel et al. 2003), confirming previous results from several other CMB experiments, like COBE (Bennett et al. 1996, [32]), QMAX (Xu, Tegmark & de Oliveira–Costa 2002), MAXIMA (Hanany et al. 2000, [12]) and BOOMERanG (de Bernardis et al. 2000, [11]).

1.2.2

Galaxy and Cluster Surveys

The fundamental question is how the Universe developed from the initial nearly homogeneous state to the present–day extremely complex form. Nowadays the visible Universe is highly inhomogeneous on small scales, where the matter is condensed into stars, which in turn are congregated into galaxies of different masses, morphologies, luminosities and so on. The galaxies, which can be thought of as the building blocks of the Universe, are themselves clustered in associations ranging from small groups (M c & 1013 M ) to rich clusters (Mc & 1015 M ). The rich clusters of galaxies, which represent the largest gravitationally bound systems in the Universe, are grouped together to form superclusters, filaments, walls and other more or less complex structures on larger scales that have not had time to relax to a state of dynamical equilibrium yet.

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The Theoretical Framework

Figure 1.1: The distribution of galaxies in the 2dFGRS, drawn from a total of about 250000 galaxies; the slices are 4 o thick and are centered at a declination of −2.5o in the North Galactic Pole (NGP) and at −27.5 o in the South Galactic Pole (SGP).

The 3–dimensional large scale structure of the Universe can be mapped using different techniques: with galaxy redshift surveys, the Sunyaev–Zeldovich effect, gravitational lensing maps, X–ray galaxy cluster surveys and Lyα forest studies. Galaxy Redshift Surveys The 3D mapping of the Universe with galaxy redshift surveys offers a very powerful tool to determine the distribution of the luminous component of matter in the Universe on very large scales. The CfA redshift survey (Geller & Huchra 1989), followed by the Las Campanas (Lin et al. 1996) and the Automated Plate Machine (APM, Maddox et al. 1990) ones, discovered that inhomogeneities in the large scale distribution of galaxies do exist. Recently, the field has received renewed attention thanks to the impressive results of two different projects, the 2 degree Field Galaxy Redshift Survey and the Sloan Digital Sky Survey. The 2dF Galaxy Redshift Survey (2dFGRS) (Colless et al. 2001) obtained spectra for about 250000 objects, mainly galaxies, which cover an area of approximately 1500 square degrees. The full data set is publicly available [2] and the final distribution of galaxies is reproduced in figure 1.1. The Sloan Digital Sky Survey (SDSS) is the most ambitious astronomical

1.2 The Large Scale Structure of the Universe

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survey project ever undertaken (York et al. 2000). The survey is mapping about one–quarter of the entire sky, determining the positions and absolute brightnesses of more than 100 million objects and the redshifts of more than a million galaxies and quasars. Part of the data set has been released in May 2003 (Abazajian et al. 2003, [3]). Apart from studying the large scale distribution of galaxies, the 2dFGRS and SDSS data can be used to investigate other astronomical open issues, like the structure of the Milky Way, the highest redshift quasars and the nature of the dark energy.

Galaxy Clusters with the Sunyaev–Zeldovich Effect The Sunyaev–Zeldovich effect (SZE, Sunyaev & Zeldovich 1970) provides a unique way to map the large scale structure of the Universe as traced by massive clusters of galaxies. As a spectral distortion of the CMB, the SZE is insensitive to the redshift of the galaxy cluster, making it well suited for studies of clusters at all redshifts, and especially at z > 1, where the cluster abundances depend critically on the assumed cosmology (Carlstrom, Holder & Reese 2002). Upcoming SZE surveys are expected to find hundreds to thousands of new galaxy clusters, with a mass selection function remarkably uniform with redshift.

Gravitational Lensing by Large Scale Structure The observation of gravitational lensing by large scale structure is a direct probe of the matter distribution in the Universe. The method gives the most unbiased picture of the matter distribution at low redshift, compared to other techniques like cosmic velocity fields, galaxy distribution or Lyα forest studies, which have to rely on assumptions about the dynamic state of the structures or the biasing between ordinary and dark matter distribution. In addition, cosmic shear is the only way to directly probe the dark matter on scales that cannot be probed by other techniques like CMB and SNIa experiments (Mellier 1999). With the advent of new wide field surveys with subarcsecond spatial resolution (like Megacam on the Canada–France–Hawaii Telescope (CFHT, [24]) or the VLT Survey Telescope (VST, [22])), or very wide field shallow surveys (such as the VLA–Faint Images of the Radio Sky at 20 cm (FIRST, [13]) survey or the SDSS), weak lensing analysis should probe the power spectrum of the projected mass density from arcminutes up to degree scales (Bartelmann & Schneider 1999). Weak lensing surveys should also be capable of providing a projected mass map of the Universe, just as the APM survey provides the visible light distribution.

The Theoretical Framework

8 X–Ray Clusters of Galaxies

Observations in the X–ray band provide and efficient method to identify clusters of galaxies and estimate their dynamical masses. The gas in the deep gravitational potential well of a cluster reaches temperatures up to 10 8 K, becomes fully ionised and emits in the X–rays via thermal bremsstrahlung (Rosati, Borgani & Norman 2002). The all–sky survey and the deep pointed observations conducted by the ROSAT satellite [14] have been a goldmine for the discovery of hundreds of new clusters in the nearby and distant Universe (Cruddace et al. 2002).

1.3

(Dark) Matter and Energy Content of the Universe

An important problem of observational cosmology, raised by the properties of the galaxy distribution, is the missing mass detected in increasing amounts at larger and larger scales. This was first noticed by Zwicky (1937), who estimated that the speed of galaxies in rich clusters is much too large to keep the systems gravitationally bound together unless the dynamical mass is at least 100 times larger than the mass one would estimate on the basis of the stellar mass content. The integrated counts of galaxies taking into account the mass–to–light ratio M/L of individual galaxies yield low mass density estimates in agreement with the primordial nucleosynthesis predictions (Binney & Tremaine 1987). However, dynamical studies of systems of galaxies on scales from cluster cores to superclusters suggest the presence of a dark matter component more uniformly distributed than the galaxies, representing a dominating fraction of the matter in the Universe. The existence of a dark component of matter got further support by the introduction of the theory of inflation (Guth 1981), that prescribes a Universe with flat geometry of space and total density parameter Ω = ρ/ρ c = 1 and curvature K = 0. ρc = 3H 2 /8πG is the critical density and H the Hubble constant. A different value of the density parameter would imply either an open Universe that expands forever (Ω > 1, K < 0 implying a hyperbolic geometry), or a closed one that eventually recollapses (Ω < 1, K > 0 implying a spherical geometry). At first, the dark matter was estimated to account for about 90% of the total matter content of the Universe, but careful studies revealed that there is no sufficient matter in the Universe to reach the critical value predicted by inflation.

1.3.1

The Dark Energy

The controversy between theories that predict a total density parameter Ω = 1 and observations that yield a matter density parameter Ω o ∼ 0.2−0.4

1.3 (Dark) Matter and Energy Content of the Universe

9

may be solved by the discovery that the expansion of the Universe has been speeding up in the last 7 billion years (Riess et al. 1998, Perlmutter et al. 1999). This effect was soon attributed to the presence of a misterious dark energy, whose energy density Ωλ helps to make the Universe geometry flat and whose negative pressure produces cosmic acceleration. The evidence for the existence of the dark energy comes principally from two independent observations: the light curves of supernovae of type Ia (SNIa) and CMB experiments.

Evidence from Supernovae Type Ia Supernovae of type Ia are considered the best standard candles in extragalactic astronomy. They are believed to mark the destruction of white dwarf stars when the mass they accrete from a companion star provokes the carbon and oxygen in their interior to erupt in a runaway thermonuclear explosion. Observations of the light curves of SNIa at high redshifts have been recently performed by Perlmutter et al. (1999) using ground based large telescopes and by Riess et al. (1998) and Tonry et al. (2003) with the Hubble Space Telescope (HST, [7]). The brightness and the spectra of SNIa determine the relation between distance and redshift: the redshifts of supernovae at different distances reveal changes in the rate of cosmic expansion that have developed when the light was in flight to us. Both teams found indications that the Universe is presently accelerating for z . 0.5, since the SNIa appear dimmer than one would expect if the Universe decelerated. Conversely, if the mass energy density dominated over the vacuum energy and the Universe were decelerating at the epoch of the detonation, the apparent magnitudes of the SNIa would be higher than expected. Independently of any large scale structure measurements, Tonry et al. (2003) find for the matter density parameter Ω o = 0.28±0.05, while the dark energy accounts for 72% of the energy content of the Universe. At present ΩΛ /Ωo ∼ 2 and the dark energy dominates slightly over the matter density, but about 7 billion years ago there has been a shift from a decelerating Universe dominated by Ωo to an accelerating one dominated by Ω Λ . This is because the sum ΩΛ + Ωo remains constant, but the two contributions change accordingly to different scaling relations. Although theoreticians are puzzled by the coincidence that we live close to the era of the shift between a decelerating and an accelerating Universe, observers are delighted, because the change is potentially within view. At the moment too few SNIa have been observed at z > 1 to draw conclusions, but future experiments like The Great Observatories Origins Deep Survey (GOODS, Riess et al. 2003, [9]) and the dedicated satellite Supernova Acceleration Probe (SNAP, Perlmutter 2003, [8]) are expected to shed light on this dark aspect of cosmology and to put tighter constraints on the equation of state of the dark matter.

10

The Theoretical Framework

Evidence from the Cosmic Microwave Background Radiation The second piece of evidence that supports the existence of the dark energy comes from CMB anisotropy measurements. The angular power spectrum of the temperature fluctuations of the cosmic background radiation can be described by a basic cosmological model with six parameters, including the total matter density Ωo h2 , the baryon density Ωb h2 and the Hubble constant Ho at z = 0 (Hu & Dodelson 2002, see subsection 1.4.2 for a definition of h). CMB experiments can estimate these parameters with high accuracy. If extra parameters are added to the cosmological model by relaxing some of the minimal assumptions, it is possible to introduce a degeneracy that can be lifted by including additional astronomical data sets (Spergel et al. 2003). As an example, WMAP data have been combined with the results of two other CMB experiments at finer scales, the Arcminute Cosmology Bolometer Array Receiver (ACBAR, Kuo et al. 2003, [23]) and the Cosmic Background Imager (CBI, Pearson et al. 2003 [16]). In this way, the available data set has been extended to larger wavenumbers in the angular power spectrum, corresponding to scales of k ∼ 0.1 Mpc −1 . The combination of CMB results with supernova measurements of the angular diameter–distance relation (Riess et al. 1998, Perlmutter et al. 1999) and the HST Key Project measurement of Ho (Freedman et al. 2001) put tight constraints on the geometry of the Universe and determine Ω = Ω o +ΩΛ = 1.02±0.02. CMB data combined with results concerning the large scale structure of the Universe from the 2dFGRS (Colless et al. 2001, Percival 2001) and the Lyα forest power spectrum (Croft et al. 2002) give Ω o h2 = 0.135+0.008 −0.009 . The same combined data sets give information about other “derived” cosmological parameters, obtained by combining the fundamental ones (Spergel et al. 2003). For example, the matter density of the Universe results Ω o = 0.27 ± 0.04 and the baryon density Ωb = 0.044 ± 0.004. The combination of the three data sets for the large scale structure, the CMB and the supernovae, which are complementary and consistent between themselves, provides strong evidence for a flat Universe dominated by a cosmological constant. Bennett et al. (2003b) find ΩΛ = 0.73 ± 0.04. In a more critical investigation, Spergel et al. (2003) speculate on the possibility to recover also other important properties of the dark energy. The Properties of the Dark Energy Although the dark energy is believed to be the dominant component of the Universe today, it remains a mystery. The properties of the dark energy are quantified by a cosmic equation of state of the form p = wρc 2 , where p and ρ are the pressure and the density of the dark energy, c the speed of light and w a proportionality factor. The dark energy may be interpreted as the modern version of Einstein’s

1.3 (Dark) Matter and Energy Content of the Universe

11

cosmological constant, with w = −1 (for comparison, ordinary matter has w = 0 and radiation w = 1/3). This interpretation does not regard the cosmological constant as a curvature but as a vacuum energy density which carries a negative pressure. Ordinary matter carries a positive pressure. If the dark energy dominates over the matter density, then repulsive effects make the galaxies accelerate exponentially away from one another. Our future is determined by the nature of the dark energy and the acceleration will continue unless the dark energy should decay or change its equation of state. The most popular alternative to the cosmological constant is quintessence. Quintessence is a dynamical, time–evolving negative pressure whose equation of state can in principle take any form conceivable by theoretical imagination. Different combinations of observational data sets can help to put some limits on the range of possible properties of the dark energy. Tonry et al. (2003) combine observations of SNIa and 2dFGRS results and find that the parameter w in equation of state lies in the range −1.48 < w < −0.72 at 95% confidence level. Spergel et al. (2003), using CMB data, the HST measurement of Ho and large scale structure data, find w = −0.98 ± 0.12.

Future supernova experiments like the “Equation of State: SupErNovae trace Cosmic Expansion” (ESSENCE, [1]), under way at the Cerro Tololo Inter–American Observatory, will allow to constrain further the value of w. The first results are expected in 2006 and we will see either that the contours shrink around w = −1, in which case the cosmological constant will be an even stronger candidate for the dark energy, or estimates will converge on a different value of w, “which will be even more exhilarating” (Kirshner 2003). However, simply learning the value of w is not the whole story, since many different forms of dark energies could obey the same equation of state.

1.3.2

The Dark Matter

As we have seen, the baryons account only for about 17% of the matter content of the Universe, while the remaining 83% is dark matter. Apart from the name, the only thing that the dark matter and the dark energy have in common is that both of them neither emit nor absorb light. Dark matter, like ordinary matter, is gravitationally self–attractive and clusters with ordinary matter to form structures like galaxies and clusters. At present, two kinds of dark matter are known, neutrinos and black holes, but they are thought to make minor contributions to the total, while the major component remains unknown. The contribution from the radiation can be calculated accurately and does not exceed Ωrad h2 ∼ 2 · 10−5 (Peacock 1999).

12

The Theoretical Framework

The Contribution from Neutrinos Experiments on atmospheric neutrinos (Fornengo, Gonzalez–Garcia & Valle 2000, Kearns 2002) and solar neutrinos (Bahcall et al. 2003) find that neutrinos do have mass and Ων h2 & 10−4 , but very likely they cannot contribute much, in order not to spoil the process of structure formation. Spergel et al. (2003), assuming that there are three degenerate stable light neutrino species, derive an upper limit of the neutrino contribution to the matter density of the Universe Ων h2 < 0.0076. This implies a neutrino mass m ν < 0.23 eV. “Warm” dark matter models composed of neutrinos or other light particles are ruled out as well by comparisons of large scale structure data with numerical simulations of structure formation (Yoshida et al. 2003). Baryonic Dark Matter Baryonic dark matter differs from nonbaryonic dark matter in that it can aggregate in massive compact objects and can produce microlensing events. Microlensing experiments towards the Magellanic Clouds, the Andromeda galaxy and the galactic bulge provide evidence on the characteristic mass and abundance of baryonic dark matter objects. They demonstrate that such candidates are unlikely to be the dominant component of dark matter in galaxy haloes. The constraints on stellar baryonic dark matter are especially harsh to rule out white, red, beige and brown dwarfs as dominant contributors (Evans 2002). Red dwarfs constitute about 80% of the number of stars in the solar neighbourhood, but they do not constitute more than 1% of the halo mass (Graff & Freese 1996). Brown dwarfs are ruled out because they would produce microlensing effects towards the Magellanic Clouds with timescales much larger than measured (Evans 2002). White dwarf counts are still problematic, but it seems that these objects are too few to account for the halo matter content (Reid, Sahu & Hawley 2001). Neutron stars and stellar mass black holes are equally ruled out. If they were formed in the abundance necessary to account for the halo dynamical mass, their progenitor stars would have produced an exceedingly large amount of metals and background light, which are not observed (Carr 1994). Intermediate and supermassive black holes remain plausible candidates, but the microlensing events they cause have timescales too long to be detected by current surveys like MACHO (Alcock et al. 2000, [17]) and EROS ((Lasserre et al. 2000), [18]). Non–Baryonic Dark Matter Candidates At present, the best candidates for dark matter are hypothetical elementary particles that are long–lived, cold and collisionless (Ostriker & Steinhardt

1.3 (Dark) Matter and Energy Content of the Universe

13

2003). Long–lived means that their lifetime must be comparable to or greater than the age of the Universe and collisionless means that they must have a negligible interaction cross–section. Particles are finally required to be cold, which means that they must have been nonrelativistic at the onset of the matter–dominated epoch, in order to be able to immediately cluster gravitationally. Particles that fulfill these requirements are generally identified as Cold Dark Matter (CDM) and constitute the basis of the widely accepted ΛCDM cosmological scenario. Several particle candidates have been proposed as CDM, between which the favourite ones are a class of neutral weakly interacting massive particles, known as WIMPS, and the axion. WIMPS arise naturally in theories of supersymmetry and their abundance can be predicted accurately at the moment of their decoupling (freeze–out) from the primordial plasma as a function of their annihilation cross section (Bottino et al. 2002). The favourite WIMP candidate is the neutralino, the lightest stable supersymmetric particle, with a mass estimated of the order of 100 GeV (Griest & Kamionkowski 2000). Another very appealing candidate is the axion, a very light (m ∼ 1 µeV) neutral particle that is important in suppressing strong CP violation in unified theories (Bradley et al. 2003). Several experiments are under way to detect dark matter particles (e.g. Bernabei et al. 2003, Asztalos et al. 2002, M¨ortsell & Goobar 2003), but detection alone does not mean that dark matter consists entirely of WIMPS or axions. In principle the dark matter could be a mixture of different candidates and current experiments do not have the power to determine the relative abundances of different species.

1.3.3

An alternative to the Dark Stuff: MOND

Despite the successes of the CDM paradigm, there have been attempts to account for the observed astronomical mass discrepancies without invoking any form of dark matter. Whereas none of these attempts has so far led to anything like a satisfactory or a complete theory, they provide some insight into the required properties of generalised theories of gravity and inertia. Of these, the most popular theory today is Milgrom’s Modified Newtonian Dynamics (MOND, Milgrom 1983, Sanders & McGaugh 2002). MOND is an empirically motivated modification of Newtonian gravity based on the assumption that deviations from Newton’s law appear in low acceleration regimes. Although MOND successfully explains many aspects of the observed properties of bound gravitating systems, e.g. the rotational curves of galaxies, its extension to cosmology and structure formation remains ambiguous. Other alternative theories to the dark matter and the cosmological constant paradigms are reviewed by Narlikar & Padmanabhan (2001).

14

1.4

The Theoretical Framework

Galaxy Formation in a ΛCDM Universe

The last ingredient to understand how the primordial density fluctuations evolved into the present day large scale structure of the Universe regards the problem of galaxy formation and the processes by which matter became organised in galaxies and clusters. Before tackling the galaxy formation problem, we need to introduce the power spectrum of density fluctuations P (k, z).

1.4.1

The Power Spectrum of Density Fluctuations

The simplest description of the distribution of galaxies on large scales is the two–point correlation function, which describes the probability in excess of the Poisson probability of finding two galaxies of the sample at relative distance r over that of galaxies extracted randomly from a uniform distribution. By means of the Wiener–Kintchin theorem, it can be shown that the two–point correlation function is the Fourier transform of the power spectrum of density fluctuations. The two–point correlation function establishes a direct relation between galaxy counts and the density fluctuations. Observations of the two–point correlation function of galaxies from galaxy surveys suggest that the spectrum of the density fluctuations must have been very broad with no preferred scales. The power spectrum might be a power– law: P (k) = |δk |2 = Ak n , where n is the spectral index and δ = 1 − ρ¯/ρ is the density contrast. The constant of proportionality A is the amplitude of the fluctuations and is fixed by comparison with astronomical data. In the 1970s the form of the spectrum was generally assumed in an ad hoc fashion to reproduce the formation of structures. Zeldovich (1972) and Harrison (1970) suggested independently what is now called the Harrison– Zeldovich spectrum, a scale–invariant spectrum with n = 1. If n equals unity, in the matter–dominated epoch fluctuations of different wavelength have the same amplitude at the time when their scale is equal to the horizon scale, because the spectrum remains unchanged until the horizon scale encompasses the fluctuation. Recently, Spergel et al. (2003) combine CMB, 2dFGRS and Lyα data sets and find A = 0.75 +0.08 −0.07 and n = 0.96 ± 0.02, which confirm Zeldovich and Harrison theory to a high degree. Although today n is widely assumed to be constant, inflationary models predict that the spectral index of fluctuations should be a slowly varying function of scale. Peiris et al. (2003) show that the variability of n might be detectable for a plausible set of inflationary models. Spergel et al. (2003) find that the best fit parameters for varying spectral index models are A = +0.016 0.83+0.09 −0.08 , n = 0.93 ± 0.03 and dn/d ln k = −0.031 −0.017 . The values of these parameters barely change for different combinations of data sets, but the error bars shrink as new data are considered. This is an indication that a slowly varying spectral index may be favoured, although not required.

1.4 Galaxy Formation in a ΛCDM Universe

1.4.2

15

The Formation of Cosmic Structures

The problem of how tiny density perturbations evolve under gravity was first solved for a stationary medium by Sir James Jeans in 1902. He established that a density perturbation is able to collapse if its size exceeds the Jeans’ length λj = cs /(Gρ/π)1/2 , where cs is the speed of sound and ρ the density of the medium. Subsequently, Lifshitz found that the same solution applies to an expanding medium. However, it was only in the 1960s that the study of the formation and development of structures in the Universe was pioneered by the Moskow school led by Zeldovich and Novikov and the Princeton group led by Peebles. Novikov showed in 1964 that the density perturbations that evolved in present day galaxies had to have an amplitude ∆ρ/ρ ∼ 10 −4 on the scale of the horizon, where the scale of the perturbation is equal to the scale of the horizon itself r ∼ ct, with t the age of the Universe. This prediction was tested for the first time in 1992, when the COBE satellite showed that the CMB temperature is homogeneous on large scales up to a level of one part over 105 . In 1970 Zeldovich showed that the nonlinear evolution of the large scale perturbations would form sheets and pancakes which he believed would resemble the filamentary structure seen in the distribution of galaxies. This scenario of galaxy formation became known as “Hot Dark Matter” model (HDM), since neutrinos, which were supposed to be the dominant component of matter, were relativistic when they decoupled from the primordial plasma. The idea of a Cold Dark Matter, composed of particles nonrelativistic at decoupling, was first introduced by Peebles in 1982. In the CDM scenario, since the matter is very cold, perturbations are not destroyed by free streaming like in HDM models. Fluctuations survive on all scales and, when the Universe becomes matter dominated, perturbations begin to grow, completely decoupled from the matter and radiation. After the epoch of recombination, the baryons collapse into the potential wells of the dark matter to form galaxies and structures. In this hierarchical scenario of structure formation, the clustering of matter proceeds bottom–up: in the power spectrum most of the power is on small scales and so the lowest mass objects form first, while the large scale structure is built up at subsequent times by the processes of coalescence and clustering. The growth of structures is well described by the Press and Schechter formalism (Press & Schechter 1974), that shows how the mass function of objects of different masses evolves with time. Because of its nonlinear character, lack of symmetry and general complexity, the formation of cosmic structure is best approached theoretically using numerical simulations. These allow to follow the development of structure from primordial perturbations to the point where models can be compared with observations.

The Theoretical Framework

16

To build a model of the large scale structure, four basic ingredients need to be specified: (i) the initial conditions for the power spectrum of the density fluctuations, (ii) the matter and energy content of the Universe, (iii) the values of the cosmological parameters and (iv) the growth mechanism. The first two points have been treated in sections 1.2.1 and 1.3. In the next paragraphs we briefly introduce two cosmological parameters we have neglected so far and the growth mechanism, before investigating the problem of structure formation. The Hubble Constant The Hubble constant is the proportionality factor between distance r and velocity vH in Hubble’s law: vH = Hr. (1.1) H is often expressed in units of 100 h km s −1 Mpc−1 , while the uncertainty in its value is condensed in the factor h. The Hubble constant varies as a function of redshift and for a ΛCDM cosmology (Lahav et al. 1991) 

H(z) Ho

2

= Ωo (1 + z)3 − (Ωo + ΩΛ − 1) (1 + z)2 + ΩΛ .

(1.2)

The Hubble constant has been measured with high accuracy by the HST Key Project (Freedman et al. 2001) using Cepheids to calibrate several different secondary distance indicators. They find H o = 72 ± 3(stat.) ± 7(systematic) km s−1 Mpc−1 . This result has been confirmed by the WMAP results, which give Ho = 72 ± 5 (Spergel et al. 2003). The Amplitude of Fluctuations The overall amplitude of fluctuations on large scales can be determined from weak lensing surveys, cluster number counts, peculiar velocities from galaxy surveys and from the abundances and clustering of galaxies. Unlike most of the other cosmological parameters, the amplitude of fluctuations, generally expressed through the normalisation parameter σ 8 estimated on scales of 8 h−1 Mpc, is the least known of all. σ8 and the amplitude of fluctuations A defined in subsection 1.4.1 are strictly related and, if either of them is known, then the other can in principle be recovered with simple calculations. Current estimates range from σ 8 ∼ 0.6 up to σ8 ∼ 1.0 (for a summary of recent results from different methods see van den Bosch, Mo & Yang 2003 and Spergel et al. 2003). Numerical simulations and galaxy formation models generally assume σ8 = 0.9. Recently van den Bosch, Mo & Yang (2003) suggested that a smaller value of σ8 might help to solve two problems of the ΛCDM cosmology: the claim that the rotation curves of dwarf and low surface brightness

1.4 Galaxy Formation in a ΛCDM Universe

17

(LSB) galaxies are inconsistent with CDM haloes and the failure of galaxy formation models to simultaneously match the galaxy luminosity function and the zero–point of the Tully–Fisher relation. Gravitational Instability Primordial fluctuations grow by gravitational instability, now widely accepted as the primary growth mechanism responsible for the formation of structures. Empirical evidence for this process was established when the inflow of matter around overdense regions was observed for the first time in the CfA redshift survey (de Lapparent, Geller & Huchra 1986). The flow gives rise to a characteristic infall pattern (Kaiser 1987) that is measurable in a galaxy redshift survey. This infall pattern has been found also in the 2dFGRS (Peacock et al. 2001). Gravity is the dominant force to determine the behaviour of the dark matter and the formation of structures in the Universe is traced quite exactly by the evolution of the dark matter up to densities where the physics of baryons becomes relevant. The formation of the visible parts of galaxies involves gas dynamics and radiative processes of various kinds, which prevent the baryons from following the dynamics of the dark matter as closely as before. In numerical applications, the dark matter is generally represented as a collisionless, dissipationless fluid, while the gas is often described by smoothed particle hydrodynamics (SPH). The implementation of both methods in cosmological simulations will be presented in chapter 2. However, we want to note here that, when simulating the large scale structure of the Universe, the dark matter alone traces all the relevant scales, while the treatment of baryonic processes becomes indispensable only when simulating the detailed structure of galaxies or subgalactic objects.

1.4.3

Problems of the CDM Paradigm

The ΛCDM scenario, in which the formation of structures is dominated by gravity, provides a remarkably successful framework for explaining a broad range of observations pertaining to structures on scales larger than ' 1 Mpc. N–body techniques have achieved the dynamic range necessary to resolve substructures within virialised structures and the new generation of very high resolution simulations has demonstrated that the presence of numerous substructures is unavoidable in every cosmological scenario invoking the cold dark matter paradigm. For example, simulations predict that dark matter haloes with a virial mass comparable to the one of the Milky Way or M31 should contain several hundred objects, whereas only about 40 such galaxies are known in the Local Group. This result has come to be known as the “substructure problem”,

The Theoretical Framework

18

and is a direct consequence of the relatively large amount of power on small scales in “standard” ΛCDM models. A variety of solutions has been proposed to solve the problem by modifying some basic tenant of the usual CDM paradigm, but none of them appears to be completely satisfying (Barkana, Haiman & Ostriker 2001, Gnedin & Ostriker 2001, Hui 2001). Other possible solutions do not require major changes in the cosmological paradigm, but invoke the physics of the baryons. This cannot be neglected on galactic scales and may therefore influence the overall evolution of galaxies and structures. It has been proven, for example, that after reionisation the accretion and cooling of gas in low mass haloes is suppressed by the presence of a strong photoionising background radiation (Navarro & Steinmetz 1997). If the gas is unable to cool, stars do not form and the small halo cannot be detected because of the lack of stellar light. Another known problem of the CDM paradigm is the cuspy halo problem, namely that CDM models predict haloes that have an inner density profile that is too steep compared to observations (Moore et al. 1998).

1.5

The Intergalactic Medium

One of the most recent developments in observational cosmology has been the ability to extend studies of the diffuse intergalactic medium and its element abundances from the local universe to high redshifts. Thanks to the new opportunities offered by the introduction of very high resolution echelle spectrographs on 10–meter–class telescopes, like the Keck II on Mauna Kea [21], the Very Large Telescope (VLT, [22]) at the European Southern Observatory facility in Paranal [25], and the japanese Subaru telescope [26], it is now possible for the first time to obtain a huge wealth of information about the IGM between us and objects so distant in time to belong to the infancy of our Universe. The work on the high redshift Universe, its inhabitants and their chemical abundances has concentrated on four main components: (i) Active Galactic Nuclei (AGN); two classes of QSO absorption lines, (ii) the damped Lyα systems (DLAs) and (iii) the Lyα forest; and (iv) galaxies detected directly via their starlight, referred to as Lyman break galaxies (LBG) and sub– millimeter or SCUBA galaxies. In this section we will review the current knowledge about the physical state of the IGM and we will introduce the main features of the last three components listed above that have allowed scientists to unveil the properties of the high redshift Universe.

1.5 The Intergalactic Medium

1.5.1

19

Cosmological Reionisation

At an epoch corresponding to about z ∼ 1000 the IGM is expected to recombine and remain neutral until the development of sources of radiation and heat that are able to reionise it. An important test for the presence of intergalactic neutral gas was described by Gunn & Peterson (1965) after the discovery of the first high redshift quasar at z > 2. The spectra of quasars show a nonthermal continuum that extends into the far–UV and X–ray wavebands. When the UV continuum of the quasar is redshifted to the wavelength of the Lyα transition at λLyα = 1216 ˚ A, the large cross section of the transition makes the radiation to be absorbed and re–emitted in some random directions many times. If there is sufficient neutral hydrogen along the line of sight, an absorption trough should be observed bluewards of the redshifted Lyα line of the quasar. The continuum absorption has been initially searched for in quasars with a redshift high enough to shift the Lyα line in the observable optical waveA)/λLyα ∼ 2. Nowadays, observations have been band, that is 1 + z > (3300 ˚ extended to the near UV by the HST and the Far Ultraviolet Spectroscopic Explorer (FUSE, [4]) satellites. No depression has been observed blueward of the Lyα emission line of quasars up to at least z ∼ 5. In the absence of continuum absorption, the number density of neutral hydrogen atoms along the line of sight has to be lower than N HI < 10−8 cm−3 . The hydrogen in the IGM is thus very highly ionised and its neutral fraction possibly does not exceed 10−4 . Observations of quasar spectra suggest that the reionisation epoch might take place at a redshift sligtly higher than 6. In fact, the Gunn–Peterson trough was first detected in the Keck (Becker et al. 2001) and VLT (Pentericci et al. 2002) spectra of the Sloan quasar SDSS 1030–0524, at z = 6.28. The detection gives a clear indication that the Universe still contains a large fraction of neutral hydrogen at z > 6, but is fastly approaching reionisation (Fan et al. 2002). On the other hand, the mean optical depth of the Universe at the reionisation epoch, measured by the WMAP satellite, yields τ = 0.17 ± 0.06. This indicates that the reionisation of hydrogen likely happened at z = 17 ± 4 (Spergel et al. 2003, Kogut et al. 2003). There is as well evidence that the double reionisation of helium may have occurred at later times, when higher energy photons were produced by quasars. Basing their analysis on the evolution of the IGM temperature and the He II opacity as measured in quasar spectra (Theuns et al. 2002a), Theuns et al. (2002d) find that the reionisation of He II may start at z ∼ 3.4 and lasts for ∆z ∼ 0.4.

The Theoretical Framework

20

1.5.2

The UV Ionising Background Radiation

Independently of the actual epoch of reionisation, which is currently under discussion, it is intriguing to determine which sources were responsible for the process itself. The reionisation of neutral hydrogen is due to a metagalactic ultraviolet ionising radiation field, whose flux spectrum J(ν) obeys a power–law of the form J(ν) = J21 × 10

−21



ν νH I

−α

erg s−1 cm−2 sr−1 Hz−1 ,

(1.3)

where α is the spectral index, J21 is the normalisation of the spectrum in units of 10−21 erg s−1 cm−2 sr−1 Hz−1 and νH I is the Lyman limit frequency. The two prime candidates for producing the background are quasars and star forming galaxies. While the contribution from quasars can be estimated with reasonable accuracy, the one from galaxies is much more uncertain. A time–varying form for the UV background spectrum as been derived by Haardt & Madau (1996), under the assumption that the ionising photons are produced by quasars. However, quasars alone appear to be inadequate to be the only source of the UV photons especially at z > 3, where their comoving space density declines steeply (Fan et al. 2001). On the other hand, there are only indirect constraints on the contribution of star forming galaxies. The main uncertainty resides in the estimate of the fraction f esc of the ionising UV photons that can escape from star forming galaxies. Madau, Haardt & Rees (1999) claim that the known population of galaxies and quasars provide ∼ 10 times too few ionising photons than necessary to produce the current state of ionisation of the IGM. Additional sources of ionising photons may have contributed at high redshift, like a still unidentified population of high redshift quasars or an early population of pregalactic stellar objects. The IGM reionisation by primeval stellar objects has been investigated numerically and gives results in good agreement with observations (Haiman & Loeb 1997, Ciardi, Stoehr and White 2003, Wyithe & Loeb 2003).

1.5.3

The Equation of State of the IGM

At low densities (δ < 10), the temperature of the intergalactic gas is determined by the balance between the photoionisation heating produced by the intergalactic ionising background radiation and the adiabatic cooling due to the expansion of the Universe. Hui & Gnedin (1997) found that the equation of state of a photoionised intergalactic medium in a low density region can be well approximated by a power law of the form T = To (1 + δ)γ−1 , (1.4)

1.5 The Intergalactic Medium

21

where γ is the adiabatic index and To a characteristic temperature that can be recovered under the assumptions that the gas is in photoionisation equilibrium and the “heating time” t heat is equal to the Hubble time tH . To is only weakly dependent on the UV background spectral index α and it can be written as (Theuns et al. 1998) To (z) =

("

Ωb ht0H L0ε (1 + z)3/2 t0heat (2 + α)

#,"

L0 t0 (1 + z)5/2 1 − cc H 0 htheat

#)γ−1

,

(1.5)

where L0ε = 1.7 · 10−20 erg s−1 cm3 K0.7 is the photoheating rate and L0cc = −7.31·10−30 erg s−1 cm3 K−1 is the Compton cooling rate. The primed time quantities are t0heat = 5.41 × 10−11 erg cm3 K−1 and t0H = 2.06 × 1017 s. This prediction was confirmed by SPH simulations of Schaye et al. (1999) and by the actual measurement of the IGM thermal history by Schaye et al. (2000b). Schaye et al. (2000b) demonstrate that the IGM becomes nearly isothermal at the redshift of reionisation (γ ∼ 1), while at lower redshifts the imprints of reionisation are eventually washed out and the equation of state approaches an asymptotic state with γ ∼ 1.6. The physical density of the IGM correlates strongly with the column density of Lyα absorption lines, which can thus be interpreted as a tracer for the IGM equation of state. The minimum temperature that the gas can reach sets a lower limit to the width of the absorption lines, which results in a cut–off in the distribution of the linewidths (also called b–parameters) as a function of column density. This cut–off was measured by Schaye et al. (1999).

1.5.4

The Lyα Forest

For many years our knowledge of the distant Universe relied almost exclusively on QSO absorption lines. Absorption lines were seen in the earliest photographic spectra of quasars in the mid–1960’s (Sandage 1965, Gunn & Peterson 1965). By 1969 quasar redshifts were recognised to be cosmological and many of the absorption lines in quasar spectra were believed to originate in intervening galaxies (Bahcall & Spitzer 1969). The most recent interpretation of the Lyα forest, also supported by hydrodynamical simulations, is that absorption lines arise from a slowly fluctuating intergalactic medium, bathed in a diffuse ionising UV background, which is the natural result of the gravitational instability process that governs the formation of the large scale structure of the Universe in hierarchical models (Cen et al. 1994, Zhang, Anninos & Norman 1995, Hernquist et al. 1996). The modern view of the Lyα forest is often referred to as the “fluctuating Gunn-Peterson” effect. Artificial spectra match real spectra of the Lyα forest remarkably well. In particular, the simulations are very successful at reproducing the column

22

The Theoretical Framework

Figure 1.2: Illustration of the technique of QSO absorption line spectroscopy (courtesy of John Webb). On the way from its source to the telescopes on Earth, the light from a background QSO intercepts galaxies and intergalactic matter which happen to lie along the line of sight. Gas in these structures leaves an imprint in the spectrum of the QSO in the form of narrow absorption lines. The task is to relate the characteristics of the absorption lines to the properties of the intervening galaxies, which are normally too faint to be detected directly, and of the IGM.

density distribution of HI, the line widths and profiles, and the evolution of the line density with redshift. The interplay between observations of increasing precision and simulations of increasing sophistication has been very productive and has allowed a deeper understanding of the high redshift IGM. The technique of QSO absorption line spectroscopy, illustrated in figure 1.2, is potentially very powerful. It allows accurate measurements of many physical properties of the ISM in galaxies and of the IGM between galaxies. The difficult challenge is to relate the data that refer to gas along a very narrow pencil beam sightline to the global properties of the absorbers. The Lyα forest appears as a multitude of individual Lyα absorption lines bluewards of the Lyα emission line of every QSO. The forest is particularly visible in the redshift range z ∼ 2 − 4, where it probes the state of gas at overdensities δ . 5 in a mildly nonlinear evolutionary stage, free of luminosity bias. Observationally, the term Lyα forest is used to indicate absorption lines with hydrogen column densities in the range 10 12 . N (HI) . 1016 cm−2 , while systems with 1017 . N (HI) . 1020 cm−2 are called Lyman

1.5 The Intergalactic Medium

23

Limit Systems (LLS) and systems with N (HI) > 10 20 cm−2 are classified as Damped Lyα Systems (DLAs) (cfr. subsection 1.5.5). The Lyα forest has two fundamental properties: one is that it is highly ionised, so that the HI we see directly is only a small fraction (∼ 10 −3 to ∼ 10−6 ) of the total amount of hydrogen present. With this large ionisation correction the forest can account for most of the baryons at high and low redshift (Rauch 1998), since ΩLyα ≈ 0.02 h−2 . The second important property is that the physics of the absorbing gas is relatively simple and the variation of the optical depth τ with redshift can be thought of as a ‘map’ of the density structure of the IGM along a given line of sight. The idea that, unlike galaxies, the forest is an unbiased tracer of mass has motivated attempts to recover the initial spectrum of density fluctuations from the spectrum of line optical depths in the forest (Croft et al. 2002, Nusser & Haehnelt 2000). The line number density per unit redshift of the Lyα forest is defined as the number of lines above a given N H I per unit redshift. The empirical relation takes the form   dn dn = (1 + z)γ , (1.6) dz dz o where (dn/dz)o is the local comoving number density of the forest and the index γ depends on the column density threshold, the redshift range and the spectral resolution. The evolution of the line number density has been measured at high redshift by Kim et al. (2002), using VLT [22] and Keck [21] observations, and at low redshift by Weymann et al. (1998), using HST data. While the line number densities at z < 1.5 and z > 1.5 are not directly comparable in a straightforward way (Kim et al. 2002), the mean H I opacity τ H I does not rely on the line counting method. The evolution of the mean optical depth in time is shown in figure 1.3, from a collection of data. The distribution of data is well fitted by a power–law and the solid line represents the least-squares fit to the UVES [19] and HIRES [20] data, with equation: τ H I (z) = (0.0032 ± 0.0009) (1 + z)3.37±0.20 .

(1.7)

The large uncertainty in the HST data is mainly due to the lower S/N, lower resolution, and lower absorption line densities with the presence of weak emission lines, resulting in an unreliable local continuum fit. As a consequence, HST data tend to underestimate τ H I . Nonetheless, there is an indication of a slow-down in the evolution of τ H I .

1.5.5

Damped Lyα Systems

Although damped Lyα systems (DLAs) are straightforward to identify spectroscopically, their nature still remains a mystery. The large equivalent

24

The Theoretical Framework

Figure 1.3: (from Kim et al. 2002) The H I opacity as a function of z. Filled symbols represent the mean H I opacity from the UVES data. The open circle at < z > = 2.0 represents τ H I of J2233–606 when two high column density systems are excluded. Other symbols at z > 1.5 are from: open circles (Hu et al. 1995), the open square (Lu et al. 1996), the open triangle (Kirkman & Tytler 1997) and diamonds (Rauch et al. 1997). Symbols at z < 1.5 with arrows are from: open diamonds (Impey et al. 1996), open triangles (Weymann et al. 1998), open stars (Impey et al. 1999) and open squares (Penton, Shull & Stocke 2000). The dotted line represents the prediction by Press, Rybicki & Schneider (1993) and the shaded area enclosed with dotdashed lines indicates the ranges of τ expected from cosmological simulations by Dav´e et al. (1999).

1.5 The Intergalactic Medium

25

widths and characteristic damping wings which signal column densities of absorbing neutral hydrogen in excess of N (HI) = 2 × 10 20 cm−2 are easy to recognise even in spectra of moderate resolution and signal-to-noise ratios. The galaxies producing DLAs, however, have proved difficult to pin down. Wolfe et al. (1986) were the first to propose that they are the progenitors of present-day spiral galaxies, observed at a time when most of their baryonic mass is still in gaseous form. The evidence supporting this scenario is mostly indirect and there are claims that in any case the interpretation of observed features like the profiles of the metal absorption lines is not unique (Haehnelt, Steimetz & Rauch 1998, Ledoux et al. 1998). Imaging studies at high redshift are beginning to identify some of the absorbers (Prochaska et al. 2002, Møller et al. 1998). At z < 1 the imaging is easier and it appears that DLA galaxies include a relatively high proportion of low surface brightness and low luminosity galaxies (Steidel et al. 1997, Bouch´e et al. 2001) and normal spirals (Boissier, P´eroux & Pettini 2003). Current data are consistent with an approximately constant value Ω DLA over most of the Hubble time. Perhaps DLAs pick out a particular stage in the evolution of galaxies and it may be the case that different populations of galaxies pass through this stage at different cosmic epochs. Despite the uncertainty concerning the nature of DLAs, their importance for studies of element abundances remains crucial. The mean metallicity of DLAs is the closest measure we have of the global degree of metal enrichment of neutral gas in the universe at a given epoch, irrespectively of the precise nature of the absorbers. In addition, it is possible to determine the abundances of a wide variety of elements with an accuracy of up to 10–20%, because the physical processes involved in the formation of the metal lines are well known and uncertainties can be accounted for with careful analyses (Vladilo 2002). DLAs are also playing a role in the determination of the primordial abundances of the light elements (Tytler et al. 2000).

1.5.6

Lyman Break Galaxies

It is a relatively recent fact that “normal” galaxies at high redshifts can be identified directly; up until 1995 the only objects known at high z were QSOs and powerful radio galaxies. The turning point came from the Hubble Deep Fields and ground–based surveys with large telescopes. The application of the so–called Lyman break technique to galaxies (Steidel et al. 1996) allowed to successfully preselect candidate z ' 3 galaxies for further spectroscopic follow–up, giving the possibility to start extended surveys of high redshift galaxies. The Lyman break galaxies (LBG) can be easily distinguished in a moderately deep exposure of a wide field on the basis of their colours alone: if they are observed through appropriate filters, they appear to be blue in the (G − R) band and red in (Un − G). Their spectra are characteristic of star forming galaxies, with a

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The Theoretical Framework

Figure 1.4: (Courtesy of Kurt Adelberger). An illustration of the principles behind the Lyman break technique. Hot stars show a flat far–UV continua and a sharp cut–off at the limit of the Lyman series of hydrogen (top panel). While crossing the ISM, the UV photons are efficiently absorbed by neutral hydrogen. The spectrum of a star forming galaxy at z ∼ 3 observed from Earth exhibits a ‘break’ near 4000 ˚ A, which can be easily identified with appropriately chosen broad–band filters.

1.5 The Intergalactic Medium

27

flat rest–frame UV continuum and a sharp cut–off at the limit of the Lyman series of lines. In the last five years large samples have been built, making it possible to trace the star formation history of the universe over most of the Hubble time and to measure the large–scale properties of this population of galaxies, like their clustering and luminosity functions (Shapley et al. 2003, Adelberger et al. 2003, Steidel et al. 2003). By means of composite spectra assembled from a database of almost 1000 LBGs, Shapley et al. (2003) find a wealth of features attributable to hot stars, H II regions, dust and outflowing neutral and ionised gas. Shapley and colleagues claim that most of the correlations found between the absorption features can be explained in terms of the properties of the large scale outflows seen in LBGs. According to this scenario, the LBG spectra are determined by a combination of the covering fraction of outflowing neutral gas which contains dust and the range of velocities over which the gas is absorbing. Collisionally excited nebular emission lines should not be affected by the outflow and are therefore sensitive to the temperatures and the metallicities of the galactic H II regions. A correlation between the age and the star formation rate of LBGs has also been found, with the younger objects typically forming stars at about ten times the rate of the older ones and being more reddened on average.

1.5.7

SCUBA Galaxies

The development of powerful detectors in the submillimeter (submm) waveband, sensitive to wavelengths in the range 200 µm to about 1 mm, made it possible to use this region of the electromagnetic spectrum for cosmological observations not directly connected with the CMB. The Submillimetre Common–User Bolometer Array (SCUBA, [31]) camera at the 15 m James Clerk Maxwell Telescope (JCMT, [30], Holland et al. 1999) on Mauna Kea has been operating in the atmospheric windows at both 450 and 850 µm since 1997. The Max Planck Millimetre Bolometer Array (MAMBO, Kreysa et al. 1998) is a 1.25 mm camera, which operates on the 30 m telescope on Pico Veleta in Spain. The Atacama Large Millimeter Array (ALMA, [5]) will be in service at the end of this decade. After the introduction of these submm telescopes, a new class of very luminous high redshift galaxies was detected, the so called SCUBA galaxies (Gear et al. 2000). These galaxies seem to be responsible for the release of a significant fraction of the energy generated by all galaxies over the history of the Universe (Blain et al. 2002). Although redshift determinations are problematic and therefore any determination of their redshift distribution is highly uncertain, the median redshift of the population is likely to be of order 2–3. Only a handful of these objects have accurate redshifts and well determined properties at other wavelengths. Because they are typically

The Theoretical Framework

28

very faint in all other wavebands, the properties of the population of submm galaxies do not overlap significantly with other types of high redshift galaxies like LBGs and faint X–ray sources. The population of SCUBA galaxies appear to be extremely dust obscured and with a very high bolometric luminosity. Assuming that the dust content of these galaxies is heated by stars, the star formation rates implied by the submm fluxes are as high as 100–1000 M yr−1 , sufficient to produce an entire galaxy worth of stars in about 1 Gyr. Lilly et al. (1999) suggested that SCUBA sources may be elliptical galaxies in the process of formation. Using simple chemical evolution models, Dunne, Eales & Edmunds (2003) demonstrate that these dusty galaxies cannot be the progenitors of local submm sources, but are rather the ancestors of the local gas and dust poor spheroids. Another class of well studied galaxies similar in luminosity, and perhaps in physical properties, to SCUBA galaxies are the ultraluminous IR galaxies (ULIRGs) discovered by the InfraRed Astronomy Satellite (IRAS, [33], Sanders & Mirabel 1996). ULIRGs usually have a bolometric luminosity dominated by dust emission in excess of 10 12 L , which places them amongst the most luminous of all galaxies, despite they number less than 0.1% of galaxies in the local Universe.

1.6

Element Abundances

When measuring element abundances in different astrophysical environments, it is common practice to compare them to the composition of the solar system determined either from photospheric lines in the solar spectrum or from meteorites. Every element heavier than helium is considered to be a “metal”. In the standard notation, the abundance of element X relative to element Y is expressed as [X/Y ] = log(X/Y )obs − log(X/Y )

(1.8)

where (X/Y) is the relative abundance in the solar system. In general, estimates of the abundance of a particular element in the ISM or the IGM do not take into account the fraction of mass that has been depleted onto dust. The “missing” fraction varies from element to element: for example O, N, S, and Zn show little affinity for dust, while Si, Fe and most Fe–peak elements can be depleted by large amounts, depending on the gas physical conditions. Estimates of element abundances at high redshift come mainly from studies of the Lyα forest, DLAs and LBGs. While DLAs and LBGs give information about metals inside or in the surroundings of galaxies, the Lyα forest traces elements which are supposed to lie in the diffuse IGM.

1.6 Element Abundances

1.6.1

29

Metals in the Lyα Forest

Although at the beginning it was common opinion that one of the defining properties of the Lyα forest was its lack of associated metal lines, new observations with the HIRES [20] spectrograph on the Keck telescope [21] were able to resolve the weak C IV λλ1548, 1550 doublet associated with Lyα clouds with column densities log N (H I)& 14.5 (Cowie et al. 1995). Typical column density ratios in these clouds are N (C IV)/N (H I) ' 10 −2 − 10−3 , indicative of a carbon abundance of about 1/300 solar, or [C/H]' −2.5, with a scatter of about a factor of ∼ 3 (Dav´e et al. 1998).

Ellison et al. (1999) and Ellison (2000) probed that C IV absorbtion lines are present in the spectrum of the Q1422+231 quasar with column densities as low as N (C IV)' 4 × 1011 cm−2 (cfr figure 1.5), corresponding to the lowest column density Lyα clouds detected so far, with N (H I)∼ 10 14 cm−2 . Carswell, Schaye & Kim (2002) confirmed these results by detecting O VI λλ1032, 1038 absorption in the Lyα forest at z ∼ 2, where most of the Lyα absorption lines with N (H I)> 1014 cm−2 have associated O VI absorption with [O/H]∼ −3 to −2. O VI lines from regions of lower Lyα optical depth have been inferred from statistical considerations (Schaye et al. 2000a). Songaila (2001) extended the search for C IV systems to z > 5, using the new high redshift SDSS QSOs, and found that the integral of the column density distribution of C IV, that is proportional to the mass density ΩC IV , from z = 1.5 to z = 5.5 does not show any evidence for evolution, once incompleteness effects are taken into account. This result is strongly dependent on the shape and normalisation of the ionising background, which determines the fraction of ionised carbon seen in QSO spectra, and it might not imply that the carbon abundance remains constant over time. Independently of evolution, the value of ΩC IV implies a lower limit for the metallicity of the IGM of ZLyα & 10−3 Z , which indicates that the IGM was enriched with the products of stellar nucleosynthesis already ∼ 1 Gyr after the Big Bang. This gives an indication that the level of metal enrichment of the IGM might be relatively widespread and not only confined to regions close to star forming sites. Regions of the IGM which are truly of primordial composition or have abundances as low as those of the most metal poor stars in the Milky Way halo have yet to be found in the Lyα forest. But where do these metals come from? Carbon and all the other elements heavier than lithium can be produced only in stars, so obviously the metals in the Lyα forest have to be produced in stars as well. The interesting question now is rather where these stars are located: in the vicinity of the Lyα clouds observed, which are still at the high column density end of the distribution of N (H I), or are these the same first stars responsible for the reionisation of the Universe before z ∼ 6 (Songaila & Cowie 2002)?

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Figure 1.5: (from Ellison 2000) C IV column density distribution in the quasar Q1422+231 at hzi = 3.15; f (N ) is the number of C IV systems per column density interval and per unit redshift path. The straight line shows the best fitting power law with slope α = 1.44. The filled circles represent the data, the open ones the values corrected for incompleteness at the low column density end; with this correction the turnover at the lowest values of N (C IV) disappears. Earlier indications of a turnover shown by the yellow (Petitjean & Bergeron 1994) and dashed (Songaila 1997) curves are due to less sensitive detection thresholds, rather than to a real paucity of weak Lyα lines.

1.6 Element Abundances

31

Figure 1.6: (from Pettini 2003) Summary of the current knowledge of element abundances at high redshift, with respect to solar abundances. The x-axis shows the typical linear dimensions of the strucures to which the abundance measurements refer, from the central regions of active galactic nuclei on scales of 10–100 pc to the intergalactic medium traced by the Lyα forest on Mpc scales. The linear scales are approximately inversely proportional to the overdensities of the structures and the depth of their potential wells.

1.6.2

Other Reservoirs of Metals

Figure 1.6 shows a snapshot of the metal enrichment scenario that emerges by combining the abundance determinations for AGN, LBGs, DLAs and the Lyα forest at z ∼ 3. The x-axis in the figure gives the typical linear dimensions of the structures to which the abundance measurements refer, from the 10–100 pc of QSOs, to the Mpc scales of the low density IGM traced by the Lyα absoption lines. Metallicities of the inner regions of active galactic nuclei are determined from analyses of the broad emission lines and outflowing gas in broad absorption line QSOs (Hamann & Ferland 1999). DLAs are generally metal poor at all the sampled redshifts, indicating that they might arise in galaxies at an early stage of chemical evolution. By using the mean abundance of Zn, it is possible to estimate that DLAs have a typical metallicity of ∼ 1/13 solar, although the metallicities of single galaxies are actually spread over a large range of about two orders of magnitude.

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The Theoretical Framework

Little evidence for any redshift evolution in the metallicity comes from the data, but there are hints that metals are less depleted onto dust with respect to more evolved systems, with a typical dust–to–gas ratio of about ∼ 1/30 that of the Milky Way (Prochaska & Wolfe 2002). The element abundances are similar to those of Population II stars in the Milky Way, perhaps indicating that DLAs represent an early stage in the formation of spiral galaxies, before most of the gas has been converted into stars. Lyman break galaxies have element abundances close to Population I stars in the Milky Way and are the sites of intense star formation. Detailed studies of the gravitationally lensed galaxy cB58 (Pettini et al. 2002a, Pettini et al. 2002b, Savaglio, Panagia & Padovani 2002) show that the galaxy has a nearly solar metallicity, but is chemically young: its interstellar medium is highly enriched with elements produced by type II supernovae, but relatively deficient in those produced by stars of intermediate and low mass stars. It is reasonable to think that cB58 is in the act of transforming its ISM into stars on a few dynamical timescales, maybe forming a bulge or an elliptical galaxy. It is difficult to assess if the results of cB58 are typical for all LGB, but there is a clear indication that LBGs are forming stars on a dynamical timescale or have already converted most of their gas into stars. In both cases, they seem to have reached a metallicity of about 1/3 solar already at z ∼ 3. The connection between LBGs and DLAs is currently the subject of considerable discussion. Adelberger & Steidel (2000) suggest that the two classes of objects may be drawn from the same luminosity function of galaxies at z = 3, with the LBGs being the brighter ones and the DLAs the far more numerous on the faint end of the luminosity function. Such a picture finds theoretical support in numerical results from simulations of galaxy formation (Nagamine et al. 2001, Mo, Mao & White 1999).

The different physical scales in figure 1.6 reflect the depths of the underlying potential wells and the typical matter overdensities that characterise the different objects. There might be a correlation between the overdensity and the degree of metal enrichment that can be achieved at a particular cosmic epoch, demonstrating that the dependence of Z on the environment is probably stronger than any age–metallicity relation (Cen & Ostriker 1999). According to this relation, SCUBA galaxies could be a large reservoir of metals at high redshift (Dunne, Eales & Edmunds 2003). If the hypothesis that they are protoellipticals is correct, they should have formed from the highest density peaks when the Universe was young and there has been little time for pollution of the low density IGM with metals. About ∼ 40% of the ISM of SCUBA galaxies at z ∼ 2.5 appears to be locked in dust grains, a fraction that remains rather constant for all the observed galaxies. A summary of the location of metals and baryons at high and low redshift is shown in figure 1.7.

1.6 Element Abundances

33

Figure 1.7: (from Dunne, Eales & Edmunds 2003) The location of metals and baryons at high redshift. The dark shaded IGM represents the amount of gas currently observed in the Lyα forest. The “IGM+” is the additional IGM which has been inferred from numerical simulations for the total Lyα forest gas but has not been directly observed. It is this gas that appears to make up most of the baryonic content of the Universe at z = 2.5. Most metals though are in the ISM of galaxies.

The Theoretical Framework

34

1.6.3

Sources of Metal Enrichment

As noted in subsection 1.6.1, the diffuse, low density intergalactic medium detected through Lyα absorption lines appears to be seeded with metals already at relatively high redshifts. The fact that these metals must have been produced by thermonuclear reactions in stars implies that there must be an efficient mechanism for transporting them from the sites of their production to the regions where they are observed. Part of these metals might have been produced by the first generation of stars, also referred to as population III stars or simply PopIII. PopIII stars were the first objects to collapse in a very young Universe and to illuminate the IGM. They are believed to be at least partly responsible for the reionisation of neutral hydrogen. The first stars formed from metal free cosmic gas and theoretical models predict that they should have been short lived and very massive. Although the first stars did seed the primordial Universe with metals, it is difficult to predict how significant and how widespread this enrichment might have been. Madau, Ferrara & Rees (2001) claim that the IGM may have been chemically enriched by outflows from low–mass subgalactic systems prior to the reionisation epoch, rather than by the massive first stars. The escape of enriched gas from protogalactic objects has been addressed by several authors (Barkana & Loeb 1999, Efstathiou 2000, Ferrara, Pettini & Shchekinov 2000) and the main conclusion is that a large fraction of the baryonic mass of galaxies with virial temperatures of around 10 4 to 105 K can be accelerated and expelled by the energy injected in their ISM by concurrent supernova explosions following an episode of star formation. If first stars and pregalactic outflows might have played a role in the early metal enrichment of the IGM before the epoch of reionisation, there is evidence that a different mechanism is active at lower redshifts. Galactic winds have first been observed in local starburst galaxies (Heckman, Armus & Miley 1990), where galactic–scale outflows of gas appear to be accelerated by the ongoing star formation activity. Galactic winds are responsible for the removal of large amounts of gas and dust from the ISM of galaxies. This gas is often observed to be flowing outwards at velocities higher than the escape velocity of the galaxies, indicating that its ultimate fate might be leaving the galaxy and being dispersed into the IGM. If winds are not energetic enough to escape the galaxy potential wells, the outflowing gas will eventually fall back onto the galaxy, creating thus what is called a “galactic fountain”. However, those winds that do escape the gravitational pull can transport metal enriched material out of galaxies in a very efficient way. In addition to representing an efficient mechanism for the pollution of the IGM with metals, galactic winds are of cosmological importance in several ways. The transport of metal enriched gas out of galaxies affects the chemical

1.7 Galactic Winds

35

evolution of galaxies. This effect is important for understanding the chemical evolution of dwarf galaxies where metal ejection efficiencies are expected to be higher (Dekel & Silk 1986). Galactic winds may be responsible for reheating the IGM, evidence of which is seen in the entropy profiles of gas in the ICM of groups and clusters (Ponman, Cannon & Navarro 1999). Finally, galactic winds are one of the possible, indeed the preferred one nowadays, feedback mechanisms between star formation and the ISM, a necessary ingredient in current numerical simulations of galaxy formation to reproduce the faint end of the galaxy luminosity function (Somerville & Primack 1999).

1.7 1.7.1

Galactic Winds Phenomenology and Energetics

Galactic winds are unambiguously detected in many local edge–on starburst galaxies (Heckman, Armus & Miley 1990, Heckman et al. 2000), and their presence has been inferred in high redshift galaxies (Pettini et al. 2001). Galactic winds, also called superwinds, are complex multiphase outflows of cool, warm and hot gas, dust and magnetised relativistic plasma. Filamentary optical emission line gas, soft thermal X–ray emission and nonthermal radio emission, all extended preferentially along the minor axis of the galaxy and emanating in a collimated flow from a nuclear starburst, are all classic signatures of galactic winds in local galaxies. In the closest and brightest edge–on starburst galaxies the outflow can be seen in all phases of the ISM, from cold (T ∼ 104 K) molecular gas to hot (T ∼ 107 − 108 K) X–ray emitting plasma. M82, shown in figure 1.8, is the most classical and best studied example of local dwarf starburst galaxy fuelling a large scale galactic wind. The engine that drives galactic outflows is the mechanical energy supplied by massive stars in the form of supernovae and stellar winds. Each supernova explosion releases an energy E SN ∼ 1051 erg into the ISM. Part of this energy is radiated away by the gas heated by the explosion and part is transferred to the gas as mechanical energy. At present there are no accurate estimates of the fraction of the energy imparted to winds. The total energy of a galactic wind has been estimated in the range 10 54 . Ew . 1058 erg (Strickland & Stevens 2000). The rate of supply of mechanical energy is of order 1% of the bolometric luminosity of the starburst and typically 10 to 20% of the Lyman continuum luminosity (Leitherer & Heckman 1995). The dynamical evolution of a starburst driven outflow has been discussed for example by Chevalier & Clegg (1985), Breitschwerdt, McKenzie & V¨olk (1991), D’Ercole & Brighenti (1999), Strickland & Stevens (2000). The deposition of mechanical energy by supernovae and stellar winds results in an overpressured cavity of hot gas inside the starburst, which expands in the surrounding medium, sweeps up ambient material and thus develops

36

The Theoretical Framework

Figure 1.8: M82 is the closest local dwarf starburst galaxy fuelling a galactic scale wind. The red image in the Hα band overposed to the optical image in the B and V bands indicates the light emitted by the ionised hydrogen gas outflowing from the central starbursting region and creating a complex web of filaments that extend as far as 10 kpc from the galactic plane.

1.7 Galactic Winds

37

a bubble–like structure. If the ambient medium is stratified like in a disk, the superbubble expands most rapidly in the direction of the vertical pressure gradient. After the superbubble size reaches several disk vertical scale heights, the expansion accelerates and Raleigh–Taylor instabilities lead to the fragmentation of the bubble’s outer wall (Mac Low, McCray, & Norman 1989). This allows the hot gas to “blow out” of the disk and into the galactic halo as a weakly collimated bipolar outflow, hence the flow makes a transition from a superbubble to a superwind.

1.7.2

Winds in Local Starbursts

Attempts to directly measure the mass and energy content of galactic winds have been made using optical, UV and X-ray observations. The observational manifestations of superwinds result from the hydrodynamical interaction between the primary energy–carrying wind fluid and the ambient interstellar medium. Martin (1999) found that in local starburst dwarf and massive galaxies the mass ejection rate of winds is comparable to the star formation rate. The result seems to indicate that, independently of the galactic rotation speed, there is an upper limit to the mass ejection efficiency, with M˙ w /M˙ ? . 5. This upper limit is linked to the areal density of stars rather than to the depth of the galaxy potential. Strickland et al. (2002) and Cecil, Bland-Hawthorn & Veilleux (2002) use X–ray observations of local galaxies by the satellite CHANDRA [6] to demonstrate that the thermal X–ray emission matches almost exactly the filamentary, limb–brightened optical Hα emission. This proves that the X– ray emission arises in interactions between the currently invisible wind and the denser, cooler, ambient ISM responsible for the optical Hα emission. Xray observations of galactic winds do not directly probe the gas that contains the majority of the energy, mass or metal enriched gas in the outflow, because this gas resides in a volume filling hot (T ∼ 10 7 K) component which is extremely difficult to probe observationally due to its low density and hence low emissivity (Strickland & Stevens 2000). Most of the total energy of winds seems to be in the kinetic energy of this hot gas. Martin et al. (2002) show that in the dwarf starburst galaxy NGC 1569 most of the oxygen mass carried by the wind comes from stellar ejecta rather than from entrained ISM gas, indicating that the wind carries nearly all the metals ejected by the starburst. With the high sensitivity and spectral resolution of the FUSE satellite [4], it is now possible to probe the kinematics and chemical composition of the hot wind phases, with temperatures of about T ∼ 10 5 to 106 K. Gas in this temperature range is responsible for most of the cooling by radiative losses, even if it does not contain the majority of the wind energy. This “coronal” phase of the wind is best probed by the O VI doublet λ =1032– 1038 (Heckman et al. 2002). FUSE observations of NGC 1705 (Heckman et

38

The Theoretical Framework

al. 2001) show that in this particular galaxy the radiative cooling associated with the coronal gas should not dominate the dynamical evolution of the outflow, which seems to be consistent with a simple model of an adiabatic superbubble whose expansion is driven by the pressure of the hot gas. The coronal phase gas is flowing out of the galaxy at higher velocity than the warm ionised gas at T ∼ 104 K, which in turn is flowing outwards at higher velocity than the warm neutral medium. The fact that the hot phases of winds can have higher outflow velocities is of great physical significance, since it supports the theoretical idea that the hot, metal enriched phases can be preferentially ejected into the IGM (Strickland & Stevens 2000). Outflow speeds in interstellar matter entrained in the wind range from ∼ 102 to 103 km s−1 (Heckman et al. 2000, Frye, Broadhurst & Benitez 2002, Pettini et al. 2002a), but the primary wind fluid itself may reach velocities as high as ∼3000 km s −1 .

1.7.3

Galactic Winds in the High Redshift Universe

In the local Universe galactic winds affect only a relatively small fraction (∼ 5%) of the total galaxy population, and in particular dwarfs and starburst galaxies. However, at higher redshifts galactic–scale outflows seem to be much more common, since many more galaxies have large star formation rates and are presently converting the bulk of their interstellar gas into stars. Signatures of galactic winds have been observed in almost all Lyman break galaxies (Pettini et al. 2001, Adelberger et al. 2003). When the redshifts of the interstellar absorption lines, of the stellar emission lines, and of the resonantly scattered Lyα emission line are compared within the same galaxy, a systematic pattern of velocity differences emerges in all the LBGs observed. The interstellar metal absorption lines appear to be blueshifted with respect to the stellar rest frame by hundreds of km s −1 , while the Lyα emission lines are shifted similarly redwards. The Lyα line may as well present a P–Cygni profile. All these effects can be interpreted as indicative of galaxy–wide outflows, with optically thick expanding regions surrounding star forming galaxies. An example of a star forming galaxy at high redshift for which the presence of a galactic wind has been inferred by such effects is shown in figure 1.9. Typical LBGs contain absorbing material flowing outward with velocities as high as 600 km s−1 (Steidel et al. 1996, Pettini et al. 2002a). Winds with such high speeds should be able to escape potential wells as deep as those of LBGs and would likely travel a distance comparable to the observed radius of the galaxy proximity effect during the ∼ 300 Myr star formation timescale of these galaxies. As a consequence, these winds may have driven intergalactic material from cavities of a radius of ∼ 0.5 Mpc comoving surrounding each galaxy, producing the observed lack of neutral hydrogen near the galaxies.

1.7 Galactic Winds

39

Figure 1.9: Evidence for a galactic wind in the high redshift galaxy ES1 (J123649.2+621539, Dawson et al. 2002). The minimum–χ 2 fit to the ES1 Lyα emission line is shown in panel (a). The line profile is the sum of a narrow central Gaussian that models the recombination in the hot ionised gas of the starburst, a broad Gaussian redshifted by 320 km s −1 from the central component that models the back–scattering off of the far side of an expanding shell, and a broad Voigt absorption component blueshifted by 360 km s−1 from the central component that models the absorption by the near side of the expanding shell. Panel (b) shows the error per pixel in the same flux units and over the same wavelength range and panel (c) the model–fit minus the data in the same flux units and over the same wavelength range. The even distribution of the residuals demonstrates a lack of systematic errors in the model.

40

The Theoretical Framework

Adelberger et al. (2003) compare the spatial distribution of galaxies to the ones of C IV and neutral hydrogen (H I) in the spectra of quasars at z ∼ 3 and find tight correlations that indicate that H I is generally depleted in the surroundings (. 0.5 Mpc) of LBGs, while C IV systems tend to be found at distances typically in the range 0.5 − 3 Mpc from LBGs. This fact may indicate that winds that emerge from LBGs actually sweep up or ionise the neutral hydrogen in their surroundings and efficiently transport carbon and most likely other metals from the galaxy ISM far into the IGM. If this is confirmed, then galactic outflows are the best candidates to explain the level of metal enrichment observed in the diffuse IGM revealed by the Lyα forest, independently of the fact that a more or less widespread low level of enrichment might have been reached previously thanks to pregalactic outflows or PopIII stars.

“Dumbledore was having real trouble to find anyone to do the job, this year.” “Not surprising, is it, when you look at what’s happened to the last four?” said George. “One sacked, one dead, one’s memory removed, and one locked in a trunk for nine months,” said Harry, counting them off on his fingers. “Yeah, I see what you mean.”

Chapter 2

Numerical Simulations of Structure Formation In this chapter we will briefly discuss the most common numerical techniques used in cosmology. N–body and SPH simulation techniques are described in section 2.2, while the semi–analytic approach is discussed in detail in section 2.3. Our new prescriptions for the physics of galactic winds are presented in section 2.4.

2.1

An Overview of Simulation Techniques

Numerical simulations of three–dimensional self–gravitating fluids have become an indispensable tool in cosmology. They are now routinely used to study the nonlinear gravitational clustering of dark matter, the formation of clusters of galaxies, the interactions of isolated galaxies, and the evolution of the intergalactic gas. Since analytic calculations are often restricted to idealised problems of high symmetry, or to approximate treatments of nonlinear problems, the immense progress made in these fields would have been nearly impossible without numerical techniques. The advances in numerical simulations have become possible both by the rapid growth of computer performance and by the implementation of sophisticated numerical algorithms. Early simulations of structure formation (e.g. Holmberg 1941, Peebles 1970, Press & Schechter 1974, White 1976, Aarseth, Turner & Gott 1979) employed the direct summation method for the gravitational N–body problem. The method is inefficient for large particle numbers N due to the O(N 2 ) scaling of its computational cost. Different groups have therefore developed N–body codes for collisionless dynamics that compute the large– scale gravitational field by means of Fourier techniques. Examples are the PM (Particle–Mesh), P3 M (Particle–Particle, Particle–Mesh), and AP 3 M (Adaptive Particle–Particle, Particle–Mesh) codes (e.g. Eastwood & Hock-

44

Numerical Simulations of Structure Formation

ney 1974, Efstathiou et al. 1985, Couchman 1991). Some of these codes supplement the force computation on scales below the mesh size with a direct summation, and/or they place (adaptive) mesh refinements on highly clustered regions. An alternative to these schemes are the so-called tree algorithms, pioneered by Appel (1985). Tree algorithms arrange particles in a hierarchy of groups, and compute the gravitational field at a given point by summing over multipole expansions of these groups. For both techniques, the computational cost of a complete force evaluation is reduced to a O(N log N ) scaling. While mesh-based codes are generally much faster for nearly homogeneous particle distributions, tree codes can adapt flexibly to any clustering state without significant losses in speed and are basically free from any geometrical restrictions. Their Lagrangian nature is a great advantage if a large dynamic range in density needs to be covered. PM and tree solvers can be combined into hybrid Tree–PM codes (Xu 1995). In this approach, the speed and accuracy of the PM method for the long-range part of the gravitational force are combined with a tree–computation of the short–range force. Yet another approach to the N–body problem is provided by specialpurpose hardware like the GRAPE (GRAvity PipE) board, that consists of custom chips that compute gravitational forces by the direct summation technique (Hut & Makino 1999), with a O(N 2 ) scaling. In recent years, collisionless dynamics has been coupled to gas dynamics, allowing a more direct link to observable quantities. Traditionally, hydrodynamical simulations have employed some kind of mesh to represent the dynamical quantities of the fluid: while a particular strength of these codes is their ability to accurately resolve shocks, the mesh imposes restrictions on the geometry and the dynamic range of the problem. Adaptive mesh refinement codes have been developed to provide a solution to this shortcoming. In cosmological applications, it is often sufficient to describe the gas by Smoothed Particle Hydrodynamics (SPH, Lucy 1977, Gingold & Monaghan 1977). SPH is a powerful Lagrangian technique to solve hydrodynamical problems with an ease that is unmatched by grid based fluid solvers (Monaghan 1992). In particular, SPH is very well suited for three-dimensional astrophysical problems that do not crucially rely on accurately resolved shock fronts, because its Lagrangian nature allows a locally changing resolution that “automatically” follows the local mass density. SPH ties naturally into the N–body approach for self-gravity, and it has been implemented in a large number of codes (e.g. TREESPH, Hernquist & Katz 1989; GRAPESPH, Steinmetz 1996; HYDRA, [34], Couchman, Thomas & Pearce 1995, GADGET, GAlaxies with Dark matter and Gas intEracT, [27], Springel, Yoshida & White 2001b).

2.2 The Physics of Cosmological Simulations

2.2

45

The Physics of Cosmological Simulations

We present the equations that govern the physics of a collisionless fluid used in N–body simulations in subsection 2.2.1. In subsection 2.2.2 we introduce the equations of gasdynamics and in subsection 2.2.3 the equations to calculate the gas densities and other important quantities with SPH. In subsection 2.2.4 we finally describe our set of high resolution N–body simulations. Our simulations are realised using a pure N–body technique, but we show here the principles of SPH because we will use it extensively to describe the state of the intergalactic gas when calculating artificial spectra. For a more detailed treatment of gravity and hydrodynamics as implemented in our simulations see Springel, Yoshida & White (2001b).

2.2.1

Collisionless Dynamics

In N–body simulations, dark matter and stars are modelled as self–gravitating collisionless fluids, that is they fulfill the Collisionless Boltzmann Equation (CBE) df ∂f ∂f ∂Φ ∂f ≡ +v − = 0, (2.1) dt ∂t ∂x ∂r ∂v where the self–consistent potential Φ is the solution to Poisson’s equation Z 2 ∇ Φ(r, t) = 4πG f (r, v, t)dv, (2.2) and f (r, v, t) is the phase–space distribution function of the mass particles. It is very difficult to solve this coupled system of equations directly with finite difference methods. Instead, in the N–body approach, the phase fluid is represented by N particles which are integrated along the characteristic curves of the CBE. In essence, it is a Monte Carlo approach whose accuracy depends crucially on a sufficiently high number of particles. The N–body problem is thus the task of following Newton’s equations of motion for a large number of particles under their own self–gravity. Softening is introduced into the gravitational potential at small separations, in order to suppress large–angle scattering in two–body collisions and to effectively introduce a lower spatial resolution cut–off. For a given softening length, the particle number has to be chosen large enough such that relaxation effects due to two–body encounters are sufficiently suppressed. The optimum choice of softening length as a function of particle density is an issue that is still actively discussed in the literature (Splinter et al. 1998).

2.2.2

Gasdynamics

A simple description of the intergalactic or the interstellar medium may be obtained by modelling it as an ideal, inviscid gas. The gas is then governed

Numerical Simulations of Structure Formation

46 by the continuity equation

dρ + ρ∇ · v = 0, dt

(2.3)

dv ∇P =− − ∇Φ. dt ρ

(2.4)

and by the Euler equation

The thermal energy u per unit mass evolves according to the first law of thermodynamics du P Λ(u, ρ) =− ∇·v− , (2.5) dt ρ ρ where we have used the Lagrangian time derivatives d ∂ = + v · ∇. dt ∂t

(2.6)

The cooling function Λ(u, ρ) describes external sinks or sources of heat for the gas. The equation of state for an ideal gas is P = (γ − 1)ρu,

(2.7)

where γ is the adiabatic index, equal to γ = 5/3 for a mono–atomic gas. The adiabatic sound speed is c2 = γP /ρ.

2.2.3

Smoothed Particle Hydrodynamics

Unlike other numerical approaches for hydrodynamics, the SPH equations do not take a unique form, but many formally different versions of them can be derived. A large variety of recipes for specific implementations of force symmetrisation, determinations of smoothing lengths and artificial viscosity have been described. While some of these choices are crucial for the accuracy and efficiency of the SPH implementation, others are only of minor importance (Thacker et al. 1998). In this subsection we show how to calculate the smoothing lengths h i and the densities ρi for the SPH particles, which we will use for the calculation of spectra. A complete account of the mathematical treatment of all the SPH quantities may be found in Monaghan (1992) or Springel, Yoshida & White (2001b). In order to estimate the densities, one needs to find all the particles closer than a search radius hi . For highly clustered particle distributions and varying search ranges hi , a flexible choice is to employ a geometric search tree (Hernquist & Katz 1989). This allows to search for neighbours by “walking the tree”. The Lagrangian nature of SPH arises when the number of neighbours to be searched is kept either exactly, or at least roughly, constant.

2.2 The Physics of Cosmological Simulations

47

The hi adjust to the local particle density adaptively, leading to a constant mass resolution independent of the density of the flow. Having found the neighbours, the density of the particles are computed as N X ρi = mj W (rij ; hi ), (2.8) j=1

where rij ≡ ri − rj are the distances between the particle i and its N neighbours and mi the particle mass. W (r, h) is the SPH smoothing kernel, for which we assume a spline of the form (Monaghan & Lattanzio 1985): 

 1 − 6 r 2 + 6 r 3 , 0 6 r 6 1, h
h h 2 8  r 3 1 r W (r, h) = (2.9) 2 1 − , < 6 1, 3 h 2 h πh   0, r h > 1.

The smoothing kernel is defined on the interval [0, h] and not on [0, 2h] as it is frequently done in other SPH calculations.

2.2.4

Our Set of Cosmological N–body Simulations

In this work, we use a set of high resolution cosmological N–body simulations realised by Felix Stoehr at the Max Planck Institut f¨ ur Astrophysik as part of his PhD thesis (2003). The simulations have been performed using the parallel treecode GADGET (Springel, Yoshida & White 2001b, [27]), while the initial conditions have been generated with the code ZIC (Tormen, Bouchet & White 1997). We assume a ΛCDM cosmology with matter density Ω m = 0.3, dark energy density ΩΛ = 0.7, Hubble constant h = 0.7, n = 1 and σ 8 = 0.9 for the slope and the normalisation of the power spectrum of primordial perturbations. A high resolution in mass is crucial to assess the effects of galactic winds and to determine the role of galaxies with different masses in polluting the IGM with metals. The use of pure N–body simulations allows us to find a good compromise between high mass resolution and a large simulated volume, although this choice implies that the physics of baryons cannot be followed directly. A large box size is necessary to study the effects of winds in their proper cosmological context. Our set of simulations are resimulations (see subsection 2.2.5 for a brief description of resimulation techniques) at higher resolution of a “typical” spherical region with a diameter of approximately 52 h −1 Mpc and mean density close to the cosmic mean. About half of the enclosed galaxies are field galaxies, while the others are in groups and poor clusters. The simulated region was identified within the much larger comsological “VLS” simulations run by the VIRGO Consortium ([28], Jenkins et al. 2001, Yoshida, Sheth &

48

Numerical Simulations of Structure Formation

Figure 2.1: Dark matter density evolution in the high resolution region of M3. The comoving dimension of each panel is about 55 h −1 Mpc, the thickness of the slices about 10 h−1 Mpc. From left to right and top to bottom, the redshifts of the snapshots are respectively z = 20, 10, 6, 5, 4, 3, 2, 1, 0.

2.2 The Physics of Cosmological Simulations Simulation Set M3 M2 M1 M0

Mp (h−1 M ) 1.7 · 108 9.5 · 108 4.8 · 109 6.8 · 1010

49

Number of Particles 68958296 12067979 2388896 168436

Table 2.1: Particle masses and number of particles in the high resolution region for our four simulation sets.

Diaferio 2001). It was resimulated four times with increasing internal mass resolution and decreased external resolution. The effects of the large scale gravity field on the region of interest are correctly retained. The particle masses and the number of particles in the high resolution region are reported in table 2.1. The dark matter evolution is followed from redshift z = 120 down to redshift z = 0 and 52 simulation outputs were stored between z = 20 and z = 0. Some of the snaphots of the high resolution region of M3 are shown in figure 2.1. Figure 2.2 shows the effect of mass resolution at z = 0 for our four sets of simulations.

2.2.5

The Mass Refinement Technique

Cosmological simulations are often realised using periodic boundary conditions, a choice that makes it easier to account for the gravitational interaction with the mass that surrounds the simulated region. Despite this advantage, the simulation of a periodic box is only reliable provided that the box is large enough so that perturbations on scales comparable to the box size are still linear by the present time. This sets a minimum size for periodic boxes designed to be run to z = 0 in a ΛCDM universe. A different technique is required in order to improve the mass and spatial resolution of the calculation while at the same time accounting properly for the effects of large scale structure. The technique most widely adopted so far selects a few systems identified from the final configuration of a periodic box and resimulates the whole box, with coarser resolution everywhere except in the selected regions. This technique has been widely used (e.g. Katz & White 1993, Navarro & White 1994, Evrard, Summers & Davis 1994, Moore et al. 1998), and has become common in high–resolution simulations targeted at individual systems. The price to pay with this procedure is that there is the possibility of introducing biases during the selection procedure. Having identified a halo in the periodic box for resimulation, all particles within ∼ 2r vir from its centre are traced back to the initial conditions and a smaller box enclosing all of these particles is defined. Not all particles in the small box will end up near the system of interest,

50

Numerical Simulations of Structure Formation

Figure 2.2: The dark matter density distribution in the high resolution region of our four simulation sets at z = 0. In the low resolution runs the distribution of matter appears smoother, while small objects are washed out. From left to right and top to bottom, the panels are for M0, M1, M2 and M3 respectively.

2.2 The Physics of Cosmological Simulations

51

Figure 2.3: Zoom–in on the dark matter density distribution of M3 at z = 0. From left to right and top to bottom, the dimensions of the boxes are respectively 479, 380, 95 and 52 Mpc. The mass resolution is increasing toward the centre of the simulated region.

52

Numerical Simulations of Structure Formation

so the location on the original grid of selected particles is used to identify an “amoeba-shaped” region within the cube that is retained at full resolution. Regions exterior to the “amoeba” are coarse-sampled using particle masses which increase with distance from the region of interest. The sampling is typically done by binning together cubes of 2 3n neighbouring particles from the initial grid. This allows us to concentrate numerical resources within the selected object without compromising the contribution from larger scales to the tidal field acting on the system. The success of this procedure may be gauged by computing the power spectrum from the displaced particle positions and comparing it with the theoretical power spectrum. A good agreement between the theoretical power spectrum and that measured in the new realisations shows that mass refined simulations faithfully follow the formation of a dark matter halo in a ΛCDM cosmogony.

2.3

Semi–Analytic Models for Galaxy Formation

The set of N–body simulations follows the evolution of the dark matter in time and allows to determine the clustering of matter and the formation of structures down to scales typical of dwarf galaxies. The dark matter, though, does not give any information about the evolution of the baryonic component of the Universe, which therefore has to be recovered with a different technique. The formation and evolution of galaxies is modelled with the semi–analytic technique proposed by Kauffmann et al. (1999) in the new implementation of Springel et al. (2001a), which extends it to deal with higher resolution simulations. Semi–analytic techniques were first used in cosmology by White & Frenk (1991), Cole (1991) and Lacey & Silk (1991). They are based on the Press and Schechter formalism (Press & Schechter 1974) and on the scenario first sketched by White & Rees (1978). Early semi–analytic models of galaxy formation used analytic models rather than N–body simulations to specify the merging histories of dark matter haloes (White & Frenk 1991, Lacey & Silk 1991, Kauffmann, White & Guiderdoni 1993, Baugh, Cole & Frenk 1996, Somerville & Primack 1999). The combination of semi–analytic galaxy formation models with cosmological N–body simulations makes it possible to track the positions and velocities of galaxies as a function of time, in addition to the properties that can be derived with pure semi–analytic methods. In these models, the physical processes involved in galaxy formation are approximated using a simplified, physically based model. Though uncertainties are introduced by these simplifying assumptions, semi–analytic techniques can access a much larger dynamic range than numerical simulations and allow a fast exploration of the parameter space and of the influence of the specific assumptions chosen. In addition, they facilitate the direct com-

2.3 Semi–Analytic Models for Galaxy Formation

53

parisons with a wide range of observational data (e.g. Kauffmann, White & Guiderdoni 1993, Baugh, Cole & Frenk 1996, Somerville & Primack 1999, Kauffmann et al. 1999, van den Bosch 2000).

2.3.1

Merging Trees and Galaxy Populations

The semi–analytic modelling consists of two main parts: (i) the identification of the dark matter merging trees from a sequence of simulation outputs and (ii) the implementation of the recipes for the galaxy formation process on top of the merging trees. Dark matter haloes are identified with the friends–of–friends algorithm SUBFIND (Springel et al. 2001a) and a catalogue is compiled with all the groups that contain at least ten particles, meaning that for M3 the minimun mass of a dark matter halo is about 10 9 h−1 M , a value consistent with the mass associated to the population of dwarf galaxies (typical values being in the range 1010 − 1011 M ). The merging trees extracted from the simulations are followed back in time to identify the progenitors of each halo. Once dark haloes have been identified, the semi–analytic technique allows to define the galaxy population. Each halo is supposed to host exactly one central galaxy, and its position is given by the most bound particle of the halo. Only the central galaxy is supplied with additional gas that cools within the halo. A halo can have one or more satellite galaxies, where the position of each of them is given by one of the particles of the halo. Satellites are galaxies whose haloes have merged with the larger halo they now reside in. At each output time, the galaxy population consists of central galaxies, satellite galaxies and field galaxies, which are not attached to any group. The galaxy population is initialised at the first output time with a set of central galaxies, one for each halo, with stellar mass, cold gas mass, and luminosity set to zero. The physical properties of these galaxies are then evolved to the next output time, where the new galaxy population is obtained by combining semi–analytic prescriptions and the merging history of the dark matter, down to z = 0. The physical properties of galaxies are defined using appropriate semi– analytic prescriptions and their evolution in time is followed by using the merging trees. Several physical processes are modelled in detail: (i) radiative cooling of the hot gas onto the central galaxy; (ii) transformation of the cold gas into stars by star formation; (iii) reheating of the cold gas by supernova explosions and its ejection out of the halo; (iv) orbital decay of the satellites and their final merging with central galaxies; (v) spectrophotometric evolution of the stellar population; (vi) a simplified morphological evolution of galaxies. Because of its extremely simple structure, the feedback prescription (iii) does not incorporate the physics of galactic winds an in particular it is

Numerical Simulations of Structure Formation

54

unable to follow the evolution of wind shells in the IGM, which is what we aim to do. In the next subsections we will describe the recipes (i)–(vi) for the galaxy formation process and in section 2.4 we will introduce the new prescriptions for the physics of galactic winds.

2.3.2

The NFW Halo Density Profile

The distribution of the dark matter inside individual haloes is modelled following a Navarro Frenk and White (NFW) density profile (Navarro, Frenk & White 1996). The virial mass of a halo is defined as the mass included in a sphere with mean overdensity δ = 200 with respect to the critical density of the Universe. The virial radius Rvir can be expressed as a function of redshift and virial mass Mvir (Mo & White 2002, White & Frenk 1991): Rvir



GMvir = 100H 2 (z)

1/3

,

(2.10)

while the virial velocity Vvir , also called circular velocity Vc , is Vc =



GMvir Rvir

1/2

.

(2.11)

The virial temperature of the halo can be defined as Tvir

2  Vc µmp Vc2 = 35.9 K, = 2kB km s−1

(2.12)

where µ = 0.588 is the mean molecular weight of the gas assuming a primordial composition with an helium mass fraction Y = 0.24, m p the proton mass, µmp the mean particle mass and kB the Boltzmann constant. Analyzing the density profiles of dark matter haloes in numerical simulations, Navarro, Frenk & White (1996) found that the matter distribution has a quite universal behaviour, independently of the total matter content of the halo. They established that the dark matter density profile obeys the law: δc ρc (z) ρN F W (r) =  (2.13) 2 . r r rs 1 + rs δc is a characteristic overdensity given by: δc =

c3 200 3 ln(1 + c) −

c . 1+c

(2.14)

The parameter c determines the concentration of the halo and is a complicated function of redshift. Despite the numerous attempts to determine

2.3 Semi–Analytic Models for Galaxy Formation

55

it with a simple scaling law, its calculation remains not trivial (Power et al. 2003, Zhao et al. 2003, Klypin et al. 2001, Bullock et al. 2001, Navarro, Frenk & White 1997). The scale radius rs is the ratio of the concentration parameter to the virial radius: Rvir rs = . (2.15) c The mass internal to a given radius R is calculated by integrating the dark matter density distributionin equation 2.13 over the spherical volume within R:     Z R R R 2 3 M (R) = ρ(r)4πr dr = 4πρc δc rs ln 1 + − . (2.16) rs R + rs 0 If Φ(r) is the gravitational potential of the halo, the escape velocity at distance R from the centre is given by: Z ∞ GM (r) 2 dr. (2.17) vesc (R) = 2 |Φ(R)| = 2 r2 R Substituting equation 2.16 into equation 2.17 and integrating, the escape velocity can be written as: 2 vesc (R) = 2Vc2

R cx F (cx) + 1+cx 2GMvir log(1 + rs ) = , xF (c) R F (c)

(2.18)

where we have defined x = R/Rvir and the function F (t) as: F (t) = log(1 + t) −

2.3.3

t . 1+t

(2.19)

Gas Cooling

Gas cooling is modelled as in White & Frenk (1991). The hot gas within a dark halo is distributed as an isothermal sphere with density profile ρ(r): ρ(r) =

Mhot , 4πRvir r 2

(2.20)

The local cooling time tcool (r) is defined as the ratio of the specific thermal energy content of the gas, and the cooling rate per unit volume: tcool (r) =

3 kB Tvir ρ(r) , 2 µmp n2e (r) Λ(Tvir , Z)

(2.21)

where ne (r) is the electron number density and Λ(T vir , Z) the cooling rate. Λ depends strongly on the metallicity Z of the gas, and on the virial temperature of the halo. We employ the cooling functions computed by Sutherland & Dopita (1993) for collisional ionisation equilibrium.

Numerical Simulations of Structure Formation

56

The cooling radius rcool is the radius where tcool equals the time necessary to the halo to cool “quasi–statically”, approximated with the dynamical time tdyn = Rvir /Vc of the halo. If the cooling radius lies within the virial radius of the halo, then the cooling rate is: dMcool 2 drcool = 4πρ(rcool )rcool , (2.22) dt dt and for an isothermal sphere dMcool Mhot rcool = . (2.23) dt Rvir 2tcool At early times or for low mass haloes the cooling radius can be much larger than the virial radius. In this case, the hot gas is never expected to be in hydrostatic equilibrium, and the cooling rate is limited by the accretion rate onto the central galaxy, approximated with Mhot dMaccr = . (2.24) dt 2tcool An upper limit on the circular velocity of haloes in which cooling gas is allowed to settle onto a central galaxy is implemented, in order to account for the fact that observed cooling flow clusters do not form stars at the observed apparent cooling rate as estimated above. We choose V cut = 350 km s−1 (Kauffmann et al. 1999, Springel et al. 2001a).

2.3.4

Star formation

The star formation rate of a galaxy is modelled as dM? Mcold =α , dt tdyn

(2.25)

where Mcold is the mass of its cold gas, α is a constant and t dyn is a dynamical time of the galaxy, here approximated as Ref f , (2.26) tdyn = Vc with Ref f = Rvir /10, assuming that the effective stellar radius is a fixed fraction of the virial radius. Since Rvir ∝ Vc , the dynamical time for star formation depends only on redshift. The dimensionless parameter α regulates the efficiency of star formation and is treated as a free parameter, constant in time. Here we assume α = 0.05. In principle a redshift dependence of α may be required to provide a better understanding of the rapid evolution of the number density of luminous quasars (Kauffmann & Haehnelt 2000) and to match the observed abundance of Lyman break galaxies at z ∼ 3 (Somerville, Primack & Faber 2000). Once a galaxy falls into a larger halo and becomes a satellite, the values of Rvir and Vc are not changed any more, so the galaxy can form stars until its reservoir of cold gas is exhausted.

2.3 Semi–Analytic Models for Galaxy Formation

2.3.5

57

Feedback

Assuming a universal initial mass function (IMF) for star formation, the energy released by supernovae per unit mass of formed stars is η SN ESN , where ηSN is the supernova rate per unit mass of formed stars, and E SN the energy released by each supernova. Thus the formation of ∆M ? of stars releases an energy of ηSN ESN ∆M? . Adopting the Scalo IMF (Scalo 1986): 51 erg. ηSN = 5.0 · 10−3 M−1 and ESN = 10 A major uncertainty is how the released energy affects the evolution of the interstellar medium and the star formation activity (Yoshida et al. 2002, Springel 1999). Assuming that the feedback energy reheats some of the cold gas back to the virial temperature of the dark halo, the amount of “reheated” gas is 4 ηSN ESN ∆M? . (2.27) ∆Mreheat =  3 Vc2 The dimensionless parameter  describes the efficiency of the process. Kauffmann et al. (1999) and Springel et al. (2001a) consider two alternative schemes for the fate of the reheated gas: (i) the retention scheme and (ii) the ejection scheme. In the retention scheme, the reheated gas is transferred from the cold phase to the hot phase, and stays within the halo. In the ejection scheme the reheated gas leaves the halo, and it is reincorporated at some later time. If ∆Mejec is the total gas mass ejected by a galaxy, the reincorporation is modelled by decreasing ∆M ejec to zero again on the dynamical timescale of the halo. Springel et al. (2001a) found that the ejection model fits the slope of the observed Tully–Fisher relation to a good degree, while the retention model is less effective in suppressing star formation in low mass haloes.

2.3.6

Galaxy Merging

In CDM universes, large haloes form by mergers of smaller haloes. The satellite galaxies orbiting within a dark matter halo experience dynamical friction and eventually merge with the central galaxy. Mergers between two satellite galaxies are also possible in our simulations, but they are rare. The merging timescale can be approximated by the dynamical friction timescale tf (Navarro, Frenk & White 1995): tf =

1 f () Vc rc2 . 2 C GMsat ln Λ

(2.28)

This is valid for a satellite of mass M sat orbiting at a radius rc in an isothermal halo of circular velocity Vc . f () describes the dependence of the orbital decay on the eccentricity of the satellites’ orbit and it is approximated by the function f () ' 0.78 (Lacey & Cole 1993). C ' 0.43 is a constant and ln Λ is the Coulomb logarithm, approximated with ln Λ = 1 + M vir /Msat .

58

Numerical Simulations of Structure Formation

When a satellite merges with a central galaxy, its stellar mass is transfered to the bulge of the central galaxy and its photometric properties are updated accordingly. The cold gas of the satellite is transferred to the disk of the central galaxy. If the mass ratio between the stellar components of the merging galaxies is larger than a threshold value fixed to 0.3, a major merger takes place, in which the disk of the central galaxy is destroyed, all the stars generate a bulge and the cold gas left is consumed in a starburst. Since the central galaxy is fed by a cooling flow, it can grow a new disk component later on.

2.3.7

Spectrophotometric evolution

The galaxy photometric properties are built using the stellar population synthesis models of Bruzual & Charlot (1993). The number of stars that form in each mass range is computed according to the initial mass function, then the stars evolve along theoretical evolutionary tracks. In this way, the spectra and colours of a stellar population formed in a burst of star formation can be followed in time. If the evolution F ν (t) of the spectral energy distribution (SED) of the population of coeval stars is known, the SED S ν (t) of a galaxy can be computed as a function of its star formation history M˙ ? (t): Sν (t) =

Z

0

t

Fν (t − t0 ) M˙ ? (t0 ) dt0 .

(2.29)

Colours and luminosities can be obtained in various bands upon convolution with standard filters. The redshifting of spectra and the incorporation of k–corrections are also possible, in order to allow direct comparison with observational photometric data at high redshift.

2.3.8

Morphological evolution

The morphological type of galaxies is assigned following the correlation found by Simien & de Vaucouleurs (1986) between the B–band bulge–to– disk ratio, and the Hubble type T . If ∆M ≡ M bulge − Mtot is the magnitude difference between the luminosity of the bulge and that of the entire galaxy, then: h∆M i = 0.324(T + 5) − 0.054(T + 5)2 + 0.0047(T + 5)3 .

(2.30)

Galaxies with T < −2.5 are classified as ellipticals, those with −2.5 < T < 0.92 as S0’s, and those with T > 0.92 as spirals and irregulars. Galaxies without any bulge are classified as type T = 9.

2.4 New Feedback Recipes for Galactic Winds

2.4

59

New Feedback Recipes for Galactic Winds

In this section we will present our new recipes for mechanical feedback from supernovae, which we introduce in order to include the physics of galactic winds in the semi–analytic code of Springel et al. (2001a). Kauffmann et al. (1999) and Springel et al. (2001a) find that a simple recipe for feedback from supernovae, implemented in the so-called “ejection” scheme, is sufficient to give rather accurate predictions for some observed properties of galaxies, like e.g. the suppression of star formation in low mass haloes and the slope of the Tully–Fisher relation. The simplicity of the prescription makes it impossible however to describe the complexity of the physics of galactic winds. In particular, the scheme does not describe the diffusion of the matter and metals lost by galaxies, because there are no recipes for following the evolution of shells and wind ejecta. This is what we aim to provide in our work. Here we use the semi–analytic model of Springel et al. (2001a) with the implementation of the ejection scheme, without modifying its prescriptions, to follow the evolution of the cold gas and the stellar component of the galaxies. We add our recipes for winds on top of this pre–existing scheme. This is not fully consistent, because we do not modify the cooling and the infall prescriptions in the semi–analytic code to match our new model for the immediate surroundings of our galaxies. One consequence of this is that the total metal and gas mass in our simulated region is not exactly conserved. However, violations are minor. Since we want to investigate the effects of winds on the IGM by applying our model to a large simulated box, we are neither able nor interested to resolve the details of the first phases of the wind evolution, when the superbubbles blow out of the ISM of galaxies. Nor do we model in detail the impact of the outflow on the physical conditions of the ISM in the host galaxy. Here, we are concerned with the long–term evolution of the winds once they have escaped the visible regions of galaxies. We make the simplifying assumption of spherical symmetry for the wind evolution. Galactic outflows observed in nearby galaxies appear to be mostly bipolar (Heckman et al. 2000), with the gas escaping preferentially along the direction where the gravitational potential gradient is stronger. However, observations of high redshift objects (Frye, Broadhurst & Benitez 2002, Pettini et al. 2002b) suggest that most galaxies are affected by large scale winds implying near spherical outflows. Together with the fact that an initially nonspherical shell approaches sphericity at later times (Ostriker & McKee 1988), this suggests that our symmetry assumption may be appropriate. The thermal energy injected by supernova explosions is converted to kinetic energy and the outflow remains approximately adiabatic until radiative losses become substantial. Hoopes et al. (2003) and Strickland & Stevens (2000) have recently proved that the energy lost through radiative cooling

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of the coronal (T ∼ 105.5 K) and the hot (T ∼ 107 K) phases of the wind in the starburst galaxy M82 is small. The wind can be thus described as a cosmological blastwave expanding in the galactic halo or in the IGM, whose dynamics obeys the virial theorem for blastwaves as stated by Ostriker & McKee (1988). In subsection 2.4.1 we present the equation of motion of an astrophysical blastwave expanding in a uniform medium in the thin shell approximation of Ostriker & McKee (1988), which we use to describe the evolution of galactic winds. In subsection 2.4.2 we report about our choice for the wind initial conditions, while in subsection 2.4.3 we describe our recipes to model the density and velocity fields of the gas surrounding galaxies. Finally, we present in subsection 2.4.4 the prescriptions for the merging of shells and in subsection 2.4.5 the prescriptions for the ejection of metals.

2.4.1

The Thin Shell Approximation

In the thin shell approximation all the gas involved in an outflow accumulates in a shell of zero thickness with the radius and velocity of the shell equal to the radius and velocity of the shock. Although for adiabatic blastwaves in a homogeneous medium the thin shell approximation is valid only in the case of a soft equation of state of the gas with γ ∼ 1, for cosmological blastwaves it is always valid, since the gas piles up just behind the shock front because of the expansion of the universe, as the shell decelerates (Ostriker & McKee 1988). In this approximation, the equation of motion of a spherical shell with energy injection at the origin results from the conservation of momentum: GMh m d − 4πr 2 cργigm − ε4πr 2 ρigm vigm (v + vigm ) , (mv) = M˙ w (vw − v) − dt r2 (2.31) where m, r and v are the mass, the radius and the outflow velocity of the shell, M˙ w and vw the mass outflow rate and the outflow velocity of the wind, ρigm and vigm the density and the infall velocity of the surrounding medium, Mh the total mass internal to the shell, γ = 5/3 the adiabatic index and ε a parameter, the entrainment fraction, defining the fraction of mass that the shell sweeps up while crossing the ambient medium. The first term on the right–hand side of the equation represents the momentum injected by supernovae, the second term takes into account the gravitational attraction of the dark matter halo and the two final terms represent the thermal and the ram pressure of the surrounding medium. The conservation of mass gives   v dm ˙ + ε4πr 2 ρigm (v + vigm ) . (2.32) = Mw 1 − dt vw The mass accumulated in the shell is the sum of the wind mass that

2.4 New Feedback Recipes for Galactic Winds

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reaches the shock and the swept–up mass. The radius of the shell is given by v = dr/dt. At blow out, that is when the wind escapes the galactic disk or spheroid, we assume that the shell is formed initially with no mass (m(r o ) = 0), a radius equal to the galaxy radius rg (ro = rg ) and zero velocity (v(ro ) = 0). After blow out, the shell starts to accumulate gas. Since our semi–analytic model does not follow the internal structure of galaxies, we have to make a further assumption for the galaxy radius, in order to link it to the properties of the dark matter halo in which the galaxy is embedded. Thus we fix r g to be a given fraction of the virial radius of the DM halo, i.e. r g = rvir /10. This choice gives values in broad agreement with the observed radii of galaxies at all redshifts. These equations have previously been used in similar works by Theuns, Mo & Schaye (2001) and Aguirre et al. (2001), but with some noteworthy differences in the initialisation of the shells properties. For instance, Theuns, Mo & Schaye (2001) fix the initial conditions at the virial radius and assume that the shell velocity equals the wind velocity, while the mass is equal to m = (Ωb /Ωm ) Mvir . This choice is quite surprising, since they blow out all the baryonic mass of the galaxy, including stars. Aguirre et al. (2001) set initial conditions for m, r and v by choosing a radius r o to include a fixed fraction ξ of the galaxy mass and the constant ξ is calibrated to give values of ro similar to the radii at which winds from starbursts are observed. The resulting shell mass is therefore m(r o ) ∝ ξMgal , but it is not clear what fraction of the galaxy mass is already entrained in the outflow when the shell emerges from the galaxy.

2.4.2

Wind Velocity and Mass Loss Rate

At present, both semi–analytic and SPH simulations use empirical prescriptions for the physics of galactic winds and the velocity and the mass outflow rate are assumed as parameters (e.g. Springel & Hernquist 2003, Aguirre et al. 2001, Theuns et al. 2002c, Thacker, Scannapieco & Davis 2002). This approach has proved useful, although the simulated results depend sensitively and in a complex fashion on the choice of the parameters. Shu, Mo & Mao (2003) recently proposed a more detailed model that links the winds and the star formation properties of galaxies. They start from two observational facts: (i) the outflow rate in galaxies at every redshift is of the order of the star formation rate (Martin 1999) and (ii) the initial wind velocities seem to be independent of the galaxy morphologies (Heckman et al. 2000, Frye, Broadhurst & Benitez 2002) and lie in the range 100–1500 km s−1 . By using the theoretical models of McKee & Ostriker (1977) and Efstathiou (2000), they predict the mass outflow rate M˙ w and the wind

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velocity vw at blow out as a function of the star formation rate M˙ ? of the host galaxy !0.71 ˙? M M˙ w = 133 K M yr−1 , (2.33) 100M yr−1

vw = 623

M˙ ? 100M yr−1

!0.145

K −1/2 km s−1 .

(2.34)

K is a constant that takes into account some typical properties of the ISM and it depends on the efficiency of conduction relative to the thermal conductivity of clouds, on the minimum radius of clouds in the ISM and on the dimension of star–forming regions (see next paragraph for a more detailed treatment). In the following, we will call the ratio between the wind mass loss rate and the star formation rate the “reheating efficiency” Ref f = M˙ w /M˙ ? of the wind. Note that the momentum input M˙ w vw in this model is only weakly dependent on K (∝ K 1/2 ), with a stronger dependence on the star formation rate (∝ M˙ ?0.855 ). The energy input is proportional to the star formation rate, but is completely independent of K and therefore of all other galaxy properties. Shu, Mo & Mao (2003) give a number of arguments in support of this very simple model which is quite similar to the earlier model of Dekel & Silk (1986). With their assumptions, galaxies with more compact star– forming regions produce winds with higher velocities and lower outflow rates and vice versa. The theoretical predictions can be fine tuned to reproduce the observations with reasonable accuracy both for the mass loss rate and the wind velocity. We choose as our fiducial value K = 0.5. In order to make our predictions consistent with the observations of Martin (1999), we fix a maxmax = 5. Equations 2.33 and 2.34 imum value for the reheating efficiency of R ef f tend to overestimate Ref f for low values of the star formation rate. The dependence of Ref f and vw on the star formation rate is shown in figure 2.4 for different choices of K. We will show in the following chapters that the numerical results of our simulations do depend on the choice of the precise value of K, but that the major dependence is on the other parameter in the model, the entrainment fraction ε.

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Figure 2.4: M˙ w and vw as a function of M˙ ? . The different lines represent models with: (1) dashed: K = 0.1; (2) dotted: K = 0.3; (3) solid: K = 0.5; (4) dashed three–dotted: K = 0.75; (5) dashed–dotted: K = 1.

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Derivation of the Initial Conditions In the original formulation of Shu, Mo & Mao (2003), equations 2.33 and 2.34 read:

M˙ w = 133

M˙ ? 100 M yr−1

!0.71 

Mps 125 M

−0.71 

R 1 Kpc

0.87

k −0.29 M yr−1 (2.35)

and 

M˙ ? vw = 623  100 M yr−1

!0.29 

Mps 125 M

−0.29 

R 1 Kpc

−0.87

1/2

k 0.29 

km s−1 , (2.36)

where R is the radius of the star–forming region, k a parameter and M ps is the amount of gas converted into stars for each supernova explosion. The number of supernovae depends on the initial mass function (IMF) and for a Salpeter IMF Mps = 125 M . The constant k takes into account the dependence of the predictions on the properties of the ISM and is a function of the parameter γ ∼ 2.5, which is the ratio of the blast wave velocity to the isothermal sound speed of the hot phase, and of a parameter f Σ :    2.5 fΣ . (2.37) k= 21.5 γ fΣ represents the evaporation parameter of clouds normalised to the value measured in the solar neighbourhood. Assuming a constant porosity equal to 1 for the gas in the star–forming region, it can be expressed as (Efstathiou 2000): fΣ = 21.5



0.01 φk



γ  2.5



al pc

2

.

(2.38)

φk is the efficiency of conduction relative to the thermal conductivity of clouds and its value lies in the range 0.1–0.01 (Efstathiou 2000). a l is the minimun radius for clouds in the ISM. Observations give a l ∼ 0.5 pc (McKee & Ostriker 1977, Olmi & Testi 2002). Since our simulations do not give information about the physical size of star forming regions R and at the same time it would be unconvenient to analyze the dependence of our results on both the parameters φ k and al that build up k, we have collected all the dependencies on parameters in equations 2.35 and 2.36 in the constant K: K=



R 1 Kpc

0.87

k −0.29 .

(2.39)

2.4 New Feedback Recipes for Galactic Winds

2.4.3

65

The Wind Environment

Once a shell is formed, it expands through the halo of the host galaxy and, if it is energetic enough, it can escape the gravitational attraction of the halo and break out into the IGM. Our simulations contain no rich clusters and fewer than half of the galaxies at z = 0 belong to groups or small clusters. The shells attached to these galaxies are subject to the gravitational field of the group and the closer a galaxy lies to the centre of a massive cluster, the more energetic the wind has to be to be able to escape the potential well of its host. When simulating the evolution of the winds, it is therefore important to know the density distribution of the gas into which the shells expand. Our semi–analytic prescriptions provide this information by assuming that inside dark matter haloes the gas follows the distribution of the dark matter. Density and Velocity Fields We model the gravitational fields of haloes and their gas distribution by using NFW profiles discussed in subsection 2.3.2. Inside haloes, the gas density is normalised to the total amount of hot gas given by the semi– analytic recipes of Springel et al. (2001a), that is ρ igm = (Mhot /M200 ) ρN F W . For galaxies in groups or clusters, we follow the density profile of the galactic halo until its density equals the density of the parent halo, where the dynamics of the group becomes dominant. Similarly, the density profile of the group is followed until the shell reaches the point where the dark matter halo density becomes equal to a fixed fraction of the mean universal density. After this point, the gas density is assumed to be constant and equal to 0.8 times the baryonic mean density. The velocity of the surrounding medium v igm is calculated assuming that the gas dynamics is dominated by infall close to galaxies and by the Hubble flow at larger distances. The inward v igm is therefore given by the sum of two contributions: vigm = vesc − H(z) · r. (2.40)

The outward escape velocity vesc at a radius r for a NFW profile is given by equation 2.18. When the velocity of the shell equals the velocity of the gas, the shell joins the Hubble flow and no more mass is accreted. Entrainment Fraction

The entrainment fraction ε represents the fraction of the ambient gas that is swept up by the shell and it is treated as a free parameter. The remaining fraction of mass 1−ε is assumed to be in dense clouds which are unperturbed by the shell. A low value ε  1 may imply either a clumpy ambient medium or a heavily fragmented shell, while ε ∼ 1 describes a near–homogeneous medium, which can be entirely swept up by the wind.

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This parameter is of particular relevance, because it plays a key role in determining the fate of the wind: the mass accretion rate of the shell depends on ε and the more massive the shell, the bigger the energy required to accelerate it. In addition, the ram pressure increases linearly with ε, influencing directly the energetics of the winds. The net effect of an increase in the entrainment fraction is thus a decrease in the shell speed, which may lead to the collapse of the shell, if the energy input from the starburst is not sufficiently large. Since the velocity of the shells is what ultimately determines how far into the IGM the winds travel, a large variation of the volume filling factor of winds is expected as ε varies. We will analyze this aspect further in chapter 4.

2.4.4

Shell Merging

When two galaxies merge, we assume that also their shells “merge”. If only one galaxy is blowing a wind, then its shell will be attached to the merged galaxy without modifications. The merging of shells is realised by assuming the conservation of volume, mass and momentum of the shells. Conservation of mass requires the final mass m of the new shell to be the sum of the masses m1 and m2 of the two merging shells, that is m = m 1 + m2 .

(2.41)

The metal mass in the merged shell is the sum of the metal masses of the single shells: mz = m1,z + m2,z . (2.42) Conservation of volumes requires that the total volume V of the final shell is equal to the sum of the volumes of the two single shells V = V 1 + V2 . Since shells are spherical, the radius of the new shell is r = r13 + r23


1/3

.

(2.43)

The velocity of the resulting shell is given by the conservation of momentum: m1 v1 + m 2 v2 v= . (2.44) m1 + m 2 Our prescriptions for the merging of shells when galaxies merge are very simple, but we reckon they are able to capture the essential physics undelying the process. The shell created during a merger becomes subject to the gravitational attraction of the central galaxy and its fate depends mostly on its energy. If the energy is small, then most probably the shell recollapses onto the galaxy, otherwise it continues to expand, carrying its mass and metal content intact. The survival of winds after galaxy merging comes out to be an important point, since most of the galaxies experience one or more merging events during their lifetime.

2.4 New Feedback Recipes for Galactic Winds

2.4.5

67

Metals in Winds

A very important aspect of our work regards the treatment of the metal mass ejected by winds from the ISM of galaxies. Results on the efficiency of winds to eject and transport metals far into the IGM will be shown in chapter 5. The mass ejected by winds is the sum of two components: the metal enriched stellar ejecta from supernova explosions and the shocked, heated and accelerated ISM entrained in the outflow. The latter represents the largest fraction of the mass lost by the galaxy, constituting more than 90% of the ejecta, since the mass loss rate is comparable to the star formation rate in galaxies driving a wind. Assuming for star formation a yield Y = 0.02, corresponding to the fraction of mass converted into stars that is returned to the ISM by supernova explosions in the form of metals, then the mass of outflowing gas which is entrained ISM is ∆ M˙ ? (Ref f − Y ). The metallicity of the wind fluid depends both on the amount of metals ejected by supernovae and on the metallicity of the ISM. In our semi–analytic model, galaxies are schematically represented as a disc of cold gas, which constitutes the ISM of the galaxy, surrounded by a halo of hot gas. As for the total mass ejected by winds, the mass of metals entrained in the wind fluid and deposited in shells is the sum of two contributions: the metals in the supernova ejecta and the metals in the ISM blown out of the host galaxy Mz,w = M˙ ? dt (Y + (Ref f − Y ) Zcold ) ,

(2.45)

where Zcold is the metallicity of the cold gas. The total mass of metals accreted by a shell reflects the form of the mass conservation equation (2.32) and is the sum of the metals accreted from the wind fluid and the metals accreted from the ambient medium: mz = mz,w + mz,e =   v ˙ + = M? dt (Y + (Ref f − Y ) Zcold ) · 1 − vw +ε4πr 2 ρ (v + vigm ) Zhot dt,

(2.46)

with Zhot the metallicity of the hot gas. The second term indicates the amount of metals swept up by the shell in the halo of the galaxy and does not give any contribution for shells that are expanding far into the IGM, since the IGM itself is assumed to contain no metals until it is traversed by an ejected shell.

“Just because you’ve got the emotional range of a teaspoon doesn’t mean we all have.”

Chapter 3

Evolution of Winds In this chapter we will discuss the evolution of winds and how our results depend on our model assumptions and parameters. In section 3.1 we show the evolution of a wind, chosen randomly from the galaxy population of M3, throughout its lifetime. We use this example to show how we solve the equation of motion of Ostriker & McKee (1988) for the shell and how the shell properties evolve with time. In section 3.2 we then focus on some general properties of the population of wind cavities and shells.

3.1

Solution for a Single Galaxy

As noted in chapter 2, the entraiment fraction ε determines what fraction of the medium that a shell crosses is swept up and joins the shell itself. New–born winds expand initially inside the dark matter halo of their host galaxies. Since the total amount of gas in haloes depends on the efficiency of cooling and may vary significantly from galaxy to galaxy, each galaxy has a “personal” history different from all the others. In figure 3.1 we show the time evolution of a shell emerging from a galaxy, chosen randomly from the galaxy population of M3, as a function of our model parameters K and ε. The galaxy is initially a central galaxy, but after z = 1 it falls into a larger group and becomes a satellite. Different lines show results for different parameter choices. The thick solid line shows our fiducial model. In the mid–right panel we show the star formation history of the galaxy, which forms stars in a rather continuous way throughout its lifetime: at low redshift the star formation rate is very low, but it never goes to zero. This galaxy gives a good example of several features that may appear during the life of galaxies and winds. For example, the vertical jump at z ∼ 2 in the bottom right panel is due to the merging of a large satellite onto the galaxy, which triggers a burst of star formation. The merging of the two wind shells is instead responsible for the jumps observed in the left panels

72

Evolution of Winds

Figure 3.1: Example of wind evolution for a galaxy extracted from the galaxy population of M3. From top to bottom and left to right, we show the evolution of the shell mass, the shell metal mass, the shell radius, the galaxy star formation rate, the shell velocity and the galaxy stellar mass. The vertical jump at z ∼ 2 is due to a merging event, which triggers star formation activity. The different lines are obtained for different choices of the parameters K and ε: (1) thick solid line (fiducial model): K = 0.5, ε = 0.1; (2) dotted line: K = 0.1, ε = 0.1; (3) dashed line: K = 1, ε = 0.1; (4) dashed dotted line: K = 0.5, ε = 1; (5) long dashed line: K = 0.1, ε = 0.01.

3.2 Properties of the Shell Population

73

of figure 3.1. Again in the left panels of figure 3.1, in some of the models the shells stop accreting mass, while the radius and the velocity increase slowly. This is because the shell has escaped the attraction of the galaxy and has finally joined the Hubble flow.

3.1.1

General Trends

As a general trend, we observe that more massive shells tend to be slower and to collapse more easily than lighter ones. The initial conditions set by equations 2.33 and 2.34 imply that the mass loss rate is inversely proportional to the velocity of the wind. Although the total momentum input is almost the same, the gravitational attraction felt by the shell increases significantly and the combined effect is a low velocity for the shell, often much smaller than the escape velocity from the galaxy as given by equation 2.18. Even when massive shells are able to escape into the IGM, the distances they can travel are much smaller than those of light shells. While changes in the parameter K only weakly affect the long term evolution of the winds, the entrainment fraction ε plays a crucial role, because it determines directly the mass accretion rate and therefore the momentum loss by ram pressure and gravity effects. A very low entrainment fraction creates an extremely light shell that can travel far into the IGM with a relatively high speed, while if ε ∼ 1 the shell sweeps up all the mass it encounters and becomes more and more massive, a condition that increases the probability of collapse. Since the mass swept up by shells in the IGM is assumed to have zero metallicity, the metal abundance in the shells increases with decreasing ε. We will show in the following chapter how a high entraiment fraction can reduce drastically the filling factors of winds.

3.2

Properties of the Shell Population

In this section we outline how varying the parameters ε and K affects the global properties of the winds, focusing our attention in particular on the mass and the radius of the shells and on the fraction of wind–blowing galaxies.

3.2.1

Properties as a Function of z

Since the total number of galaxies in M3 is very large, we calculate various “mean” quantities to describe the global properties of the winds, and do not focus further on individual cases. We would like to point out that this necessarily gives a partial idea of the whole picture, since there are no strong correlations between the properties of the galaxies and those of the winds. It is likely that if a massive galaxy is blowing a wind, then that wind started before most of the halo mass was accreted and the shell was expelled

74

Evolution of Winds

Figure 3.2: The mean shell radius (top panel) and the mean shell mass (bottom panel) for all the galaxies that are presently blowing a wind, as a function of the stellar mass M? of the host galaxy. The data are shown for our fiducial model with K = 0.5 and ε = 0.1 at different redshifts: (1) solid line: z = 5; (2) dotted line: z = 3; (3) dashed line: z = 2; (4) dashed three–dotted line: z = 1; (5) dashed dotted line: z = 0.

3.2 Properties of the Shell Population

75

to a large radius at early times. Winds from massive galaxies can also reach large distances in relatively short times if the burst of star formation that powers them is strong enough. Furthermore, there is no clear connection between the present star formation rate of a galaxy and the properties of the wind. The star formation activity of a galaxy may switch off or decrease to very low values, while the wind still has sufficient energy to escape the gravitational pull without further energy input. It is common in our simulations to find winds expanding in the IGM a considerable time after the star formation activity and the momentum input from the source galaxy have ceased. Both bursts of star formation and quiescent star formation activity are able to power the winds and drive them far into the IGM. It is not obvious a priori when a wind will escape the gravitational pull of a galaxy. A shell that is collapsing onto a galaxy may receive new energy from increased star formation activity, triggered by mergers or gas accretion, for example, and it may start expanding again. On the other hand, an expanding shell may start to recollapse because its host galaxy merges and the gravitational attraction increases by a large factor. The final fate of winds is linked to several factors, like the star formation and the mass accretion history of the galaxy, the potential well of the dark matter halo in which it expands, the amount of mass accreted on the shell both from the wind material and the IGM and so on. Keeping all this in mind, in figure 3.2 we consider only those galaxies which are blowing a wind and we plot the mean values of the radii and the shell masses of all the winds as a function of the stellar mass M ? for different epochs of our fiducial model. The data have been binned according to intervals of M? of variable extension and the mean values have been calculated for each group. Clearly, the mean radius and the mean mass increase with time, as the winds have more time to expand further from the galaxies. For galaxies of larger masses the mean radius appears to be considerably larger than for less massive ones. This effect has two explanations: first, these winds need higher velocities to be able to escape from the gravitational attraction of their haloes and therefore can cover larger distances; secondly, they often started earlier in time.

3.2.2

Properties at z = 3 as a Function of Parameters

In figure 3.3 we plot the same quantities, but for different choices of the model parameters at z = 3. The scatter in the plot is large and the results differ from our fiducial model by as much as a factor of five in the most extreme cases. Once again, this is due to the scatter in the initial velocities and the accretion of mass onto the shells, as already noted in the case of a single galaxy in figure 3.1. The most massive shells tend to travel to shorter distances than the less massive ones, their mass being determined both by

76

Evolution of Winds

Figure 3.3: The mean shell radius (top panel) and the mean shell mass (bottom panel) for all the galaxies blowing a wind at z = 3, as a function of the stellar mass M? of the host galaxy. The data are shown for different combinations of the model parameters (these same notations will be maintained throughout all the paper for the model parameters): (1) thick solid line (fiducial model): K = 0.5, ε = 0.1; (2) dotted line: K = 0.1, ε = 0.1; (3) dashed line: K = 1, ε = 0.1; (4) dashed dotted line: K = 0.5, ε = 1; (5) dashed three–dotted line: K = 0.5, ε = 0.01; (6) long dashed line: K = 0.1, ε = 0.01; (7) thin solid line: K = 1, ε = 1.

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77

Figure 3.4: The fraction of wind–blowing galaxies as a function of redshift and model parameters. Here we consider only galaxies with M ? > 108 M . A large amount of swept up mass from the surrounding medium strongly suppresses the ability of galaxies to power outflows. The lines correspond to different parameter choices as in Fig. 3.3. the fraction of entrained gas from the IGM determined by ε and/or the mass injected by the wind linked to the parameter K.

3.2.3

The Fraction of Wind–Blowing Galaxies

In Fig. 3.4 we show the fraction of galaxies with M ? > 108 M blowing a wind as a function of redshift. In Fig. 3.5 we show the fraction of galaxies with winds as a function of stellar mass at z = 3. Both quantities are plotted for different parameter choices. The number of galaxies blowing a wind depends strongly on the model parameters. In particular, the entrainment fraction greatly affects the ability of galaxies with low stellar masses, which dominate the stellar counts, to power a wind. A large amount of mass in a shell requires a larger rate of energy injection from the galaxy for the shell to escape. When this does not happen, the shell collapses back onto the galaxy. The overall effect is to reduce the number of wind–blowing galaxies by a large factor. A similar but much weaker effect is produced by the

78

Evolution of Winds

Figure 3.5: The differential fraction of wind–blowing galaxies as a function of our model parameters at z = 3. The ability of galaxies to power outflows is strongly suppressed in low stellar mass galaxies, when the mass loading of winds is high. The lines correspond to different parameter choices as in figure 3.3. parameter K. Why can winds with a very low entrainment fraction escape galaxies so much more efficiently than more mass loaded ones? Why is this effect particularly strong in low stellar mass galaxies? Let’s consider equation (2.31) for the conservation of momentum. A shell receives energy from the wind and is slowed down by the gravitational attraction of the central galaxy and by the ram pressure of the ambient medium. Thermal pressure effects are generally negligible. If the mass entrained by a wind is small, as in the case of ε = 0.01, then the shell mass is roughly comparable to the mass of supernova ejecta that reaches the shell. These are outflowing from the galaxy with a velocity which is often much larger than the escape velocity of the galaxy. Since little energy has to be spent by the wind to accelerate the entrained IGM, the velocity of the shell is less sensitive to energy losses by ram pressure and gravity. Such a wind thus has a higher probability to overcome the gravitational pull and break free from the halo than more mass loaded winds. When the mass loading is substantial, a significant part of

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79

the wind energy is consumed to accelerate the entrained gas and the shell slows down. If the amount of energy spent to accelerate the swept up IGM is large, the velocity of the shell may become lower than the escape velocity of the galaxy. In this case, the shell cannot escape and recollapses onto the galaxy. The mass loading of a shell immediately after blow out is therefore crucial to determine the fate of a wind. In models with efficient mass loading, the suppression of winds is particularly strong in galaxies with low stellar masses. This is because the delicate momentum balance at blow out is easily dominated by momentum losses by ram pressure, which sum up to the ones by gravity. To make the situation worse, the energy input in low mass galaxies is often not as large as in more massive ones, due to a less intense star formation activity.

“That wasn’t bad,” said Harry, “but there’s definite room for improvement. Let’s try again.”

Chapter 4

Filling Factor In section 4.1 we present our results for the volume filling factor of winds. A brief discussion on the importance of estimating the filling factor of winds for studying the Lyα forest is given in subsection 4.1.1. After introducing our definition of the volume filling factor f v in section 4.1.2, we show some graphic examples in subsection 4.1.3 and give more quantitative results in subsection 4.1.4. In subsection 4.1.5 we investigate the effect of clustering and the effect of shell overlapping. In section 4.2 we give our results about the fraction of IGM mass in shells and finally in section 5.5 we investigate the effects of the resolution in mass of the simulations on our results.

4.1 4.1.1

Volume Filling Factor Connections with the Lyα Forest

An estimate of the volume filling factor f v of galactic winds at the redshifts where absorption in quasar spectra is observed can be translated into an estimate of the probability to find disturbances in the Lyα forest due to feedback effects and, in particular, to the presence of wind cavities and shells. Disturbances here mean regions of the spectra where there are significant variations in the optical depth, due to non gravitational processes stirring the IGM. Observationally, it is quite challenging to estimate f v with any accuracy. Published estimates range from 0.003 to 40% (Heckman et al. 2001, Cecil et al. 2001, Rauch 2002) at z ∼ 3. Surely the large scatter is due to the fact that the estimates are mostly indirect and are based on different, perhaps incompatible, assumptions, for example, about the geometry of the disturbances. Rauch (2002) claims that the assumption that the IGM is disturbed by spherically symmetric galactic winds allows one to derive upper limits for the actual value of fv .

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In our case, although we assume spherical symmetry for the evolution of shells, we cannot consider our estimates of f v as upper limits, since our model does not deal correctly with the overlapping of shells. When two shells come in contact with each other, in analogy with what happens in the ISM for bubbles of ionised gas created by stellar winds and SN explosions, it is reasonable to expect that they would create a supershell, powered by both winds. In our wind implementation we assume that each shell evolves in dependently from all the others. In this way, when bubbles overlap, the energy that could be used to power the supershell is instead used to power two separate shells. As a consequence, part of the energy imparted to outflows is lost, instead of being transferred to supershells and make them travel faster into the IGM. The total volume filled by shells as we estimate it might therefore not represent all the volume that would be filled by winds whose combined evolution is calculated self–consistently.

4.1.2

Definition

We define the volume filling factor of winds f v as the ratio of the total volume occupied by cavities Vs to the total volume V of our simulated spherical region of diameter 26 h−1 Mpc: fv =

Vs . V

(4.1)

We calculate the filling factor of winds by superimposing a 3–dimensional grid on our high resolution region and identifying all the grid points inside winds. Since fv represents the fraction of space occupied by winds, its value is given simply by the ratio between the number of points flagged and the total number of points in the grid. Note that this estimate ignores the mass fraction 1 − ε of the IGM which is in “dense clouds” and so avoided entrainment. We start drawing a N ×N ×N cubic grid, centered on the centre of mass of the high resolution region and with a side of 52 h −1 Mpc. For simplicity, we limit our analysis to a sphere of diameter 52 h −1 Mpc, but a larger region with irregular contours could be identified. We include in our calculations only grid points in the interior of the sphere. In our analysis, we always use N = 512.

4.1.3

Graphic Visualisations

In figures 4.1 and 4.2 we show two examples of the evolution of winds from z = 5 to z = 0, for different choices of the model parameters K and ε. A thin slice is cut through the central plane of the simulation and the density distribution of the gas in the slice is shown. The contours indicate the surface of the wind shells and the black regions inside these contours represent the regions which have been depleted of low density gas by winds.

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Figure 4.1: Structure of wind–filled region as a function of time. The simulations have been realised for M3 assuming ε = 0.1 and K = 0.5. From top to bottom and left to right, the redshifts of the presented snapshots are respectively z = 5, z = 3, z = 1 and z = 0. The colour coding is the same for all snapshots and the diameter of the region shown is 52h −1 Mpc in comoving units.

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Figure 4.2: Same as figure 4.1, for ε = 0.01 and K = 0.5.

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Figure 4.3: Volume filling factor of winds in M3 as a function of time for different values of the parameters K and ε. The lines are obtained for different parameter choices as in figure 3.3. To obtain these simulated distributions, we proceeded as follows. First we recover the density of the gas by applying an SPH smoothing to the distribution of the dark matter particles and by assuming that the distribution of the gas follows the distribution of the dark matter. We then identify the portion of space which is inside one or more shells and we consider only those particles that are found inside this region. Particles outside this region are of course not affected by winds. We compute the fraction x of baryons removed from the IGM as the ratio of the total baryon mass of the shells plus the galaxies to the total baryonic mass initially associated with the dark matter inside shells. We then tag the lowest density particles in the region affected by winds until the same fraction x of the enclosed mass is marked. Finally, we cut a thin slice through the density distribution of the remaining particles in our simulated region, as represented in figure 4.1. The amount of mass in shells varies strongly as a function of the entrainment fraction.

4.1.4

Evolution with Time

Our model parameters affects strongly the long term evolution of winds. In particular, the distance to which a shell can travel depends crucially on the

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total amount of mass accreted by the shell and therefore on the fraction of the IGM mass entrained in the outflow as set by ε. The general trend highlighted in section 3.1 for a single wind is recovered also for the behaviour of the volume filling factor. Once again, the smaller values for f v are related to the cases where more massive shells are formed and expand in the IGM with relatively low velocities. In figure 4.3 the volume filling factor is shown as a function of time and of the two model parameters. By varying K and ε we are able to obtain a very broad range of values of fv at every redshift. After z ∼ 2 the fraction of volume occupied by winds still increases steadily, but, keeping into account the conversion between redshift and cosmic time, less strongly than before. This is probably due to the clustering of the wind sources, which becomes more prominent at lower z: as the galaxies get closer one to each other because of the formation of structures in the universe, the probability that two shells overlap increases.

4.1.5

Clustering and Overlapping

We do not model the overlapping of shells in a complete way, since our one–dimensional approach does not allow us to take into account the three– dimensional distribution of galaxies and shells on the sky, but we can quantify a posteriori the overlapping of wind bubbles. In the following, we define fo as the fraction of our simulated volume which is reached by more than one wind. This definition allows an analogous measurement to our definition of the wind filling factor, since in practice it can be evaluated simply by counting the fraction of grid points that lie in two or more spherical wind bubbles. In figure 4.4 we show the results of such a measurement for our fiducial model. Because the galaxies are associated in groups, the wind cavities occupy a smaller fraction of space than they would if they were randomly distributed. At the same time, shells can run into each other much more easily, so the overlapping of winds becomes significant already at high redshift, as is shown in the bottom panel of figure 4.4. The ratio f o /fv represents the fraction of the cavity volume which is reached by two or more winds. While for randomly distributed galaxies overlapping would become significant only at low redshifts, when the total volume of the shells approaches the volume of the entire region, for clustered galaxies the volume with overlapping winds is already twice as big as in the other case at z ∼ 10. The fact that f o /fv at z ∼ 0 for clustered galaxies becomes smaller than for randomly distributed ones is a result of overlapping of multiple winds in the same region. Note that we are here dealing with a “field” region. We would expect the ratio fo /fv to behave differently in a region with more groups or clusters. There would be even more overlapping of winds, if the shells could expand as far as they do for field galaxies.

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Figure 4.4: The top panel shows the volume filling factor of winds f v and the overlapping of shells fo for M3 in the case of clustered sources and in the case that the sources were randomly distributed in our simulated region. Both cases have been realised for our fiducial model with K = 0.5 and ε = 0.1. The lines represent respectively: (1) thick solid line: fiducial model; (2) dotted line: overlapping for the fiducial model; (3) dashed line: random positions; (4) dashed dotted line: overlapping for the random positions model. In the bottom panel we compare the ratio fo /fv in the cases of clustered sources (solid line) and randomly distributed sources (dashed line).

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Figure 4.5: Fraction of IGM mass in shells as a function of redshift. f m indicates the fraction of IGM mass which is swept up by winds and accumulated onto shells. The different lines correspond to different parameter choices as in figure 3.3.

4.2

The Wind Mass Budget

A second important indicator of the impact of winds on the surrounding medium is the fraction of intergalactic gas that they affect. This “shell mass fraction” (fm , hereafter) is directly dependent on the entrainment fraction and on the mass of gas ejected by the galaxies. We estimate f m as the ratio of the mass in shells to the total mass of IGM in our simulated box. We show our results in figure 4.5. While fv is determined only by the physical extension of shells, f m is somewhat more difficult to estimate. In fact, one has to deal correctly with the overlapping of bubbles, which is not treated self–consistently in our semi– analytic prescriptions. To do this, we have to correct approximately for the fact that in our spherical wind model the same material can effectively be swept up two or more times when wind bubbles overlap. We first calculate the total mass of IGM inside shells in two different ways, that is from the dark matter particle distribution (m igm,p ) and from our semi–analytic prescriptions for the distribution of gas around galaxies, given in subsection 2.4.3, (migm,sa ). The first method reflects the “real” 3–

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dimensional distribution of matter in our simulated region. We then define y as the ratio between the two, that is y = m igm,p /migm,sa . The shell mass, defined in equation 2.32, is the sum of the mass from supernova ejecta and of the gas mass entrained along the way: m = m w +me . The mass of supernova ejecta mw is independent of overlapping effects. Conversely, the entrained mass me does depend on overlapping and we thus rescale it by the factor y to obtain the actual swept up mass m0e = yme . The rescaled shell mass is thus m0 = mw + m0e . Finally, we calculate the fraction of IGM mass in shells as fm = m0 /migm,p . The shell mass fraction fm varies differently from the volume filling factor fv of winds. By comparing Fig. 4.5 and 4.3, it is immediately clear that, particularly at low redshifts, winds with low entrainment fraction have in most cases the largest fv and the smallest fm , and vice versa. fm is often lower than the volume filling factor, indicating that although shells can travel far into the IGM, the effective amount of mass affected is small. Consistently with this, the models with the highest values of f m at z = 0 are those with ε = 1. The shell mass fraction is lower than 10% for every model at z > 3, and at z . 2 is still lower than 20%. The volume filling factor can already reach much higher values at these redshifts. Although our model of partial entrainment does not address the detailed physics of shells, it could, for example, represent a scenario in which wind shells fragment because of Rayleigh–Taylor instabilities. Shell fragments then stream across the IGM without necessarily modifying the density and temperature of the regions responsible for most of the absorption features in the Lyα forest. Alternatively, if the effective clumping factor of the undisturbed IGM is large enough, much of it may avoid being swept up onto shells.

“You see, Dumbledore?” said Phineas slyly. “Never try to understand the students. They hate it. They would much rather be tragically misunderstood, wallow in self–pity, stew in their own...” “That’s enough, Phineas.”

Chapter 5

Metals in Winds In this chapter we will show our results for the ejection of metals from galaxies by galactic winds and we will discuss their implications for the metal enrichment of the intergalactic medium.

5.1

Metal Ejection and Galaxies at z ∼ 3

Which galaxies produce the metals we observe in the IGM? When were the metals ejected by galaxies? Two scenarios are favoured today for the pollution of the IGM with metals: early enrichment by outflows from pregalactic objects (Madau, Ferrara & Rees 2001, Mac Low & Ferrara 1999) and late enrichment by galactic winds after the epoch of reionisation. In the latter, galaxies are in the process of assembling their mass or have already assembled most of it. In both cases, the energy to power outflows is provided by star formation, which at lower redshifts may be further triggered by merging of satellites. In our model we can investigate directly the second scenario. We study the impact of galactic winds on the IGM and investigate the role of different galaxy populations in enriching the IGM with metals. To answer the first question, we plot in figure 5.1 the cumulative distribution of metal mass in shells as a function of the stellar mass of the ejecting galaxies. Different curves are for different model parameters at z = 3. Different parameter choices lead to different shapes for the distribution. Half of the metals appear to have been ejected from galaxies with intermediate to large stellar masses (M? & 109 M ). Galaxies with M? < 108 M give a significant contribution only in models with ε = 0.01, where the total number of wind–blowing galaxies is higher than in all other models by a factor of five to ten, as shown in figure 3.4. Although models with ε = 0.01 clearly favour ejection from low stellar mass galaxies and at early times, there is no suppression of the efficiency of ejection from larger galaxies. For a comparison, in figure 5.2 we show the cumulative distribution of

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Figure 5.1: The cumulative distribution of the total metal mass in shells at z = 3 as a function of the stellar mass of the parent galaxies. The different lines correspond to different parameter choices as in figure 3.3.

Figure 5.2: The cumulative distribution of the stellar mass in galaxies at z = 3 as a function of the stellar mass of the parent galaxies.

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the stellar mass in galaxies, at z = 3. The contribution of galaxies with M? < 107 M to the total amount of stars formed in our simulated region is negligible and no winds are powered by such objecs. The shape of the distribution is similar to the one of the metal mass ejected in models with ε = 0.01. Metals can be efficiently ejected by massive galaxies if their star formation activity is powerful enough to sustain an outflow. In models with a high entrainment fraction the energy input necessary to blow a wind out of a massive galaxy is often too large to be provided by quiescent star formation alone. On the other hand, quiescent star formation does succeed to power such outflows in models with ε = 0.01, where the energy required to overcome the gravitational attraction and the ram pressure of the ambient medium is smaller. Mergers can provide a further key to understand why galaxies with intermediate and large masses play such an important role to pollute the IGM with metals in all our models. Satellites falling onto central galaxies may be powering a wind whose shell is accreted by the central galaxy, following the prescriptions in subsection 2.4.4. These merged shells receive a strong kick from the burst of star formation that follows the merger and the resulting wind energy may be easily high enough to allow the shell to escape the gravitational pull of the central galaxy.

5.2

Metals in Shells at z ∼ 3

In the top panel of figure 5.3 we plot the total mass of metals in shells, as a function of our model parameters. For comparison, we overplot the total mass of metals in our simulated region, as a thick dashed line. The metal mass accumulated in shells is sensitive to factors that depend on redshift. At z > 3 more metals are ejected for models with ε = 0.01, while at z < 3 metal ejection is more efficient for higher mass loading efficiency. In the bottom panel of figure 5.3 we show the efficiency of metal ejection by galactic winds, which we calculate as the ratio between the metal mass ejected by winds, shown in the upper panel of figure 5.3, and the total amount of metals in stars and in the gaseous phases of galaxies, given by the thick dashed line in the same plot. In models with ε = 0.01, the efficiency is rather high at every redshift and remains almost constant with time. In these models, winds blow into the IGM about a third of the total mass of metals in galaxies. Models with ε > 0.01 favour ejection mostly at low redshifts, while metals are preferentially retained by galaxies at higher redshifts. In these models, the efficiency of the ejection increases steeply with time and at very low redshifts a large fraction of the metals produced in galaxies are ejected into the IGM. The metal ejection efficiency is not always higher for those winds which

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Figure 5.3: Upper panel: the total metal mass contained in shells, as a function of redshift. For comparison, the thick dashed line represents the total mass of metals in our simulated region. Bottom panel: the fraction of metal mass in shells, as a function of redshift. The total mass of metals in our simulated region is calculated taking into account all the metals contained in stars and in the gaseous phases of galaxies. In both panels, the different lines correspond to different parameter choices as in Fig. 3.3.

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Figure 5.4: The metallicity of shells as a function of redshift. The different lines correspond to different parameter choices as in figure 3.3. are best able to escape from galaxies. In fact, at z . 2 we find that models with ε > 0.01, in which only about 25% of the galaxies blow winds, can eject more metals than models with ε = 0.01, in which most of the galaxies do have winds. About half of the synthesised metals are generally retained by galaxies at all redshifts.

5.3

Shell Metallicity

In figure 5.4 we show the mean metallicity of shells in solar units, as a function of redshift. This depends on the ratio between the mass entrained in the shell from the metal–free IGM and the metal rich gas accreted directly from the wind. Of crucial importance is the ability of winds to travel far into the IGM, where they can accrete more mass from the IGM than from the wind. The metallicity of shells may be an important indicator of the metallicity of the IGM, once the total amount of intergalactic gas affected by winds is known. The mean metallicity of the IGM may be roughly estimated by multiplying fm by the shell metallicity. At z ∼ 1 to 4 our results overestimate the metallicity of the low density IGM, with respect to the observed values,

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by a factor of about 10–100. There are two possible explanations for this: either our model expels more metals into the IGM than actually happens in real galaxies, or the metals are really ejected but they are not mixed into the observed gas. While our models might overestimate the total amount of mass and metals ejected by galaxies by a factor of up to a few, it is unlikely that such a correction would change our result that the mean IGM metallicity is well above the observed values. Thus, the discrepancy between the two values must be explained by the non–detection of the metals in winds and shells.

5.4

Missing Metals?

Why should we be unable to detect metals in the IGM? The C IV detected in the spectra of quasars is generally photoionised and its temperature is not higher than a few times 105 K. For higher temperatures, collisional ionisation becomes efficient, so that carbon is fully ionised and does not absorb the UV photons anymore. The temperature of the wind shells, where we assume all the gas and metals are accumulated, may be a crucial factor in determining their observability in absorption. Our semi–analytic prescriptions for winds do not give any indication of this temperature, but, as a simple test, we can estimate it by using the radiationless shock model (Dopita & Sutherland 2002). As in our semi–analytic prescriptions for wind evolution, this model assumes that radiative losses are negligible. The temperature of the shocked gas in the shell is T = 3µmH vs2 /16k, with µ the mean molecular weight, m H the mass of atomic hydrogen, k the Boltzmann constant and v s the shock velocity. Here we assume that the shock velocity is given by the difference between the wind and the shell velocity. For shock velocities in the range 150 to 500 km s−1 , the shell temperatures fall in the range between 10 6 K and 107 K. In our simulations, most of the shells that have escaped the potential wells of haloes have velocities above 100 km s −1 , while the wind velocity is always higher than that by a factor of a few. According to the radiationless shock model, their temperatures are therefore generally high enough for collisional ionisation of carbon to take place. This simple calculation confirms the idea that the IGM is actually enriched to a higher level than observations prove, but that the metals blown out of galaxies by galactic winds are in most cases too hot to produce any absorption in the spectra of high redshift quasars. The fraction of IGM mass involved in outflows is small but still significant, as proved by our calculations of f m . Gas at temperatures as high as 107 K is expected to emit radiation in the X–ray band and one would expect to find X–ray emission in the IGM not associated with jets or collapsed objects. Indeed, X–ray emission from highly ionised metal species (O VIII and

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Ne X) in a warm–hot IGM (WHIGM) may have been recently discovered by CHANDRA (e.g. Nicastro et al. 2002, McKernan et al. 2003). This hot gas may be shock heated by galactic winds as well as from the process of structure formation or jets from active galaxies. If the first case is true, this gas may represent the hot metal enriched gas accumulated in our shells, which is too highly ionised to produce absorption in the Lyα forest.

5.5

The Role of Galaxies with Different Masses

In this section we investigate the role of galaxies with different masses in polluting the IGM with metals, by comparing the results obtained from our four sets of simulations with increasing mass resolution. The same results can be obtained by running a version of M3 in which galaxies with halo masses lower than a fixed threshold are not allowed to blow winds. While a large population of dwarf galaxies is already forming at z . 20 in M3, only a few objects are assembling in M2 at the same epoch and in the lower resolution runs M1 and M0 the first galaxies appear only at z < 15 and z < 7, respectively. The total number of galaxies in M3 is five times as large as in M2 at z = 0 and the number of galaxies with winds six times as large. In figure 5.5 we show the dependence of the volume filling factor (top panels), the fraction of mass in shells (mid panels) and the total metal mass in shells (bottom panels) on the mass resolution of the simulations. The left panels show the results for a model with high mass loading efficiency, while the right panels for a model with low mass loading. In models with a high entrainment fraction, whose results are shown in the left panels, all quantities depend strongly on the mass resolution of the simulations and on the ability to resolve low mass galaxies. These are responsible for about half of the filled volume at z = 0 and an even larger fraction at higher redshifts. Similar results hold for the fraction of IGM mass in shells and for the ejected metals. The very massive galaxies resolved in M0 give negligible contributions at every redshift, while the galaxies with M? & 2 · 109 M , resolved by M1, become important at z ∼ 0. At z < 1 there is a factor of 2 to 3 difference between the results of M3 and M2. This is an indication that the relative importance of intermediate and massive galaxies, while small at early times, grows steadily with redshift. In general, however, the contributions of dwarf galaxies are dominant over the ones from massive galaxies. On the other hand, almost all galaxies with M ? > 107 M blow winds in models with ε = 0.01. In these models, the mass and metal budget at z . 3 are dominated by winds driven by galaxies with stellar masses between a few times 108 and 1010 M , mostly resolved by M2. The relative contributions of winds blowing out of galaxies with M ? & 1010 M are larger than in models with higher mass loading, but at z ∼ 0 still do not exceed a few

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Figure 5.5: Dependence of fv , fm and of the total metal mass in shells on the mass resolution of the dark matter simulations. In the left panels we show results for the model with parameters ε = 0.1 and K = 0.5, while in the right panels for the model with ε = 0.01 and K = 0.1. The two different behaviours are typical of two groups of model we identify in section 5.5. The lines represent respectively our four simulation sets: (1) thick solid line: M3, Mp = 1.7 · 108 h−1 M ; (2) dotted line: M2, Mp = 9.5 · 108 h−1 M ; (3) dashed line: M1, Mp = 4.8 · 109 h−1 M ; (4) dashed dotted line: M0, Mp = 6.8 · 1010 h−1 M .

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percent. The role of massive galaxies in determining f v , fm and the ejection of metals becomes more and more important with time. At z ∼ 0, galaxies with M? < 2 · 108 M contribute no more than about 20 to 30% to the volume filling factor. At z < 2, the galaxies with M ? > 108 M , resolved in M2, account for nearly half the fraction of IGM in shells and for about 90% of the total mass of metals ejected by winds. In these models, low mass galaxies are important for the chemical enrichment of the IGM at high redshifts, while at lower redshifts massive galaxies dominate. One may ask if objects with stellar masses lower than about 10 7 M might give a substantial contribution to pollution of the IGM at redshifts where larger objects have not yet assembled. Indeed, Madau, Ferrara & Rees (2001) claim that the IGM has been polluted by outflows from pregalactic objects, with total masses well below 10 8 − 109 M . In principle, winds may escape very easily the shallow potential wells of such objects, in a scenario where little mass is accreted onto the shell from the surrounding medium. On the other hand, winds would not escape at all in case of efficient mass loading, according to our model. Unfortunately, our simulations do not have sufficient resolution to follow the evolution of these objects. At lower redshifts, the evolution of objects with total masses lower than 109 M may be affected by feedback effects that inhibite their star formation activity (e.g. Haiman, Rees & Loeb 1997, Mac Low & Ferrara 1999). As a result, these objects would be unable to blow winds, making their contribution to the pollution of the low redshift IGM negligible with respect to other galaxy populations with higher stellar masses.

“And do I look like the kind of man that can be intimidated?” barked Uncle Vernon. “Well...” said Moody, pushing back his bowler hat to reveal his sinisterly revolving magical eye. Uncle Vernon leapt backward in horror and collided painfully with a luggage trolley. “Yes, I have to say you do, Dursley.”

Chapter 6

Artificial Spectra In this chapter we will describe our method to extract synthetic spectra from our simulated box. The spectra reproduce the Lyα forest observed blueward of the Lyα emission line in the spectra of high redshift quasars. In section 6.2 we present the fundamental ingredients and in section 6.3 we discuss the procedure to calculate the optical depth of gas and its flux spectrum. Examples of spectra extracted from an unperturbed IGM are shown in subsection 6.3.6. We include the effects of feedback and search for wind signatures due to wind shells and cavities in sections 6.4 and 6.5.

6.1

Feedback and the Lyα Forest

The Lyα forest is one of the most powerful sources of information about the high redshift IGM, which at z ∼ 3 is thought to contain about 70% of all the baryons in the Universe. Despite attempts to investigate the effects of feedback on the statistical properties of the forest (e.g. Theuns, Mo & Schaye 2001), it is still unclear how and to which extent the forest may be affected. The cosmic reionisation makes the Universe transparent to the UV radiation emitted by stars and quasars and determines a strong decrease in the neutral fraction of hydrogen, which is detectable by means of the Gunn– Peterson effect. Although many uncertainties remain in the identification and definition of the reionisation epoch, the global picture is much clearer than the one we possess for the chemical evolution of the IGM. The diffuse IGM shows traces of chemical enrichment down to the lowest densities proved today. Feedback mechanisms from galaxies may have played an important role in polluting the low density IGM with the products of stellar nucleosynthesis. But did they leave a detectable footprint on the Lyα forest and on the absorption features redwards of the Lyα emission line in the spectra of quasars? Or the widespread level of metal enrichment is the only outcome of feedback?

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Galactic outflows, as we have seen in the previous chapters, are responsible for the displacement of large amounts of matter and probably of a significant heating of the IGM. As a consequence, the distribution of the neutral hydrogen responsible for the absorption of the UV radiation might have changed significantly, both because of the heating and of the displacement. Little work has been done so far in this field. Theuns, Mo & Schaye (2001) claim that signatures due to cavities in the IGM evacuated by galactic winds can be found in the spectra of quasars whose lines of sight pass in the vicinity of Lyman break galaxies. These patterns have been confirmed by only a handful of observations (Adelberger et al. 2003), but, if they are true, they would indicate that the Lyα forest is affected by feedback. On the other hand, it remains unclear how much feedback can actually affect its properties: do galactic winds have the power to modify sensibly or even shape the characteristics of the Lyα forest, or are their signatures so tiny that they cannot be detected by current spectrographs? Do they produce an effect at all on the Lyα forest? Is this effect distinguishable between the other patterns of the forest? In the following sections we will present our method to investigate the effects of galactic winds on the Lyα forest. Artificial spectra are extracted from our simulated box along random directions. The optical depth of the gas is calculated by integrating the relevant quantities (density, temperature and velocity) along a given line of sight (LoS, hereafter). Our semi–analytic prescriptions for the evolution of winds give the necessary information about the position, the dynamics and the chemical state of wind shells and cavities. The density and the temperature of the IGM, together with its ionisation state, are recovered by means of the equation of state of the low density IGM (Hui & Gnedin 1997) and of simple recipes to determine the physical conditions of the gas in clusters. Since this work is in progress, we will give only a qualitative description of some preliminary results. Absorption spectra are computed at z = 3 and z = 2 and their effective optical depth is normalised to the observed value to allow a direct comparison with the observed spectra. A more detailed and quantitative analysis will be presented in future publications, together with a comparison with current observations.

6.2

The Ingredients for the Spectra

In this section we will use the notions introduced in chapters 1 and 2 to describe the physical state of the intergalactic medium and to recover the necessary quantities for computing synthetic spectra.

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Figure 6.1: The temperature To of the IGM at ρ = ρ¯, as calculated from equation 1.5. Different lines are from different choices of the spectral index α of the UV ionising background radiation: (1) dashed line: α = 1; (2) dotted line: α = 1.3; (3) thick solid line: α = 1.5; (4) dashed dotted line: α = 1.7; (5) dashed three–dotted line: α = 2.

6.2.1

Particle Densities

Given the positions and the mass of the dark matter particles in an N–body simulation, it is possible to compute their densities using the SPH technique. The fundamental equations of smoothed particle hydrodynamics have been presented in subsection 2.2.3. We recover the density of the intergalactic gas from the dark matter distribution, assuming that the evolution of the baryons follows the dark matter. As demonstrated by Viel et al. (2002) this is a reasonable hypothesis, when considering the diffuse gas for which cooling is not efficient. In general this happens when the overdensity of the gas is small, e.g. δ < 10. The densities to be associated to the dark matter particles are calculated using equations 2.8 and 2.9. The density of the gas is then simply the product of the dark matter density and the baryon fraction, which we assume f b = 0.12.

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Figure 6.2: The temperature of the gas particles in M3 at z = 3. The narrow straight line indicates the low density gas that follows the equation of state of Hui & Gnedin (1997). The spread dots at higher temperatures and densities indicate the hot gas in groups and clusters, at the virial temperature of the halo in which it resides.

6.2.2

Particle Temperatures

The temperature of the particles is calculated separately for low and high density particles. This double treatment is necessary since the physical conditions of the gas in the two cases are different: the low density gas is mostly unshocked, it cools adiabatically and is photoionised by the UV background radiation from young stars and quasars. On the other hand, the gas in clusters, groups and haloes is shock heated because of structure formation and does not obey any more to the same equation of state. In this case, its temperature has to be calculated from the properties of the dark matter halo in which it resides. The low density particles represent the diffuse IGM, with overdensities usually δ < 10, and are not bound to groups and haloes. In our simulations fewer than half of the particles belong to haloes at all redshifts. For these particles, we calculate the temperature from the equation of state (1.4) of Hui & Gnedin (1997), introduced in section 1.5.3. The equation of state approximates a power law and is valid when the gas is in photoionisation equilibrium. The dependence of To on the UV background spectral index α is shown in figure 6.1. In our calculations of spectra we assume α = 1.5.

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The temperature of particles bound in groups is the virial temperature of their dark matter halo given in equation 2.12. The equation is valid under the assumption that the gas behaves like an isothermal gas sphere (White & Frenk 1991). Note that the virial temperature is proportional to the circular velocity of the halo squared. To particles belonging to satellites in groups we assign the temperature of the group. In figure 6.2 we show the temperature of the gas in the M3 simulation at z = 3. The low density gas obeying the equation of state 1.4 is distributed along a narrow straight line, while the high temperature gas in small groups and clusters is spread into a cloud–like region. The horizontal lines crossing the cloud are due to gas with different densities residing in the same halo, which is assumed to behave as an isothermal gas sphere.

6.2.3

Hydrogen Ionisation State

To calculate how much radiation of a desired wavelenght is absorbed by a gas cloud, one needs to know the composition and the ionisation state of the gas, which determine its optical depth. The transmission of UV radiation with λ = 1215.6 ˚ A through an hydrogen gas is possible when the gas is highly ionised, that is the fraction of neutral hydrogen atoms in the gas, defined as X H I = nH I /nH , is lower than about 10−4 –10−5 . The equation of ionisation evolution for hydrogen is: dXH I = αH II ne XH II − XH I (ΓγH I + ΓeH I ne ) , dt

(6.1)

where ne = enH is the electron number density, αH II is the recombination rate of H II, ΓγH I is the photoionisation rate and ΓeH I the collisional ionisation rate of H I. We calculate the fraction of neutral hydrogen X H I from equation 6.1 by assuming ionisation equilibrium, that is dX H I /dt = 0. If the gas is highly ionised, then XH II ∼ 1 and we can calculate the fraction of neutral hydrogen as: αH II ne . (6.2) XH I = ΓγH I + ΓeH I ne The electron fraction e represents the ratio between the number of electrons and the total number of particles in the plasma and can be expressed as e = (2 − Y ) / [2 (1 − Y )]. The primordial abundance of helium is Y = 0.24. Substituting in the formula for the electron density: ne =

2−Y nH . 2 (1 − Y )

(6.3)

The recombination rate of hydrogen is a function of the temperature of

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112 the gas and, defining Tn = T /(10n K), is given by: αH II = 6.30 × 10−11

T −0.5 T3−0.2 −1 s . 1 + T60.7

(6.4)

The ionisation of hydrogen is realised through two different mechanisms, that is collisional ionisation and photoionisation. Photoionisation is the dominant process in the low density, cold intergalactic gas, with T . 10 5 K. The rate of photoionisation of any species i depends on the flux spectrum of the ionising ultraviolet background radiation J(ν, z): Z ∞ 4πJ(ν, z)σi (ν) Γγi (z) = dν, (6.5) hν νi where σi (ν) is the photoionisation cross–section and ν i the ionising threshold frequency of species i. Assuming an ionising background of the form of equation 1.3, the photoionisation rate of hydrogen can be expressed as ΓγH I = 1.26 × 10−11

J21 −1 s , 3+α

(6.6)

where we choose J21 = 1.5 at z ∼ 3. At temperatures higher than about 10 5 K, ionisation by collisional excitation becomes the dominant mechanism. In this regime, the collisional ionisation rate is ΓeH I = 1.17 × 10−10 T 0.5 e−157809.1/T

6.3

1 cm3 s−1 . 0.5 1 + T5

(6.7)

Construction of Spectra

Given the positions, the velocities, the densities, the SPH smoothing lengths and the temperatures of the gas along a given line of sight at redshift z, we compute the Lyα spectrum as follows.

6.3.1

Identification of a Random LoS

A random direction through our simulated region is identified by generating a pair of random 3–D points within our simulated region with the random number generator Mersenne Twister [15]. We then calculate the equation of the straight line across the points in cartesian coordinates. We request the distance l between the line and the centre of mass x c of the sphere to be no larger than half the radius R of the high resolution region itself, that is d(l, xc ) < R/2 = 13 h−1 Mpc. This choice implies that the length of our line of sight inside our high resolution region falls between 45 and 52 h −1 Mpc in comoving coordinates. When calculating the absorption in the spectrum, contributions from gas outside the fiducial region of diameter 52 h −1 Mpc have to be taken

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113

into account. To do this, when we integrate the density, the velocity and the temperature of the gas along the line of sight as in equations 6.8–6.10, we integrate over all the high resolution particles present in a larger sphere with radius 3R/2 = 39 h−1 Mpc. The high resolution region in the N– body simulations has irregular contours and extends actually far outside our sphere. Contributions from gas outside the sphere may be important if its peculiar velocity is such to displace the absorption in the fiducial region of the spectrum, corresponding to the central spherical region. Once we have calculated the spectrum along the line of sight crossing the extended sphere with radius 39 h −1 Mpc, we eliminate the pixels corresponding to regions outside our fiducial sphere. This precaution is necessary since we are dealing with a resimulation with no periodic boundary conditions. We are thus confident that our spectra are not affected by border effects.

6.3.2

The Integration along the LoS

We identify a sightline through the high resolution sphere and we divide its total length L into N pixels of equal width ∆ = L/N . We choose N = 3000. The density and the density–weighted temperature and velocity for each bin j at position x(j) are computed by integrating the relevant quantities along the LoS (Theuns et al. 1998): X ρX (j) = a3 X(i)Wij , (6.8) i

(ρT )X (j) = a3

X

X(i)Wij T (i),

(6.9)

i

(ρv)X (j) = a3

X i

X(i)Wij {ax(i) ˙ + a˙ [x(i) − x(j)]} ,

(6.10)

where the sum is over all the particles intersecting the LoS. a = (1 + z) −1 is the scale factor and X(i) is the abundance of the species X for particle i, assuming ionisation equilibrium. For Lyα absorption spectra, X is the neutral hydrogen H I. The normalised SPH kernel is: Wij =

mW (rij /hi ) , h3i

(6.11)

with W (rij /hi ) given by equation 2.9, as used in GADGET, and m the mass of the dark matter particles. r ij is the distance between particle i and particle j and hi is the smoothing length of the dark matter particle. The pixel temperatures and velocities are computed by dividing the quantities in equations 6.9 and 6.10 by the densities calculated in equation 6.8. The number density nX (j) of the species X in each pixel is recovered by diving equation 6.8 by the mass of element X.

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114

6.3.3

From the Optical Depth to the Spectrum

The next step in the construction of spectra is the calculation of the optical depth of the gas along the LoS. This task requires the conversion of the labelling of bins from the positions x(j) into the velocities v(j) = x(j) · H(t), given essentially by the Hubble velocity with respect to the initial pixel in the LoS. The spectra can then be converted from velocity to the observed wavelength λ using the relation:  v . (6.12) λ = λo (1 + z) 1 + c In redshift space, a pixel at velocity v(k) suffers absorption from a pixel at velocity v(j) by an amount e−τ (k) , where τ (k) is the contribution to the optical depth of bin k given by bin j: (   ) v(k) − v(j) 2 c 1 nX (j)a∆ · exp − . (6.13) τ (k) = √ σα VX (j) π VX (j) The Doppler width VX (j) of the species X with mass mX in pixel j is VX2 (j) =

2kB TX (j) , mX

(6.14)

where nX (j) is the numer density, TX (j) the temperature in pixel j and c the speed of light. The Doppler width V X (j) is often called the b–parameter and determines the thermal broadening of the absorption lines. The Lyα cross section for H I is   3πσT 1/2 σα = f λo = 4.45 · 10−18 cm2 , (6.15) 8 with λo = 1215.6 ˚ A the rest wavelength of the transition and σ T = 6.625 · 10−25 cm2 the Thomson cross section. f = 0.41615 is the oscillator strength and measures the quantum mechanical departure from the classical harmonic oscillator.

6.3.4

The Voigt Line Profile

Absorption lines can be fitted with the so–called Voigt profile. Its absorption coefficient is given by the convolution of a Gaussian and a Lorentzian function: α (a, x) = =

1 πe2 γ/4π 2 − ∗√ f e 2 2 me c (ν − νo ) + (γ/4π) π∆νD Z 2 πe2 1 a ∞ e−y f√ dy, me c π∆νD π −∞ (x − y)2 + a2

“

ν−νo ∆νD

”2

(6.16)

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115

where ∆νD = VX ν/c is the Doppler frequency shift, e the electron charge and me the electron mass. γ is the damping parameter and ν o = c/λo the central frequency of the line. For simplicity, we have defined a = γ/ (4π∆ν D ) and x = (ν − νo ) /∆νD . Physically, the Voigt profile arises from the combination of thermal and natural broadening of lines. The thermal broadening reflects the Maxwellian velocity distribution of the absorbing atoms and ions via the Doppler effect. The natural broadening is the absorption line profile of an individual atom, considered as an harmonic oscillator. The Voigt integral cannot be evaluated analytically. Here we have approximated the profile of our absorption lines with a Gaussian with absorption coefficient α g “ ”2 √ 2 o 1 − ν−ν πe ∆νD f e . αg (ν) = me c ∆νD

(6.17)

The approximation is satisfactory when the thermal broadening dominates over the natural broadening of lines. For the Lyα transition, the natural broadening is small with respect to the thermal broadening when the column density of neutral hydrogen is low and the absorption line is not saturated. The situation is reversed for high column density systems like DLAs, whose absorption profiles show the typical Lorentzian wings and can be approximated by an absorption coefficient α l which is a Lorentzian function of frequency ν: γ/4π 2 πe2 f . (6.18) αl (ν) = me c (ν − νo )2 + (γ/4π)2 The optical depth of the gas is calculated by integrating the absorption coefficient along the line of sight: Z (6.19) τνo = nανo dl, where n is the number density of the gas. The absorption coefficients α have the dimension of a cross–section, that is cm 2 .

6.3.5

Normalisation of Spectra

We normalise our synthetic spectra by rescaling the mean flux he −τH I i in each artificial spectrum to the mean flux measured in real spectra, e −τef f . τH I is the H I opacity along our simulated LoS. The effective optical depth τef f derived from observations is calculated as a function of redshift by using equation 1.7 (Kim et al. 2002, see also figure 1.3). We calculate the effective optical depth τ oss in our spectra as: τoss = − lnhe−τH I i.

(6.20)

116

Artificial Spectra

With an iterative procedure we rescale τ oss to τef f until the difference between the two is no larger than a few percent, that is, typically, |τoss − τef f | < 0.005. This procedure allows us to make the artificial spectra directly comparable to the observed ones in each given redshift range. In addition, it somewhat washes out the dependence of the optical depth on the normalisation coefficient of the UV ionising background radiation J 21 , which determines the ionisation fraction of hydrogen and therefore the absorption of the UV radiation.

6.3.6

Some Examples of Unperturbed Spectra

In figure 6.3 we show in some detail how we extract an artificial spectrum from the dark matter distribution of particles in M3. In the uppermost panel we show the flux spectrum and in the second panel from top the optical depth along the LoS, in redshift space. In the four bottom panels, we show, in real space, the fraction of neutral hydrogen XH I , the total baryon density ρ, the temperature T and the velocity v of the gas, all integrated along the line of sight, as calculated from equations 6.8–6.10. The pixel velocity is calculated with respect to a fixed point P that we assume as the first pixel of our line of sight and it is the sum of the projection of the peculiar velocity of the gas along the LoS and of the Hubble flow with respect to P . The contribution of the peculiar velocity is significant for gas in high density regions, generally groups or clusters. Examples of this are visible in the bottom panel of figure 6.3 at λ ∼ 4860, λ ∼ 4886 and λ ∼ 4910. The jumps in the velocity distribution are due to the presence of extended overdense regions, which stir significantly the velocity field in their surroundings from the Hubble flow. The temperature and the total baryon density along the line of sight are tightly correlated, as shown in the second and third panels from the bottom, respectively. This is to be expected, given the relation between temperature and density established both by the equation of state of the low density IGM and by the state of the gas in haloes, as shown in figure 6.2. In figure 6.4 we show more examples of spectra extracted along random directions in our simulated region, which do not include the effects of winds. The length of the spectra depends on the position of the LoS in the sphere. The properties of these spectra are independent of our wind models, because here we consider only the distribution of the dark matter particles.

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117

Figure 6.3: An example of line of sight construction at z = 3. The top panel shows the spectral flux, while the second the optical depth of the gas along the line of sight, in redshift space. The four bottom panels, from top to bottom, show respectively the fraction of neutral hydrogen X H I , the total baryon density ρ, the temperature and the velocity of the gas integrated along the LoS in real space.

118

Artificial Spectra

Figure 6.4: Examples of unperturbed spectra extracted along random directions from our simulated region at z = 3. Feedback effects are not included.

6.4 Shell Contributions to the Optical Depth

6.4

119

Shell Contributions to the Optical Depth

The spectra presented so far have been extracted from our simulated region by assuming that the distribution of the gas follows precisely the one of the dark matter. In this section we show how we include the effects of galactic winds in the calculation of spectra. In the next section we will discuss how the presence of cavities (6.5.1) and shells (6.5.2) modifies the artificial spectra calculated above.

6.4.1

Shell Optical Depth

We will see in section 6.5 that cavities are regions of space whose gas content has been evacuated by winds. Inside them, the transmitted flux of UV radiation may increase because of the reduced absorption. By contrast, shells may have densities higher than the surrounding medium and therefore may be expected to be responsible for absorption in the Lyα spectra, if their temperatures are low enough to allow a significant fraction of hydrogen and metals to be neutral. To calculate the contribution of shells to the optical depth along a LoS we adopt a procedure similar to the one we have used in subsection 6.3.3. The linear dimension of our pixels in real space is about 20–26 h −1 kpc, depending on the position of the LoS through the high resolution region. Because of our assumption that shells are thin, each shell affects only one pixel along the LoS. The optical depth of a pixel j corresponding to the position of a shell is: c (6.21) τs = σα nΣH I √ πvxj where vxj is the projection of the shell velocity on the LoS and n ΣH I is the surface number density of H I in the shell. Again, v xj is responsible for the thermal broadening of the absorption lines. A pixel i suffers absorption from pixel j by an amount "   # vi − v j 2 τi = τs · exp − . (6.22) vxj We approximate again the profile of absorption lines with a Gaussian profile, as we have done in section 6.3. We will see that the approximation is satisfactory, since the optical depth of the shells is very low.

6.4.2

Surface Number Density and Temperature of Shells

The optical depth of the shell as given in equation 6.21 is a function of the surface number density of H I in the shell, n ΣH I , which we calculate as: m nΣH I = (1 − Y − Z) XH I , (6.23) 4πr 2 mp

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120

where mp is the protom mass, m and r are the mass and the radius of the shell, Y is the mass fraction of helium, Z the mass fraction of metals and XH I is the fraction of neutral hydrogen as given by equation 6.2. To calculate XH I , one has to know the temperature and the density of the shell. Our prescriptions for the evolution of winds do not give any information about the state of the gas that is accreted by the shells. We have therefore to introduce new recipes to describe properties of this gas such as the temperature and the density. To do this, we use the assumption we have made about the energetics of winds, that is that bubbles expand adiabatically. If we now make the further assumption that the shock is a strong shock, we can apply the Rankine– Hugoniot jump conditions at the interface between the shell and the IGM. These determine the density ρ1 , the pressure P1 and the velocity v1 of the gas behind the shock as a function of the properties ρ o , Po and vH of the surrounding medium and of the shock velocity v s (Ostriker & McKee 1988): ρ1 (vs − v1 ) = ρo (vs − vH ) , 2

P1 + ρ1 (vs − v1 ) γ P1 1 (vs − v1 )2 + 2 γ − 1 ρ1

(6.24) 2

= Po + ρo (vs − vH ) , (6.25) 1 γo Po = (vs − vH )2 + + εc2 . (6.26) 2 γo − 1 ρo

For a monoatomic, nonrelativistic gas the adiabatic index is γ = γ o = 5/3. The term εc2 represents the energy injection per gram at the shock front, in detonation waves. If we relax the assumption of thin shell, the above equations can be written as (Dopita & Sutherland 2002): ρ1 = 4ρo , 3ρo vs2 P1 = , 4 1 v1 = vs . 4

(6.27) (6.28) (6.29)

If the gas behind the shock front obeys the equation of state for an ideal gas, kB T P = , (6.30) ρ µmH with µ the molecular weight and mH the hydrogen atomic mass, then the temperature of the gas in the shell is given by: T =

3µmH vs2 . 16kB

(6.31)

We assume for the shock velocity the difference between the wind and the shell velocity vs = vw − v. We can now calculate the density of the gas in the shell from equation 6.24 and its temperature from equation 6.31.

6.4 Shell Contributions to the Optical Depth

6.4.3

121

Shell Cooling Time

Equation 6.31 is valid is the case of adiabatic expansion, that is when radiative losses are negligible and the wind energy is conserved. To check if this assumption is correct, we calculate the cooling time of the shell and we compare it to its age, estimated as t shell = r/v. The cooling time of the gas is (Theuns et al. 1998): tcool =

3kT mH , 2µ ρ (1 − Y )2 (C − H)

(6.32)

where C is the total cooling rate and H the heating rate. The gas is heated by photoionisation by the photons of the UV background radiation. The net photoheating rate depends on the slope α of the UV background and on the temperature of the gas (Theuns et al. 1998): H=

Lε T −0.7 , 2+α

(6.33)

with Lε = 1.7 × 10−20 erg s−1 cm3 K0.7 . Two processes contribute to the gas cooling, namely Compton cooling Lcomp and radiative cooling Lrad : C = Lcomp + Lrad .

(6.34)

The Compton cooling rate is a function of the temperature and of the number density n of the gas: Lcomp = 1.7 × 10−36

T (1 + z)4 erg cm3 s−1 , n

(6.35)

where z is the redshift. Physically, it is due to the scattering of electrons in the gas with the photons of the CMB radiation. The total radiative cooling is due to the combination of several concurrent processes, namely free–free emission from an hydrogen–helium plasma, free–bound emission from helium atoms and free–bound emission from hydrogen ions. The resulting radiative loss rate has the form (Ikeuchi, Tomisaka & Ostriker 1983): Lrad = 2.4 × 10−27 T 0.5 ,

T > 7 × 105 K,

= 5.9 × 10−16 T −1.4 ,

7 × 105 > T > 8 × 104 K,

= 8.1 × 10−16 T −1.7 ,

5 × 104 > T > 3 × 104 K.

= 1.9 × 10−42 T 4 ,

8 × 104 > T > 5 × 104 K,

(6.36)

Lrad is again expressed in units of erg cm 3 s−1 . This formula is valid for a plasma of primordial composition. Radiative cooling can be neglected for temperatures below ∼ 3 × 104 K, where the integrated flux of UV photons of the background radiation is most efficient to heat the IGM.

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122

6.5 6.5.1

Wind Signatures in Spectra Wind Cavities

As we have shown in chapter 4, when the shells cross the IGM, they sweep up a fraction of the gas, thus creating a “cavity”. Cavities are therefore regions of space with a density lower than the one of the surrounding IGM, because part of the gas has been removed and accumulated in shells. If the fraction of swept up gas is sufficiently high, the cavities can be partially or completely empty. How do we create these cavities in our simulated region? What is the effect of cavities created by winds on the total absorption in Lyα spectra? To simulate the effect of wind cavities on the density distribution of the intergalactic gas, we follow a procedure analogous to the one we have used to calculate the fraction of particles in winds in section 4.1.3. We flag a fraction x of the lowest density particles inside shells as wind particles. When extracting the spectrum along a random LoS through our simulated region, we remove all the flagged particles from the calculation of the gas optical depth. This results in a decrease of the optical depth of the gas along the LoS where we remove the wind particles. The gas surrounding wind–blowing galaxies may be completely depleted, leaving behind an empty cavity, if the entrainment fraction is sufficiently high. As a consequence, we find “holes” in the pixel density, temperature and velocity, as is shown for example in figure 6.5. These holes are present in nearly symmetric pairs when the LoS crosses a cavity and intercepts the galaxy at its centre, where unperturbed particles lie. This happens for example in figure 6.5 at λ ∼ 4890 ˚ A and λ ∼ 4910 ˚ A. The second pair is almost exactly symmetric, indicating perhaps that the LoS crosses a large cavity produced by a single shell, while the first pair is clearly asymmetric. The asymmetry may arise from the combination of two or more shells originated by different galaxies. In this case, the LoS may punch the extended cavity at variable distances from the object(s) we see in absorption, thus explaining the unequal width of the pair of holes. However, some of the holes do not appear in pairs. This is because the LoS crosses a cavity, but it does not intercept any galaxy. Typical examples are the holes at λ ∼ 4862 ˚ A and λ ∼ 4885 ˚ A in figure 6.5. In figure 6.6 we show the same spectra as in figure 6.4, in red. To these, we have overplotted in blue the new spectra we have obtained by including the effects of winds. Even at first sight, the spectra with and without wind cavities present some differences. One difference is due to the normalisation process. The removal of a certain number of wind particles during the construction of the spectra results in a decrease in the effective optical depth. As a consequence, even if the difference in the effective optical depth is small, the line profiles in the two cases are not exactly the same, after the

6.5 Wind Signatures in Spectra

123

Figure 6.5: Example of line of sight where wind cavities and shells have been included. The chosen LoS is the same of figure 6.3 at z = 3. Cavities show up in the pixel density, temperature and velocity as “holes”, that is regions from where all particles have been evacuated. The contributions of shells are visible in the three bottom panels as small density and temperature peaks and as velocity shifts with respect to the velocity of the gas along the LoS. The contribution of shells to the optical depth is negligible, since the gas in the shells is completely ionised.

124

Artificial Spectra

Figure 6.6: The Lyα forest at z = 3. To show the effects of winds on the Lyα forest, we show the unaffected spectra of figure 6.4, in red, and we overplot the spectra we obtain by including wind shells and cavities, in blue.

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125

normalisation. In general the normalisation to the observed value of τ ef f does not affect the shape of lines, but it may change slightly their amplitude. Consider, for example, the series of pixels corresponding to λ = 4900 to 4920 ˚ A of the uppermost spectrum. The two fluxes are very similar, but at a more carefull analysis they actually show a tiny difference. This difference would be much more significant, if the initial values of τ ef f for the two spectra differed more. Spectral signatures directly connected with wind cavities are easily identified in figures 6.5 and 6.6. Absorption lines in the unperturbed spectra, in red, are washed out by the presence of cavities. The removal of particles from cavities produces therefore an increase of the transmitted flux of UV photons around wind–blowing galaxies. Examples of this behaviour are the feature at λ = 4850 to 4985 ˚ A in the uppermost spectrum in figure 6.6 and ˚ the one at λ ∼ 4887 A in figure 6.5. However, it may happen that the variation in the pixel optical depth corresponding to cavities is so small that the net effect on the transmitted flux is negligible. In fact, the neutral hydrogen in pixels outside cavities still gives Gaussian–weighted contributions to the optical depth of the pixels inside the cavity. This happens in particular if a shell is evacuating material in the outskirts of an optically thick system with a large thermal velocity. As a result, the transmitted flux inside the cavity may not be affected as much as one would expect. Consider for example the system at λ ∼ 4910 ˚ A in the two upper panels of figure 6.5. Here the decrement in the optical depth created by the two cavities is negligible in comparison with the total optical depth contributed by the central object. The decrement is clearly visible at λ ∼ 4912 ˚ A because of the logarithmic scale, but is so tiny that it does not change the resulting spectral flux.

6.5.2

Shell Signatures

The identification of shell signatures in spectra is more problematic. Consider again figure 6.5. We know that cavities create holes in the density, velocity and temperature distributions along the LoS. A more careful look at the three bottom panels reveals that in the vicinity of these holes the total pixel density shows little narrow peaks, while the pixel velocities show distortions with both positive and negative sign with respect to the unperturbed pixel velocities. A clear and beautiful example of shell signatures can be found at λ ∼ 4910 ˚ A. Here the LoS passes almost exactly through a galactic object that emerges as a peak in the distribution of the total gas density ρ. The overdensity at the centre of the peak is about 300 and the peculiar velocity of the halo induces a distortion in the Hubble flow of about 200 km s −1 . Around the peak, two symmetric holes indicate the cavity evacuated by a wind. On the outer edges of the holes, the total pixel density ρ shows two little spikes,

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126

whose amplitude is about 4 times the amplitude of the surrounding pixels. These are the signatures of the wind shell, expanding symmetrically around the galaxy. The pixel density corresponding to the shell is set according with equation 6.24. Since the linear dimension of each bin in real space is about 20–26 h−1 kpc, our shells can be contained entirely in a single pixel. In the bottom panel, the velocity of the shell introduces small deviations in the velocity field around the galaxy. Two tiny spikes are visible as a negative contribution on the left–hand side and a positive one on the right– hand side of the wind cavity. These are due to the expansion velocity of the shell. The amplitude of the distortions in the pixel velocities is given by the peculiar velocity of the shell with respect to the local velocity field. The temperature of the shell determines the ionisation state of the gas it contains. We find that in general shells have temperatures higher than 106 K, implying that the fraction of neutral hydrogen X H I in the gas is lower than 10−7 − 10−8 . Evidence of this is found in the third panel from top, where the peaks in the total pixel density due to shells correspond to narrow troughs in the distribution of X H I along the LoS. To check if our assumption for the shell temperature is correct, we calculate the cooling time of the shell using equation 6.32. We find that t cool is always much larger then the age of the shell, by at least two orders of magnitude. The cooling time is mostly determined by radiative cooling. The energy lost by Compton cooling is generally a few orders of magnitude smaller than the energy lost by emission of radiation. The shell cooling times are always of the order of 102 Gyr or sometimes larger, while the age of the shells at z = 3 does not exceed 1 Gyr at maximum. This guarantees that energy losses are negligible and our estimate of the shell temperature is a good approximation. Here we use recipes for cooling in which we assume a primordial gas composition. However, our conclusions would not change, at least at z = 3, by assuming metal dependent cooling recipes, because of the large difference between tcool and the ages of the shells. Because of the very high temperature and ionisation state, the gas in the shell does not give any significant contribution to the optical depth along the LoS. As a consequence, in the top two panels of figure 6.5 there are no signatures due to absorption of radiation by shells. The same is true for all the spectra in 6.6. All the spectra are extracted from simulations that use our fiducial wind model with ε = 0.1 and K = 0.5.

6.6

Discussion

We have shown in this chapter that galactic winds do affect the Lyα forest, but their effects are so tiny to be hardly detectable at z = 3. Wind shells are always too hot to produce any absorption features in the spectra and their signatures are only visible in the total density and velocity

6.6 Discussion

127

distributions of the gas along the LoS. However, to recover these quantities from a real spectrum is not trivial, if not impossible. We do not expect to find shell signatures in absorption in the Lyα forest, in real spectra. Our result for shells, although preliminary, is in broad agreement with recent claims that the energy losses by radiative cooling are negligible in superwinds. Hoopes et al. (2003), using FUSE [4] observations in the UV band of the superwind in the starburst dwarf galaxy M82, find that the wind coronal phase at temperatures of about 10 5.5 K cannot cool efficiently, because no O VI emission is detected in the outflow. Similarly, Strickland & Stevens (2000) demonstrate that the energy losses from hot gas at T & 10 6 K are negligible, because the wind luminosity in the X–rays cannot account for more than a few percent of the total energy estimated for the wind. These observations do not rule out the possibility that radiative losses become significant in later stages of the wind evolution, but give a good indication that at least young shells preserve most of their energy. Signatures of wind cavities evacuating material around wind–blowing galaxies might be more promising to detect. We do find that the transmitted flux around galaxies may be increased because of a wind cavity. The actual increase depends on the optical depth of the gas surrounding the cavity, but in some cases it may leave a detectable imprint on the spectrum. Absorption lines are in general more deeply affected when their optical depth is close to unity. As a further example, consider the set of spectra at z = 2 in figure 6.7. No absorption signatures due to shells are visible in the spectra. At z = 2 the UV background radiation can ionise the intergalactic gas more efficiently than at z = 3. As a consequence, the effective optical depth decreases by a factor of about 3. Here the flux increment due to cavities is more evident that at z = 3. The effect could be partly ascribed to the fact that winds had more cosmic time to expand and therefore cavities are more extended. Our results are in broad agreement with results of Theuns, Mo & Schaye (2001), who find that feedback from LBGs may modify the flux of UV photons in their surroundings. Observational evidence of cavities surrounding star–forming galaxies has been recently claimed by Adelberger et al. (2003) in a limited sample of Lyman break galaxies at z ∼ 3. The result is still controversial, but it is consistent with our findings. Hopefully, further observations will shed more light on this still obscure aspect of cosmology. Although our results for the effects of winds on the Lyα forest are very preliminary, they confirm our findings for the volume filling factor and the fraction of mass in shells of chapter 4. These last two quantities indicate that the probability to find wind signatures in spectra is not higher that 10–15% at z ∼ 3 for our fiducial model. The occurrence of distortions in the set of spectra of figure 6.6 is in very good agreement with this probability, independently of the actual amplitude of the distortions. Normalisation effects

128

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Figure 6.7: The Lyα forest at z = 2. As in figure 6.6, the blue spectra are calculating by including the effects of winds, the red the unperturbed ones.

6.6 Discussion

129

are not considered as distortions. Since its temperature is higher than about T & 10 6 K, the gas accumulated in shells cannot be seen in absorption in the Lyα forest. However, this gas might not be totally invisible, since at these temperatures it is expected to emit radiation in the X–rays. Although its emissivity might be very tiny, as Strickland & Stevens (2000) claim, may we have some chances to detect it, in the form of X–ray emission not associated with jets or other collapsed objects? The answer may well be yes, thanks to new results by the satellite CHANDRA [6]. X–ray emission from highly ionised metal species (O VIII and Ne X) in a warm–hot IGM (WHIGM) may have been recently discovered for the first time by Nicastro et al. (2002) and McKernan et al. (2003). The hot gas they detect may be shock heated by galactic winds as well as from the process of structure formation or jets from active galaxies. If the first case is true, this gas may represent the hot metal enriched gas accumulated in our shells, which we are looking for. The detectability of the WHIGM in the soft X–ray band by current and future satellites like MBE (Missing Baryon Explorer, [29]) is discussed by Fang et al. (2003).

6.6.1

Future Prospects

In this chapter we have given a qualitative description of the effects of winds on the Lyα forest. Our next step will be to quantify them and to make more accurate predictions to apply to real spectra. An important extension of what we have presented here will be the simulation of the spectral region redwards of the Lyα emission line in the spectra of quasars, where metal absorption lines like C IV, Mg II and Si IV lie. This will be an important step, since it will allow us to study the correlation between Lyα and metal absorbers. However, metal absorption lines associated with shells can exist only if the gas in the shells can cool down to temperatures of about 104 − 105 K. According to our model, shells remain hot throughout most of their lives, so in principle we should not find any metal line associated with wind shells. We have determined the temperature of shells using the simple model of a radiationless shock expanding adiabatically into a homogeneous medium. In future we would like to verify to which extent this approximation is valid, by calculating more precisely the cooling time and the cooling rate of the gas in the shell with fully consistent, metallicity dependent prescriptions. However, if we assume a primordial composition, the cooling time is at least two orders of magnitude larger than the age of the shells. Therefore, the calculation of tcool assuming a metal dependent cooling rate should not change the results significantly.

“What else are you?” “You may well ask. It no doubt is invisible. Yet I’m something – to myself, at least. I can see the point of my own existence – though I can quite understand nobody else’s seeing it.” D.H. Lawrence

Conclusions We have presented semi–analytical simulations of galaxy formation in a cosmological context, which include the physics of galactic winds. The semianalytic prescriptions are applied to high resolution N–body simulations of a typical “field” region of the Universe. We have focused our attention on the effects of winds on the diffuse IGM and in particular on their efficiency in polluting the IGM with metals. The dependence of the wind properties on our model parameters K and ε is investigated in chapter 3. The mass accumulated in shells is directly linked to the amount of mass entrained from the IGM, mostly set by ε, and the ultimate fate of winds is strongly dependent on this swept–up mass. The results of our models seem to fall broadly into two groups, as a consequence of the mass loading of shells. The first group includes all the models with ε > 0.1, while models with ε = 0.01 belong to a different category. Shells that load little mass from the surrounding medium escape the gravitational potential well of their host haloes very efficiently at every redshift. These shells are mostly composed of metal rich supernova ejecta and shocked ISM and they need to spend little of their energy to accelerate the entrained gas. On the other hand, the formation of highly mass loaded winds is suppressed in galaxies with M ? . 1010 M . The suppression is particularly strong in dwarf galaxies. In these models, the energy provided by star formation is not sufficient to overcome the ram pressure of the infalling material and the gravitational pull of the galaxy. In all our models, dwarf galaxies play a key role at z > 3, when larger objects have not yet assembled. However, their contributions become less important at later times, when more massive galaxies are formed. In chapter 4 we have estimated the volume filling factor of winds and we have calculated the fraction of IGM mass in shells, which gives a different view of how the IGM is affected by outflows. In general, low values of f v are associated with more mass loaded shells, while the opposite is true for f m . The fraction of mass in shells is usually lower than the volume filling factor, suggesting that the actual fraction of intergalactic mass affected by outflows is small even when the winds physically fill a large region of space. The values of fv and fm suggest that winds are unlikely to significantly modify the properties of the Lyα forest.

134

Conclusions

We investigate the efficiency of winds in seeding the IGM with metals in chapter 5. In models with ε = 0.01 winds from low stellar mass galaxies can efficiently pollute the IGM with metals at relatively high redshifts, while models with a higher entrainment fraction imply a later enrichment. In the majority of the models, at least half of the produced metals are retained by galaxies. We have presented our preliminary results on artificial spectra extracted randomly from our simulated region in chapter 6. Our spectra reproduce the Lyα forest blueward of the Lyα emission line in the spectra of high redshift quasars. Since we cannot follow the physics of baryons in detail in high density regions, we can calculate the correct spectral absorption only for systems with column densities lower than about 10 16 − 1017 g cm−2 . Higher column density systems, like LLSs and DLAs, are not represented in our spectra. We use simplified prescriptions to determine the temperature and ionisation state of the gas that contributes to the absorption. The effects of galactic winds are taken into account during the construction of spectra in a twofold way. First, low density, “wind” particles are identified and excluded from the computation of the optical depth along the LoS, to simulate the effect of cavities and bubbles; secondly, the contributions of shells to the optical depth are computed. We find that at z ∼ 3 wind cavities produce an increase in the transmitted flux of UV photons around wind–blowing galaxies, while there are no significant absorption signatures in our simulated spectra, because the temperatures of shells are sufficiently high for the gas to be completely ionised. Our estimates of the mean metallicity of the IGM are significantly higher than the observed values at z ∼ 1 to z ∼ 5 and we have argued that metals in the IGM might not be observable in absorption in the spectra of quasars because of the high temperatures induced in shells. Nonetheless, some shell material may turbulently mix with other IGM gas and become subject to radiative cooling. The temperature of such shell material may therefore decrease until hydrogen recombines and the metals reach lower ionisation states, for example C IV, Si IV and O VI. In forthcoming publications we will investigate possible observable signatures of galactic winds in the Lyα forest and we will discuss the possibility of finding absorption features due to cooled shells in the spectra of quasars.

Bibliography Aarseth S.J., Turner E.L., Gott J.R., 1979, ApJ, 228, 664 Abazajian K. et al. (The SDSS Collaboration), 2003, AJ, in press Adelberger K.L., Steidel C.C., 2000, ApJ, 544, 218 Adelberger K.L., Steidel C.C., Shapley A.E., Pettini M., 2003, ApJ, 584, 45 Aguirre A., Hernquist L., Schaye J., Katz N., Weinberg D.H., Gardner J. 2001, ApJ, 561, 521 Alcock C., Allsman R.A., Alves D.R., Axelrod T.S., Becker A.C., Bennett D.P., Cook K.H., Dalal N., Drake A.J., Freeman K.C., Geha M., Griest K., Lehner M.J., Marshall S.L., Minniti D., Nelson C.A., Peterson B.A., Popowski P., Pratt M.R., Quinn P.J., Stubbs C.W., Sutherland W., Tomaney A.B., Vandehei T., Welch D., (The MACHO collaboration), 2000, ApJ, 542, 281 Appel A.W., 1985, SIAM, J. Sci. Stat. Comp, 6, 85 Asztalos S.J., Daw E., Peng H., Rosenberg L.J., Yu D.B., Hagmann C., Kinion D., Stoeffl W., van Bibber K., LaVeigne J., Sikivie P., Sullivan N.S., Tanner D.B., Nezrick F., Moltz D.M., 2002, ApJL, 571, 27 Bahcall J.N., Gonzalez–Garc´ıa M.C., Penya–Garay C., 2003, JHEP02, 009 Bahcall J.N., Spitzer L., 1969, ApJL, 156, 63 Barkana R., Loeb A., 1999, ApJ, 523, 54 Barkana R., Haiman Z., Ostriker J.P., 2001, ApJ, 558, 482 Bartelmann M., Schneider P., 1999, A&A, 345, 17 Baugh C.M., Cole S., Frenk C.S., 1996, MNRAS, 282, L27 Becker R.H., Fan X., White R.L., Strauss M.A., Narayanan V.K., Lupton R.H., Gunn J.E., Annis J., Bahcall N.A., Brinkmann J., Connolly A.J., Csabai I., Czarapata P.C., Doi M., Heckman T.M., Hennessy G.S., Ivezic

136

Bibliography

Z., Knapp G.R., Lamb D.Q., McKay T.A., Munn J.A., Nash T., Nichol R., Pier J.R., Richards G.T., Schneider D.P., Stoughton C., Szalay A., Thakar A.R., York D.G., 2001, AJ, 122, 2850 Bennett C.L., Banday A.J., Gorski K.M., Hinshaw G., Jackson P., Keegstra P., Kogut A., Smoot G. F., Wilkinson D.T., Wright E.L., 1996, ApJL, 464, 1 Bennett C.L., Bay M., Halpern M., Hinshaw G., Jackson C., Jarosik N., Kogut A., Limon M., Meyer S.S., Page L., Spergel D.N., Tucker G.S., Wilkinson D.T., Wollack E., Wright E.L., 2003a, ApJ, 583, 1 Bennett C.L., Halpern M., Hinshaw G., Jarosik N., Kogut A., Limon M., Meyer S.S., Page L., Spergel D.N., Tucker G.S., Wollack E., Wright E.L., Barnes C., Greason M.R., Hill R.S., Komatsu E., Nolta M.R., Odegard N., Peiris H.V., Verde L., Weiland J.L., 2003b, ApJS, 148, 1 Bernabei R., Belli P., Cappella F., Cerulli R., Montecchia F., Nozzoli F., Incicchitti A., Prosperi D., Dai C.J., Kuang H.H., Ma J.M., Ye Z.P., 2003, Riv. N. Cim., 26, 1 Binney J., Tremaine S., 1987, Galactic Dynamics, Princton University Press, Princeton Blain A.W., Smail I., Ivison R.J., Kneib J.–P., Frayer D.T., 2002, Phys.Rep., 369, 111 Boissier S., P´eroux C,˙ Pettini M., 2003, MNRAS, 338, 131 Bottino A., Donato F., Fornengo N., Scopel S., 2002, APh, 18, 205 Bouch´e N., Lowenthal J.D., Charlton J.C., Bershady M.A., Churchill C.W., Steidel C.C., 2001, ApJ, 550, 585 Bradley R., Clarke J., Kinion D., Rosenberg L.J., van Bibber K., Matsuki S., M¨ uck M., Sikivie P., 2003, Rev. M. P., 75, 777 Breitschwerdt D., McKenzie J.F., V¨olk H.J., 1991, A&A, 245, 79 Bruzual A.G., Charlot S., 1993, ApJ, 405, 538 Bullock J.S., Kolatt T.S., Sigad Y., Somerville R.S., Kravtsov A.V., Klypin A., Primack J.R., Dekel A., 2001, MNRAS, 321, 559 Carlstrom J.E., Holder G.P., Reese E.D., 2002, ARAA, 40, 643 Carr B.J., 1994, ARAA, 32, 531 Carswell R., Schaye J., Kim T.–S., 2002, ApJ, 578, 43

Bibliography

137

Cecil G., Bland-Hawthorn J., Veilleux S., 2002, ApJ, 576, 745 Cecil G., Bland-Hawthorn J., Veilleux S., Filippenko A.V., 2001, ApJ, 555, 338 Cen R., Miralda–Escud´e J., Ostriker J.P., Rauch M., 1994, ApJL, 437, 83 Cen R., Ostriker J.P., 1999, ApJL, 519, 107 Chevalier R.A., A.W. Clegg A.W., 1985, Nature, 317 Ciardi B., Stoehr F., White S.D.M., 2003, MNRAS, 343, 1101 Cole S., 1991, ApJ, 367, 45 Colless M., Dalton G., Maddox S., Sutherland W., Norberg P., Cole S., Bland–Hawthorn J., Bridges T., Cannon R., Collins C., Couch W., Cross N., Delley K., De Propris R., Driver S.P., Efsthatiou G., Ellis R.S., Frenk C.S., Glazebrook K., Jackson C., Lahav O., Lewis I., Lumsden S., Madgwick D., Peacock J.A., Peterson B.A., Price I., Seaborne M., Taylor K., 2001, MNRAS, 328, 1039 Couchman H.M.P., 1991, ApJ, 368, 23 Couchman H.M.P., Thomas P., Pearce F., 1995, ApJ, 452, 797 Cowie L.L., Songaila A., Kim T.–S., Hu E.M., 1995, AJ, 109, 1522 Croft R.A.C., Weinberg D.H., Bolte M., Burles S., Hernquist L., Katz N., Kirkman D., Tytler D., 2002, ApJ, 581, 20 Cruddace R., Voges W., B¨ohringer H., Collins C.A., Romer A.K., MacGillivray H., Yentis D., Schuecker P., Ebeling H., De Grandi S., 2002, ApJS, 140, 239 Dav´e R., Hernquist L., Katz N., Weinberg D. H., 1999, ApJ, 511, 521 Dav´e R., Hellsten U., Hernquist L., Katz N., Weinberg D.H., 1998, ApJ, 509, 661 Dawson S., Spinrad H., Stern D., Dey A., van Breugel W., de Vries W., Reuland M., 2002, ApJ, 570, 92 de Bernardis P., Ade P.A.R., Bock J.J., Bond J.R., Borrill J., Boscaleri A., Coble K., Crill B.P., De Gasperis G., Farese P.C., Ferreira P.G., Ganga K., Giacometti M., Hivon E., Hristov V.V., Iacoangeli A., Jaffe A.H., Lange A.E., Martinis L., Masi S., Mason P.V., Mauskopf P.D., Melchiorri A., Miglio L., Montroy T., Netterfield C.B., Pascale E., Piacentini F., Pogosyan D., Prunet S., Rao S., Romeo G., Ruhl J.E., Scaramuzzi F., Sforna D., Vittorio N., 2000, Nature, 404, 955

138

Bibliography

Dekel A., Silk J., 1986, ApJ, 303, 39 de Lapparent V., Geller M.J., Huchra J.P., 1986, ApJL, 302, 1 D’Ercole A., Brighenti F., 1999, MNRAS, 309, 941 Dopita M.A., Sutherland R.S., 2003, Astrophysics of the diffuse universe, Berlin, Springer Dunne L., Eales S.A., Edmunds M.G., 2003, MNRAS, 341, 589 Eastwood J.W., Hockney R.W., 1974, J. Comp. Phys., 16, 342 Efstathiou G. 2000, MNRAS 317, 697 Efstathiou G., Davis M., Frenk C.S., White S.D.M., 1985, ApJS, 57, 241 Einstein A., 1917, Sitz. Preuss. Akad. d. Wiss., 142 Ellison S.L., 2000, Ph.D. Thesis, University of Cambridge Ellison S.L., Lewis G.F., Pettini M., Chaffee F.H., Irwin M.J., 1999, ApJ, 520, 456 Evans N.W., 2002, Invited Review for “IDM 2002: The 4th International Workshop on the Identification of Dark Matter”, eds. N. Spooner, V. Kudryavtsev, World Scientific Evrard A.E., Summers F.J., Davis M., 1994, ApJ, 422, 11 Fan X., Narayanan V.K., Lupton R.H., Strauss M.A., Knapp G.R., Becker R.H., White R.L., Pentericci L., Leggett S.K., Haiman Z., Gunn J.E., Ivezic Z., Schneider D.P., Anderson S., Brinkmann J., Bahcall N.A., Connolly A.J., Csabai I., Doi M., Fukugita M., Geballe T., Grebel E.K., Harbeck D., Hennessy G., Lamb D.Q., Miknaitis G., Munn J.A., Nichol R., Okamura S., Pier J.R., Prada F., Richards G.T., Szalay A., York D.G., 2001, AJ, 122, 2833 Fan X., Narayanan V.K., Strauss M.A., White R.L., Becker R.H., Pentericci L., Rix H.–W., 2002, AJ, 123, 1247 Fang T., Croft R.A.C., Sanders W.T., Houck J., Dav´e R., Katz N., Weinberg D.H., Hernquist L., 2003, pre–print astro–ph/0311141 Ferrara A., Pettini M., Shchekinov Y., 2000, MNRAS, 319, 539 Fornengo N., Gonzalez–Garcia M.C., Valle J.W.F., 2000, Nucl.Phys. B, 580, 58

Bibliography

139

Freedman W.L., Madore B.F., Gibson B.K., Ferrarese L., Kelson D.D., Sakai S., Mould J.R., Kennicut R.C., Ford H.C., Graham J.A., Huchra J.P., Hughues S.M.G., Illingworth G.D., Macri L.M., Stetson P.B., 2001, ApJ, 553, 47 Frye B,. Broadhurst T., Benitez N. 2002, ApJ, 568, 558 Gamow G., 1970, My World Line, Viking, New York Gear W.K., Lilly S.J., Stevens J.A., Clements D.L., Webb T.M., Eales S.A., Dunne L., 2000, MNRAS, 316, 51 Geller M.J., Huchra J.P., 1989, Science, 246, 897 Gingold R.A., Monaghan J.J., 1977, MNRAS, 181, 375 Gnedin O.Y., Ostriker J.P., 2001, ApJ, 561, 61 Graff D.S., Freese K., 1996, ApJL, 456, 49 Griest K., Kamionkowski M., 2000, Phys. Rep., 333, 167 Gunn J.E., Peterson B.A., 1965, ApJ, 142, 1633 Guth A.H., 1981, Phys. Rev. D, 23, 347 Haardt F., Madau P., 1996, ApJ, 461, 20 Haehnelt M.G., Steimetz M., Rauch M., 1998, ApJ, 495, 647 Haiman Z., Loeb A., 1997, ApJ, 483, 21 Haiman Z., Rees M.J., Loeb A., 1997, ApJ, 476, 458 Hamann F., Ferland G., 1999, ARA&A, 37, 487 Hanany S., Ade P.A.R., Balbi A., Bock J.J., Borrill J., Boscaleri A., de Bernardis P., Ferreira P.G., Hristov V.V., Jaffe A.H., Lange A.E., Lee A.T., Mauskopf P.D., Netterfield C.B., Oh, S.; Pascale E., Rabii B., Richards P.L., Smooth G.F., Stompor R., Winant C.D., Wu J.H.P., 2000, ApJL, 545, 5 Harrison E.R., 1970, Phys. Rev. D, 1, 2726 Heckman T.M., Armus L., Miley G.K., 1990, ApJSS, 74, 833 Heckman T.M., Lehnert M.D., Strickland D.K., Armus L., 2000, ApJS, 129, 493 Heckman T.M., Sembach K.R., Meurer G.R., Strickland D.K., Martin C.L., Calzetti D., Leitherer C., 2001, ApJ, 554, 1021

140

Bibliography

Heckman T.M., Norman C.A., Strickland D.K., Sembach K.R., 2002, ApJ, 577, 691 Hernquist L., Katz N., 1989, ApJ, 70, 419 Hernquist L., Katz N., Weinberg D.H., Miralda–Escud´e J., 1996, ApJL, 457, 51 Holland W.S., Robson E.I., Gear W.K., Cunningham C.R., Lightfoot J.F., Jenness T., Ivison R.J., Stevens J.A., Ade P.A.R., Griffin M.J., Duncan W.D., Murphy J.A., Naylor D A., 1999, MNRAS, 303, 659 Holmberg E., 1941, ApJ, 94, 385 Hoopes C.G., Heckman T.M., Strickland D.K., Howk J.C., 2003, ApJL, 596, 175 Hu E.M., Kim T.-S., Cowie L.L., Songaila A., Rauch M., 1995, AJ, 110, 1526 Hu W., Dodelson S., 2002, ARAA, 40, 171 Hui L., 2001, Ph. Rv. L., 86, 3467 Hui L., Gnedin N.Y., 1997, MNRAS, 292, 27 Hut P., Makino J., 1999, Science, 283, 501 Ikeuchi S., Tomisaka K., Ostriker J.P., 1983, ApJ, 265, 583 Impey C.D., Petry C.E., Malkan M.A., Webb W., 1996, ApJ, 463, 473 Impey C.D., Petry C.E., Flint K.P., 1999, ApJ, 524, 536 Jenkins A., Frenk C.S., White S.D.M., Colberg J.M., Cole S., Evrard A.E., Couchman H.M.P., Yoshida N., 2001, MNRAS, 321, 372 Kaiser N., 1987, MNRAS, 227, 1 Katz N., White S.D.M., 1993, ApJ, 412, 455 Kauffmann G., Haehnelt M., 2000, MNRAS, 311, 576 Kauffmann G., Colberg J.M., Diaferio A., White S.D.M. 1999, MNRAS, 303, 188 Kauffmann G., White S.D.M., Guiderdoni B., 1993, MNRAS, 264, 201 Kearns E.T., 2002, Frascati Phys. Ser., 28, 413 Kim T.-S., Carswell R. F., Cristiani S., D’Odorico S., Giallongo E., 2002, MNRAS, 335, 555

Bibliography

141

Kirkman D., Tytler D., 1997, AJ, 484, 672 Kirshner R.P., 2003, Science, 300, 1914 Klypin A., Kravtsov A.V., Bullock J.S., Primack J.R., 2001, ApJ, 554, 903 Kogut A., Spergel D.N., Barnes C., Bennett C.L., Halpern M., Hinshaw G., Jarosik N., Limon M., Meyer S.S., Page L., Tucker G.S., Wollack E., Wright E.L., 2003, ApJ, in press Komatsu E., Kogut A., Nolta M., Bennett C.L., Halpern M., Hinshaw G., Jarosik N., Limon M., Meyer S.S., Page L., Spergel D.N., Tucker G.S., Verde L., Wollack E., Wright E.L., 2003, ApJS, 148, 119 Kreysa E., Gemuend H.–P., Gromke J., Haslam C.G., Reichertz L., Haller E.E., Beeman J.W., Hansen V., Sievers A., Zylka R., 1998, SPIE, 3357, 319 Kuo C.L., Ade P.A.R., Bock J.J., Cantalupo C., Daub M.D., Goldstein J., Holzapfel W.L., Lange A.E., Lueker M., Newcomb M., Peterson J.B., Ruhl J., Runyan M.C., Torbet E., 2003, ApJ, in press Lacey C., Cole S., 1993, MNRAS, 262, 627 Lacey C., Silk J., 1991, ApJ, 381, 14 Lahav O., Lilje P.B., Primack J.R., Rees M.J., 1991, MNRAS, 251, 128 Lasserre T., Afonso C., Albert J.N., Andersen J., Ansari R., Aubourg E., Bareyre P., Bauer F., Beaulieu J.P., Blanc G., Bouquet A., Char S., Charlot X., Couchot F., Coutures C., Derue F., Ferlet R., Glicenstein J.F., Goldman B., Gould A., Graff D., Gros M., Haissinski J., Hamilton J.C., Hardin D., de Kat J., Kim A., Lesquoy E., Loup C., Magneville C., Mansoux B., Marquette J.B., Maurice E., Milsztajn A., Moniez M., Palanque– Delabrouille N., Perdereau O., Pr´evot L., Regnault N., Rich J., Spiro M., Vidal–Madjar A., Vigroux L., Zylberajch S., (The EROS collaboration), 2000, A&A Letters, 355, 39 Ledoux C., Petitjean P., Bergeron J., Wampler E.J., Srianand R., 1998, A&A, 337, 51 Leitherer C., Heckman T., 1995, ApJS, 99, 173 Lilly S.J., Eales S.A., Gear W.K.P., Hammer F., Le F´evre O., Crampton D., Bond J.R., Dunne L., 1999, ApJL, 518, 641 Lin H., Kirshner R.P., Shectman S.A., Landy S.P., Oemler A., Tucker D.L., Schechter, P.L., 1996, ApJ, 471, 617

142

Bibliography

Linde A.D., 1982, Phys. Lett., 108, 389 Lu L., Sargent W.L.W., Womble D. S., Takada–Hidai M., 1996, ApJ, 472, 509 Lucy L.B., 1977, AJ, 82, 1013 Mac Low M.–M., Ferrara A., 1999, ApJ, 513, 142 Mac Low M.–M., McCray R., Norman M., 1989, ApJ, 337, 141 Madau P., Ferrara A., Rees M.J., 2001, ApJ, 555, 92 Madau P., Haardt F., Rees M.J., 1999, ApJ, 514, 648 Maddox S.J., Efstathiou G., Sutherland W.J., Loveday J., 1990, MNRAS, 243, 692 Martin C.L., Kobulnicky H.A., Heckman T.M., 2002, ApJ, 574, 663 Martin C.L. 1999, ApJ, 513, 156 McKee C.F., Ostriker J.P. 1977, ApJ, 218, 148 McKernan B., Yaqoob T., Mushotzky R., George I.M., Turner T.J., 2003, pre–print astro–ph/0310476. Mellier Y., 1999, ARAA, 37, 127 Milgrom M., 1983, ApJ, 270, 365 Mo H.J., White S.D.M., 2002, MNRAS, 336, 112 Mo H.J., Mao S., White S.D.M., 1999, MNRAS, 304, 175 Monaghan J.J., 1992, ARAA, 30, 543 Monaghan J.J., Lattanzio J.C., 1985, A&A, 149, 135 Moore B., Governato F., Quinn T., Stadel J., Lake G., 1998, ApJL, 499, 5 M¨ortsell E., Goobar A., 2003, JCAP, 4, 3 Møller P., Warren S.J., Fall S.M., Fynbo J.U., Jakobsen P., 2002, ApJ, 574, 51 Nagamine K., Fukugita M., Cen R., Ostriker J.P., 2001, ApJ, 558, 497 Narlikar J.V., Padmanabhan T., 2001, ARA&A, 39, 211 Navarro J.F., Frenk C.S., White S.D.M., 1997, ApJ, 490, 493

Bibliography

143

Navarro J.F., Frenk C.S., White S.D.M., 1996, ApJ, 462, 563 Navarro J.F., Frenk C.S., White S.D.M., 1995, MNRAS, 275, 56 Navarro J.F., Steinmetz M., 1997, ApJ, 478, 13 Navarro J.F., White S.D.M., 1994, MNRAS, 267, 401 Nicastro F., Zezas A., Drake J., Elvis M., Fiore F., Fruscione A., Marengo M., Mathur S., Bianchi S., 2002, ApJ, 573, 157 Nusser A., Haehnelt M., 2000, MNRAS, 313, 364 Olmi L, Testi L., 2002, A&A, 392, 1053 Ostriker J.P., McKee C.F. 1988, Rev.Mod.Phys. 60, 1 Ostriker J.P., Steinhardt P., 2003, Science, 300, 1909 Peacock J. A., 1999, Cosmological physics, Cambridge University Press, UK Peacock J.A., Cole S., Norberg P., Baugh C.M., Carlton M., Bland– Hawthorn J., Bridges T., Cannon R., Colless M., Collins C., Couch W., Dalton G., Deeley K., De Propris R., Driver S.P., Efsthatiou G., Ellis R.S., Frenk C.S., Glazebrook K., Jackson C., Lahav O., Lewis I., Lumsden S., Maddox S., Percival W.J., Peterson B.A., Price I., Sutherland W., Taylor K., 2001, Nature, 410, 169 Pearson T.J., Mason B.S., Readhead A.C.S., Shepherd M.C., Sievers J.L., Udomprasert P.S., Cartwright J.K., Farmer A.J., Padin S., Myers S.T., Bond J.R., Contaldi C.R., Pen U.-L., Prunet S., Pogosyan D., Carlstrom J.E., Kovac J., Leitch E.M., Pryke C., Halverson N.W., Holzapfel W.L., Altamirano P., Bronfman L., Casassus S., May J., Joy M., 2003, ApJ, 591, 556 Peebles P.J.E., 1970, AJ, 75, 13 Peiris H.V., Komatsu E., Verde L., Spergel D.N., Bennett C.L., Halpern M., Hinshaw G., Jarosik N., Kogut A., Limon M., Meyer S.S., Page L., Tucker G.S., Wollack E., Wright E.L., 2003, ApJS, 148, 213 Pentericci L., Fan X., Rix H.–W., Strauss M.A., Narayanan V.K., Richards G.T., Schneider D.P., Krolik J., Heckman T.M., Brinkmann J., Lamb D.Q., Szokoly G.P., 2002, AJ, 123, 2151 Penton P. J., Shull J. M., Stocke J. T., 2000, ApJ, 544, 150

144

Bibliography

Percival W.J., Baugh C.M., Bland–Hawthorn J., Bridges T., Cannon R., Cole S., Colless M., Collins C., Couch W., Dalton G., De Propris R., Driver S.P., Efsthatiou G., Ellis R.S., Frenk C.S., Glazebrook K., Jackson C., Lahav O., Lewis I., Lumsden S., Maddox S., Moody S., Norberg P., Peacock J.A., Peterson B.A., Sutherland W., Taylor K., 2001, MNRAS, 327, 1297 Perlmutter S., 2003, Phys. Today, 56, 54 Perlmutter S., Aldering G., Goldhaber G., Knop R.A., Nugent P., Castro P.G., Deustua S., Fabbro S., Goobar A., Groom D.E., Hook I.M., Kim A.G., Kim M.Y., Lee J.C., Nunes N.J., Pain R., Pennypacker C.R., Quimby R., Lidman C., Ellis R.S., Irwin M., McMahon R.G.,Ruiz– Lapuente P., Walton N., Schaefer B., Boyle B.J., Filippenko A.V., Matheson T., Fruchter A.S., Panagia N., Newberg H.J.M., Couch W.J., (The Supernova Cosmology Project), 1999, ApJ, 517, 565 Petitjean P., Bergeron J., 1994, A&A, 283, 759 Pettini M., 2003, Lectures for the XIII Canary Island Winter School of Astrophysics, pre–print astro–ph/0303272 Pettini M., Shapley A. E., Steidel C.C., Cuby J.–G., Dickinson M., Moorwood A.F.M., Adelberger K.L., Giavalisco M., 2001, ApJ, 554, 981 Pettini M., Rix S., Steidel C., Adelberger K., Hunt M.P., Shapley A.E., 2002a, ApJ, 569, 742 Pettini M., Rix S., Steidel C., Hunt M.P., Shapley A.E., Adelberger K., 2002b, Ap&SS, 281, 461 Ponman T. J., Cannon D. B., Navarro J. F., 1999, Nature, 397, 135 Power C., Navarro J.F., Jenkins A., Frenk C.S., White S.D.M., Springel V., Stadel J., Quinn T., 2003, MNRAS, 338, 14 Press W.H., Schechter P., 1974, ApJ, 187, 425 Press W.H., Rybicki G.B., Schneider D.P., 1993, ApJ, 414, 64 Prochaska J.X., Wolfe A.M., 2002, ApJ, 566, 68 Prochaska J.X., Gawiser E., Wolfe A.M., Quirrenbach A., Lanzetta K.M., Chen H.–W., Cooke J., Yahata N., 2002, AJ, 123, 2206 Rauch M., 2002, ASP Conference Proc. Ed. J.S. Mulchaey & J. Stocke, 254, 140 Rauch M., 1998, ARAA, 36, 267

Bibliography

145

Rauch M., Miralda-Escud´e J., Sargent W. L. W., Barlow T.A., Weinberg D.H., Hernquist L., Katz N., Cen R., Ostriker J.P., 1997, ApJ, 489, 7 Reid I.N., Sahu K.C., Hawley S.L., 2001, ApJ, 559, 942 Rosati P., Borgani S., Norman C., 2002, ARAA, 40, 539 Riess A.G., Strolger L.–G., Tonry J., Tsvetanov Z., Casertano S., Ferguson H.C., Mobasher B., Challis P., Panagia N., Filippenko A.V., Li W., Chornock R., Kirshner R.P., Leibundgut B., Dickinson M., Koekemoer A., Grogin N.A., Giavalisco M., 2003, ApJL, in press Riess A.G., Filippenko A.V., Challis P., Clocchiatti A., Diercks A., Garnavich P.M., Gilliland R.L., Hogan C.J., Jha S., Kirshner R.P., Leibundgut B., Phillips M.M., Reiss D., Schmidt B.P., Schommer R.A., Smith R.C., Spyromilio J., Stubbs C., Suntzeff N.B., Tonry J., 1998, AJ, 116, 1009 Sandage A., 1965, ApJ, 141, 1560. Sanders R.H., McGaugh S.S., 2002, ARAA, 40, 263 Sanders D.B., Mirabel I.F., 1996, ARA&A, 34, 749 Savaglio S., Panagia N., Padovani P., 2002, ApJ, 567, 702 Scalo J.M., 1986, Fundamentals of Cosmic Physics, 11, 1 Schaye J., Rauch M., Sargent W. L. W., Kim T.-S., 2000a, ApJL, 541, 1 Schaye J., Theuns T., Rauch M., Efstathiou G., Sargent W.L.W., 2000b, MNRAS, 318, 817 Schaye J., Theuns T., Leonard A., Efstathiou G., 1999, MNRAS, 310, 57 Shapley A.E., Steidel C.C., Pettini M., Adelberger K.L., 2003, ApJ, 588, 65 Shu C., Mo H.J., Mao S. 2003, pre–print astro–ph/0301035 Simien F., de Vaucouleurs G., 1986, ApJ, 302, 564 Somerville R.S., Primack J.R., 1999, MNRAS, 310, 1087 Somerville R.S., Primack J.R., Faber S.M., 2000, MNRAS, 320, 504 Songaila A., 2001, ApJ, 561, L153 Songaila A., 1997, ApJL, 490, 1 Songaila A., Cowie L.L., 2002, AJ, 123, 2183

146

Bibliography

Spergel D.N., Verde L., Peiris H.V., Komatsu E., Nolta M.R., Bennett, C.L., Halpern M., Hinshaw G., Jarosik N., Kogut A., Limon M., Meyer S.S., Page L., Tucker G.S., Weiland J.L., Wollack E., Wright E.L., 2003, ApJS, 148, 175 Splinter R.J., Melott A.L., Shandarin S.F., Suto Y., 1998, ApJ, 497, 38 Springel V., 2000, MNRAS, 312, 859 Springel V., Hernquist L. 2003, MNRAS, 339, 312 Springel V., White S.D.M., Tormen G., Kauffmann G. 2001a, MNRAS, 328, 726 Springel V., Yoshida N., White S.D.M. 2001b, New Astronomy, 6, 79 Steidel C.C., Giavalisco M., Pettini M., Dickinson M., Adelberger K.L., 1996, ApJL, 462, 17 Steidel C.C., Dickinson M., Meyer D.M., Adelberger K.L., Sembach K.R., 1997, ApJ, 480, 568 Steidel C.C., Adelberger K.L., Shapley A.E., Pettini M., Dickinson M., Giavalisco M., 2003, ApJ, in press Steinmetz M., 1996, MNRAS, 278, 1005 Stoehr F., 2003, PhD Thesis, Ludwig Maximilian Universit¨at, M¨ unchen Strickland D.K., Stevens I.R., 2000, MNRAS, 314, 511 Strickland D.K., Heckman T.M., Weaver K.A., Hoopes C.G., Dahlem M., 2002, ApJ, 568, 689 Sunyaev R.A., Zeldovich Y.B., 1970, Comments Astrophys. Space Phys., 2, 66 Sutherland R.S., Dopita M.A., 1993, ApJS, 88, 253 Thacker R.J., Scannapieco E., Davis M., 2002, ApJ, 581, 836 Thacker R.J., Tittley E.R., Pearce F.R., Couchman H.M.P., Thomas P.A., 2000, MNRAS, 319, 619 Theuns T., Schaye J., Zaroubi S., Kim T.–S., Tzanavaris P., Carswell B., 2002a, ApJ, 567, 103 Theuns T., Viel M., Kay S., Schaye J., Carswell R.F., Tzanavaris P. 2002c, ApJL, 578, 5

Bibliography

147

Theuns T., Bernardi M., Frieman J., Hewett P., Schaye J., Sheth R.K., Subbarao M., 2002d, ApJL, 574, 111 Theuns T., Mo H.J., Schaye J., 2001, MNRAS, 321, 450 Theuns T., Leonard A., Efstathiou G., Pearce F.R., Thomas P.A., 1998, MNRAS, 301, 478 Tonry J., Schmidt B.P., Barris B., Candia P., Challis P., Clocchiatti A., Coil A.V., Filippenko A.V., Garnavich P., Hogan C.J., Holland S.T., Jha S., Kirshner R.P., Krisciunas K., Leibundgut B., Li W., Matheson T., Phillips M.M., Riess A.G., Schommer R.A., Smith R.C., Sollerman J., Spyromilio J., Stubbs C., Suntzeff N.B., 2003, ApJ, in press Tormen G., Bouchet F.R., White S.D.M. 1997, MNRAS, 286, 865 Tytler D., O’Meara J.M., Suzuki N., Lubin D., 2000, Phys. Scripta T, 85, 12 van den Bosch F.C., 2000, ApJ, 530, 177 van den Bosch F.C., Mo H.J., Yang X., 2003, MNRAS, submitted Viel M., Matarrese S., Mo H.J., Theuns T., Haehnelt M.G., 2002, MNRAS, 336, 685 Vladilo G., 2002, ApJ, 569, 295 Weymann R.J., Jannuzi B.T., Lu L., Bahcall J.N., Bergeron J., Boksenberg A., Hartig G.F., Kirhakos S., Sargent W.L.W., Savage B.D., Schneider D.P., Turnshek D.A., Wolfe A.M., 1998, ApJ, 506, 1 White S.D.M., 1976, MNRAS, 177, 717 White S.D.M., Frenk C.S.,1991, ApJ, 379, 52 White S.D.M., Rees M.J., 1978, MNRAS, 183, 341 Wolfe A.M., Turnshek D.A., Smith H.E., Cohen R.D., 1986, ApJS, 61, 249 Wyithe S., Loeb A., 2003, ApJ, 586, 693 Xu G., 1995, ApJS, 98, 355 Xu Y., Tegmark M., de Oliveira–Costa A., 2002, Phys. Rev. D, 65, 83002 York D.G. et al. (The SDSS Collaboration), 2000, AJ, 120, 1579 Yoshida N., Sheth R.K., Diaferio A. 2001, MNRAS, 328, 669 Yoshida N., Sokasian A., Hernquist L., Springel V., 2003, ApJL, 591, 1

148

Bibliography

Yoshida N., Stoehr F., Springel V., White S.D.M., 2002, MNRAS, 335, 762 Zhang Y, Anninos P., Norman M.L., 1995, ApJL, 453, 57 Zhao D.H., Mo H.J., Jing Y.P., B¨orner G., 2003, MNRAS, 339, 12 Zeldovich Y.B., 1972, MNRAS, 160, 1 Zwicky F., 1937, ApJ, 86, 217

References 1. ESSENCE: http://www.ctio.noao.edu/essence/ 2. 2dFGRS: http://magnum.anu.edu.au/ TDFgg/ 3. SDSS: http://www.sdss.org 4. FUSE: http://fuse.pha.jhu.edu/ 5. ALMA: http://www.alma.nrao.edu 6. CHANDRA: http://chandra.harvard.edu/ 7. HST: http://www.stsci.edu/hst/ 8. SNAP: http://snap.lbl.gov/ 9. GOODS: http://www.stsci.edu/science/goods/ 10. WMAP: http://map.gsfc.nasa.gov/ 11. BOOMERanG: http://cmb.phys.cwru.edu/boomerang/ 12. MAXIMA: http://cosmology.berkeley.edu/group/cmb/index.html 13. FIRST: http://sundog.stsci.edu/top.html 14. ROSAT: http://wave.xray.mpe.mpg.de/rosat 15. MERSENNE TWISTER: http://www.math.keio.ac.jp/matumoto/emt.html 16. CBI: http://www.astro.caltech.edu/ tjp/CBI/ 17. MACHO: http://wwwmacho.mcmaster.ca/ 18. EROS: http://eros.in2p3.fr/ 19. UVES: http://www.eso.org/instruments/uves/ 20. HIRES: http://www2.keck.hawaii.edu/inst/hires/hires.html

150

References

21. KECK: http://www2.keck.hawaii.edu/ 22. VLT: http://www.eso.org/paranal/ 23. ACBAR: http://cosmology.berkeley.edu/group/swlh/acbar/ 24. MEGACAM: http://www.cfht.hawaii.edu/Instruments/Imaging/Megacam/ 25. ESO: http://www.eso.org/ 26. SUBARU: http://www.naoj.org/ 27. GADGET: http://www.mpa-garching.mpg.de/galform/gadget/index.shtml 28. VIRGO Consortium: http://www.virgo.dur.ac.uk/ 29. MBE: http://www.ssec.wisc.edu/baryons/index.html 30. JCMT: http://www.jach.hawaii.edu/JACpublic/JCMT 31. SCUBA: http://www.jach.hawaii.edu/JACpublic/JCMT/ Continuum observing/SCUBA/ 32. COBE: http://lambda.gsfc.nasa.gov/product/cobe/ 33. IRAS: http://irsa.ipac.caltech.edu/IRASdocs/iras.html 34. HYDRA: http://coho.mcmaster.ca/hydra/

Acknowledgements I would like to thank all the people that have made it possible for me to realise an old dream: becoming a cosmologist. Or at least getting closer to becoming one. That means a long list of people spanning a wide range of times, starting from my parents, who always supported all my choices, as crazy as they were (my choices, not my parents); my teacher Giancarla Marini; my math teacher Caterina Ghiringhelli, who used every trick she could imagine to convince me to attend classical studies before University; my teacher of Natural Sciences Marisa Maroso; my PhD advisor Antonaldo Diaferio. A special thanks to all my friends in MPA, who made my stay here look like a holiday, and in particular to Corina, who never let things rotten in my fridge and always prevented me from working too much; to Hans–Jakob, for not giving me the Pitch Fork and for an open window on real life; to Pere; to Patricia; and then to Claudia, Jens, Carlos, Jorge, Gabriella, Daniele, Roberto, Luigi, Alberto, Stefano, Anna, Lidia, Harry and Kees. Thanks to all my brave friends who happily joined me during holidays, trips, “concerts”, games, movies, snowboard and many other moments of my daily life. Many thanks to Simone, who is still buying my favourites comics, agaist every evidence that he would ever get any money back. And to Paola, for filling my e–mail box every day with all the crap she could collect on the web. I am infinitely gratefull to Felix for his patience in trying to heal my ignorance about computers and simulations and for some useful translations. My stay at MPA was sponsorised both by the European Association for Research in Astronomy (EARA) and by the European Research and Training Network “The Physics of the Intergalactic Medium”. I want to thank them again for having given me the great opportunity of living, shopping and doing research in Germany. Finally, a very special thanks to Simon D.M. White, for offering me the opportunity to develop my PhD project at the MPA and for anticipating Christmas in June.

Thanks to Harry Potter and the Order of the Phoenix for the exhilarating citations. At first I chose another novel as a source of inspiration, but I gave it up when I discovered I might as well have copied all the 300 pages of the book.