Black hole formation and growth with primordial non-Gaussianities 

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Black holes as a key component of galaxies

In this section, we will see that BHs are a key component of galaxies. Indeed most of the local galaxies host a massive BHs, including the Milky Way and some dwarf galaxies. The discovery of luminous quasars at z > 6, 15 years ago (Fan, 2001 ; Fan et al., 2003, 2006b), showed us that massive BHs were already in place at the end of reionization epoch.

Black holes as a key component for galaxy evolution

We have seen that BHs are an important ingredient of galaxies, in the local Universe, but also at high redshift, which is probed by the observation of quasars. The comoving density of quasars at high redshift (z ∼ 6) is 40 times smaller than the one at z ∼ 3 (Fan et al., 2006b), this (2002), and McConnell & Ma (2013) 10 years later.
suggests that we are actually tracing the initial rise of the BH evolution history, and with this the premise of their co-evolution with their host galaxies. We will describe in the next section, the empirical relations between BH masses and the properties of their host galaxies, which indicate this co-evolution. Powerful BHs are also thought to impact their galaxies, by means of several feedback mechanisms, that we describe in the second section.

Co-evolution between BHs and their host galaxies

Several empirical relations have been found between BHs and their host galaxies. First of all, the luminosity of the stellar component of the host galaxies (the entire galaxies or their bulges) correlates with the mass of their central massive BHs (Kormendy & Richstone, 1995). BH masses also correlate with the mass of their host galaxy bulge (Kormendy & Richstone, 1995 ; Magorrian et al., 1998 ; Ferrarese & Merritt, 2000 ; McLure & Dunlop, 2001 ; Marconi & Hunt, 2003), with the relation MBH ∝ 10−3 Mbulge. An even tighter empirical relation is derived between BH masses and the velocity dispersion of the spheroids (Gebhardt et al., 2000 ; Ferrarese & Merritt, 2000 ; Tremaine et al., 2002). We show in Fig 1.4, the BH mass – galaxy velocity dispersion of Tremaine et al. (2002) and the one derived by McConnell & Ma (2013) 10 years later. Coevolution between BHs and their host galaxies is still a hot topic in the field of galaxy evolution today. This is perceivable in the debate regarding the power of the relation between BH mass and the galaxy velocity dispersion, MBH ∝ σgalα with an incertitude on the power parameter α = 4 − 5. Finally, a possible relation between BH masses and dark matter halos has been proposed by Ferrarese (2002), whereas Kormendy & Bender (2011) disagree on this relation, and claim that BHs only correlate with bulge, and do not correlate directly with either dark matter halo or galactic disks.
BHs and their host galaxies are co-evolving, as indicated by the empirical correlations MBH − Mbulge, and the BH mass – galaxy velocity dispersion, and the debated BH – dark matter halo relation. BH growth must have been impacted by host galaxies properties, but BH evolution may also have influenced galaxy evolution as well, through what we call feedback processes. In the next section, we focus on the mechanism of BH feedback on the host galaxies.

AGN feedback

When gas is accreted onto a BH, there is a release of rest-mass accreted energy back to the galactic gas, which can impact the host galaxy by feedback processes (Silk & Rees, 1998). AGN feedback acts as an interaction between the energy, radiation produced by gas accretion onto the central BH, and the gas in the host galaxy. Theoretically, the energy released by the BH, can be sufficient to entirely unbind the gas of its host galaxy. If BH growth is dictated by accretion, the BH energy is expressed as EBH = ( /1 − )MBH c2, whereas the binding energy of the galaxy is expressed by Egal = Mgal σ2. The ratio between the energy released by the BH and the binding energy of the host galaxy is: EBH MBH ! c 2 = > 60 (1.28) Egal 1 − Mgal σ.
if we assume the radiative efficiency to be ∼ 0.1. If only a small fraction of the BH accretion energy was released as kinetic energy transferred to the gas, AGN feedback would be able to unbind the gas of the galaxy.
Three main mechanisms can alter the galaxy gas content through AGN feedback: radiation feedback, kinetic feedback, and the ejection of energetic particles. These mechanisms have been implemented and tested in both isolated and cosmological simulations, leading to both negative and positive feedback. In the following, we explain the different modes of AGN feedback, and how they have been implemented in numerical simulations. We then explain the positive and negative feedback effects, and review some studies which result in either one or the other aspects of AGN feedback, and their implications.

Theoretical models for black hole formation in the early Universe

Currently, three main models are popular to explain theoretically the formation of massive BH seeds in the early Universe (Rees, 1978, 1984): the PopIII remnants model, the compact stellar cluster model, and the direct collapse model.
These three models for BH formation rely on different physical processes, but the main idea is to form a massive BH out of a massive star. The mass of the star that forms out of the gas, is relied to the Jeans mass of the medium, that we can write as: MJ ≈ 700M T 3/2 n − 1/2 (1.50).
The composition of the gas, and so its temperature, sets the Jeans mass. For exemple, in minihalos of Mmini halo ≈ 105−6 M , where cooling is done by molecular hydrogen, the temperature of the gas goes below 104K (see left panel of Fig 1.7). If we assume T = 200 K, the Jeans mass is MJ ≈ 700 M . We will see that massive stars of the first generation are predicted to form in minihalos.
However, in atomic cooling halos of Mhalo ≈ 107−8 M , where the temperature can be T = 5000 K for example, the Jeans mass is much higher MJ ≈ 105 M , which can lead to the formation of an even more massive star, which may collapse into a direct collapse BH.
Finally if the gas is metal-enriched, cooling is more efficient. Indeed on Fig 1.7 right panel, we see that the cooling curve for metal-enriched gas is above the cooling curve for a primordial composition of the gas. In the presence of metals, the gas can also cool to lower temperatures. Molecules made of heavy elements are responsible for lowering the temperatures to a few K. Therefore the Jeans mass will be much lower. For example, for T = 10 K, the Jeans mass is around MJ ≈ 10 M . This is an intermediate model between the two previous ones, which is called stellar compact cluster model. A compact stellar cluster can form in the central region of proto-galaxies, stars are very close to each other, and can merge together to form a very massive star, that can collapse and form a massive BH.

Remnants of the first generation of stars

In the PopIII star remnants model, BHs are predicted to form in mini-halos (Mh ≈ 105 M ) with gas below a critical metallicity (Z < 10−3.5 Z , Bromm et al., 2001 ; Schneider et al., 2002) at redshift z = 30 − 20 from the remnants of the first generation of stars (PopIII stars, Carr, Bond & Arnett, 1984 ; Madau & Rees, 2001 ; Volonteri, Madau & Haardt, 2003). As we have said in Section 1.3, observational evidence on the initial mass function (IMF) of PopIII stars are lacking, but theoretical studies suggest that they could have masses in the range 10 − 1000 M (Bromm & Yoshida, 2011 ; Hirano et al., 2014). A massive star M? & 260 M can lead to the formation of a BH seed of ≈ 100 M (Fryer, Woosley & Heger, 2001), which retained at least half the mass of the star.

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Diagnostics to distinguish between BH formation scenarios

BHs form in the early Universe, out of any possible observation with current facilities. Investigat-ing the formation of BHs, therefore requires to derive observational diagnostics on the galaxies we can observe today, the local galaxies, in analogy with galactic archeology. Two theoretical diagnostics to distinguish between the different BH formation models, have been discussed in the literature (Volonteri, Lodato & Natarajan, 2008 ; Volonteri & Natarajan, 2009 ; van Wassenhove et al., 2010). The BHs we observe today, have grown over cosmic time from lower-mass BH seeds. Initial conditions are likely to be erased if accretion onto BHs is efficient. BHs grow by accretion and BH-BH mergers. Accretion onto a BH is boosted when galaxy-galaxy major mergers occur. Massive galaxies have a high probability that their central BH is not pristine anymore. The central BH may indeed have increased its mass through accretion, which is boosted by several major mergers of the host galaxy, but also BH-BH mergers and dynamical interactions. Clues on the BH initial mass are erased. However, low-mass galaxies, which have a much quieter cosmic evolution, host a BH today with a mass that is expected to only differ slightly from the initial BH seed mass. Therefore the mass of BHs in today’s low-mass galaxies can provide us crucial information on the initial BH mass distribution.
Accretion and mergers alter the initial mass of BHs. The presence of a BH or not within a galaxy is, however, not affected. The probability for a galaxy to host a BH, the BH occupation fraction, is therefore a sensitive clue on the efficiency of BH formation mechanisms at high redshift. Moreover, signatures in low-mass galaxies are even stronger (Volonteri, Lodato & Natarajan, 2008). This can help us to distinguish between BH formation models, as illustrated in Fig. 1.10 reproduced from Greene (2012). On the top, the two most popular scenarios to form BHs are reproduced. On the left, the direct collapse scenario is predicted to form BHs only in few massive halos, because of the many conditions required by the scenario. On the right, we see that many galaxies will host a PopIII remnants BH: conditions to form these BHs are less strict. Using semi-analytical models, associated with the extended Press-Schechter formalism, Volonteri, Lodato & Natarajan (2008) study comparisons of the BH mass – galaxy velocity relation for different seeding models, and show that the fraction of galaxies without BH increases with decreasing halo mass at z = 0. Moreover, while PopIII remnants scenario leads to populate nearly all z = 0 galaxies, the direct collapse scenario has a much smaller efficiency to establish BH in galaxies. van Wassenhove et al. (2010) use similar techniques to simulate specifically the evolution of BHs in satellite galaxies of a Milky Way size halo, and study the properties of BHs in satellites surviving until today. They seed the high redshift progenitor halos with BH seeds, formed through the PopIII remnants and direct collapse models. They find that the direct collapse BH population is present in only a few percent of dwarf galaxies, but that they are more massive, and could be detected more easily. Whereas the PopIII remnant BHs are more abundant in low-mass galaxies, but they are predicted to be difficult to observe because of their very low masses.
Finally, the idea of a plume emerges in Volonteri & Natarajan (2009). Stellar remnant-like scenarios predict the formation of light seeds (MBH,ini ∼ 100 M ), the direct collapse scenario, instead, predicts the formation of heavy seeds (MBH,ini ∼ 104−6 M ). As discussed earlier, crucial clues on BH formation can remain in low-mass present-day galaxies, BHs there are predicted to not have grown much over cosmic time. Therefore, if the direct collapse model was the predominant model of BH formation, we should detect in low-mass galaxies a threshold for the minimal mass of BHs, which would correspond to an asymptote, or a plume, in the BH mass – galaxy velocity dispersion diagram, when moving to lower galaxy velocity dispersions. Investigating this plume requires to have the resolution to detect large samples of low-mass galaxies, and to go to lower and lower galaxy mass, what we are starting to do (Reines, Greene & Geha, 2013).

Table of contents :

1 Introduction 
1.1 Brief historical introduction
1.2 Structure formation in a homogeneous Universe
1.2.1 The homogeneous Universe
1.2.2 Linear growth of perturbations and spherical collapse model
1.3 Formation of galaxies and first stars
1.4 Black holes as a key component of galaxies
1.4.1 BHs and AGN
1.4.2 Local galaxies
1.4.3 Population of quasars at z = 6
1.5 Black holes as a key component for galaxy evolution
1.5.1 Co-evolution between BHs and their host galaxies
1.5.2 AGN feedback
1.6 Black hole growth over cosmic time
1.7 Theoretical models for black hole formation in the early Universe
1.7.1 Remnants of the first generation of stars
1.7.2 Compact stellar clusters
1.7.3 Direct collapse of gas
1.7.4 Other models
1.8 Diagnostics to distinguish between BH formation scenarios
1.9 Organization of the thesis
2 Numerical simulation 
2.1 Ramses: a numerical code with adaptive mesh refinement
2.1.1 Adaptive mesh refinement
2.1.2 Initial conditions
2.1.3 Adaptive time-stepping
2.1.4 N-body solver
2.1.5 Hydrodynamical solver
2.2 Sub-grid physics to study galaxy formation and evolution
2.2.1 Radiative cooling and photoheating by UV background
2.2.2 Star formation
2.2.3 Equation-of-state
2.2.4 SN feedback and metal enrichment
2.2.5 BH formation
2.2.6 BH accretion
2.2.7 AGN feedback
2.3 Smoothed particle hydrodynamics code Gadget
3 Pop III remnants and stellar clusters 
3.1 Introduction
3.2 Simulation set up
3.3 Seeding cosmological simulations with BH seeds
3.3.1 Selecting BH formation regions
3.3.2 Computing BH initial masses
3.3.3 BH growth and AGN feedback
3.4 The influence of star formation and metallicity on BH formation
3.5 Black hole mass function and occupation fraction
3.6 Black hole growth regulated by efficient SN feedback
3.7 Comparisons with a sample of local galaxies, and Lyman-Break Analogs
3.8 Conclusions
3.9 Perspectives
3.9.1 BH growth in the delayed cooling SN feedback simulation
3.9.2 Need for further comparisons with observations, preparing future observational missions
4 Direct collapse model 
4.1 Introduction
4.2 Simulation set up
4.3 Method
4.4 Impact of SN feedback on metallicity and star formation
4.5 Number density of direct collapse regions in Chunky
4.6 Horizon-noAGN simulation: Can DC model explain z = 6 quasars?
4.7 Comparison between hydro. simulations and (semi-)analytical models
4.8 Conclusions
4.9 Perspectives: Applications of hybrid SAMs
5 Black hole formation and growth with primordial non-Gaussianities 
5.1 Introduction on primordial non-Gaussianities
5.1.1 Primordial bispectrum
5.1.2 Introduction of fNL parameter
5.1.3 Observational constraints, room for non-Gaussianities at small scales
5.1.4 Previous work, and the idea of running non-Gaussianities
5.2 Halo and galaxy mass functions
5.2.1 Numerical methods: from non-Gaussian N-body simulations to galaxy formation model
5.2.2 Predicted halo mass functions from theory
5.2.3 Results on halo and galaxy mass function
5.2.4 Conclusions
5.3 Reionization history of the Universe
5.3.1 Far-UV luminosity function and reionization models
5.3.2 Fraction of ionized volume of the Universe
5.3.3 Electron Thomson scattering optical depth
5.3.4 Conclusions
5.4 BH formation and growth with primordial non-Gaussianities
5.4.1 BHs formed through direct collapse
5.4.2 BHs formed from the remnants of the first generation of stars
5.4.3 BHs in the most massive halos at z = 6.5
5.4.4 Conclusions
6 Conclusions 
References

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