Key problems in the formation and evolution of massive black holes: a preparation to the era of gravitational wave astronomy.

In the current hierarchical structure formation paradigm small DM haloes are the building blocks of the observed structures. Inside them the gas falls by gravity to form the first stars (inside ~10^5-6 Msun DM haloes) and first proto-galaxies (inside ~10^7-8 Msun DM haloes) in a bottom-up way where the big objects are formed by mergers between the smaller ones. It is inside the so-called atomic cooling haloes (DM haloes with mass above ~5×10⁷ Msun) where we currently believe that the seeds for massive black holes (MBHs, masses of order ~10^4-6 Msun) were probably formed, grown mainly by gas accretion and eventually become the most luminous quasars we can observe today from the Earth (with masses as high as ~109 Msun).

As mentioned above, galaxies grow in mass mainly through mergers with other galaxies and therefore, mergers of galaxies (with their MBHs) is a basic ingredient in the current galaxy formation theory. Numerical simulations of BH seeds formation, their growth by accretion, and galaxy mergers with MBHs, have greatly improved in terms of resolution and physics included, however, several key physical processes are still unknown. Our work will focus on 3 fundamental questions, critical to understand key smaller scale processes in formation and evolution of MBHs. Namely: (1) How these seeds of MBHs are formed in the early Universe? (2) How they can grow to reach the billions of solar masses in less than 1 giga year? (3) How the MBH growth is triggered in observed major merger of galaxies?

To address these questions, we will perform Adaptive Mesh Refinement (AMR) simulations of different astrophysical environments: i) cosmological simulations of the gas inside DM haloes of ~108 Msun at redshift z=10; ii) cosmological simulations of 1011-12 Msun DM haloes at z~6; and iii) hydrodynamic simulations of galaxy mergers specially designed to match observed systems. All these experiments will include the state-of-art physical ingredients in numerical simulations. The aim is to conduct a comprehensive study of high-resolution simulations of MBH evolution under different conditions using the RAMSES code. The idea is to determine how important is the fragmentation process in the formation of MBH seeds at high redshift, how the most luminous quasars were formed in the early Universe and which physical processes trigger the MBH growth by gas accretion in galaxy mergers. To successfully perform this study, we assembled a team leaded by the PI of the proposal, the CoI and graduate students.

To advance in our understanding of these three questions, will be important steps in the understanding of the formation and evolution of MBHs. In addition, this project is on an excellent timing, a decade before the launching of eLISA mission that will detect gravitational waves from MBHs sources, directly mapping the gravitational universe up to high redshift, leading to definite constrains in the formation and evolution of MBHs.

Dark matter (DM) haloes are the building blocks of the universe and inside them the first galaxies were formed. To have a predictable theory of galaxy formation, starting from the primordial perturbations, is one of the major goals of cosmology. Modern ideas of galaxy formation are based in the standard Cold Dark Matter (CDM) cosmological structure formation paradigm. In the hierarchical structure formation theory, the first proto-galaxies were born from gravitational collapse of gas inside ~108 Msun DM haloes at high redshifts (~500 million years after the Big Bang; e.g. Greif et al. 2008, 2010; Bromm et al., 2009) and then continued to grow in mass through mergers with other galaxies, and smooth filamentary accretion (e.g. Dekel et al., 2009; Anglés-Alcázar et al. 2016).

Observationally, there is a strong correlation between the mass of a central Massive Black Hole (MBH) and properties of the host galaxy such as velocity dispersion (Ferrarese & Merritt, 2000; Gebhardt et al., 2000), stellar mass in the spheroidal component (Marconi & Hunt, 2003) and total baryonic plus DM mass (Bandara et al. 2009). This suggest a connection between the formation of the central MBH and the galaxy that hosts it, which has been widely suggested to be due to a critical role of feedback from the MBH, in the regulation of star formation (SF) (see for example Hopkins et al. 2006 and Volonteri et al. 2016). However, it is quite difficult to establish the exact physical connection, because the processes of black hole accretion and star formation through the host galaxy, have very different spatial scales.

In this cosmological context, our current understanding favours that the seeds of the first massive black holes were formed inside DM haloes with masses above ~5×107 Msun , the so-called atomic cooling haloes (ACH; Loeb & Rasio 1994; Oh & Haiman 2002; Lodato & Natarajan 2006; Begelman et al. 2006, Begelman et al. 2008). In these systems, warm and low angular momentum (AM) gas could favour the formation of 104-6 Msun SMBHs seeds (Agarwal et al. 2012; Latif et al. 2013, 2014a,b) which will become the predesors of the luminous quasars that appeared before the first giga-year of our Universe (Fan et al. 2001; Willott 2007; Mortlock et al. 2011; De Rosa et al. 2014).

The observed joint cosmic evolution of MBH and galaxies motivates to include the evolution of MBHs in hierarchical galaxy formation theory. Using numerical simulations (e.g. Di Matteo et. al. 2003; Hopkins et al., 2006; Dubois et al. 2016; Volonteri et al. 2016; Feng et al. 2016) is possible to follow the hierarchycal growth from early times until the present in a Lambda-CDM cosmology. Using simple recipes for the evolution of MBH binaries and for the growth of MBHs, they are able to reproduce and predict several observables, such as the luminosity function of optically selected quasars in the redshift range 0 < z < 6. This kind of studies show that mergers of galaxies with massive black holes, are basic ingredients in this hierarchical theory and processes within them, are crucial for galaxy formation.

In a non-cosmological context, galactic scales simulations have reached enough resolution to study the gas fragmentation of inter-stellar medium (ISM) and to follow the formation and destruction of giants molecular clouds (GMCs) in both isolated galaxies (Tasker & Bryan 2006; Robertson & Kravtsov 2008; Gnedin & Kravtsov 2010; Becerra & Escala 2014) and in galaxy mergers (Bournaud et al. 2008; Saitoh et al. 2009; Teyssier et al. 2010; Matsui et al. 2012; Hopkins et. al 2013; Chapon et al. 2013; Perret et al. 2014; Renaud et al. 2015). Moreover, advances in resolution have allowed the study of AGN occurrence in galaxy mergers (Blecha et al 2013, Van Wassenhove et al. 2012; Volonteri et al. 2015; Gabor et al. 2016). Despite these advances in the understanding of formation and evolution of MBHs, leading to an overall coherent picture within Lambda-CDM cosmology, it remains open a set of key unsolved problems on small scales. To solve them is a crucial part of the roadmap for the future gravitational wave astronomy that started by the recent first LIGO detection (Abbott et al. 2016) and with the future eLISA mission (Amaro-Seoane et a. 2013). Such experiments will revolutionize our vision of the formation and evolution of MBHs.
Within the problems needed to be understood before eLISA, are the following: is the effect of gas fragmentation on the formation of the first seeds of SMBHs: does the fragmentation stop their growth? What processes are involved in the very fast growth of redshift ~6 quasars? Are they accreting at below, near or at super-Eddington rates? In either case, what is the effect of the radiation emitted from the MBH vicinity on the surrounding media? What trigger the AGN activity in galaxy merger? Besides the works of Teyssier et al. (2010) and Renaud et al. (2015) about the Antenae merging system (without actives MBHs) there are not studies about the light-up of MBHs based on observed systems. Below we describe the three specific goals of this proposal that are crucial for the understanding of the smaller scale physics in MBH evolution, in no particular order.

Objective 1: How the first seed of MBHs were formed in our universe? Are these seeds affected by the gas fragmentation around them?

The observation of very luminous quasars above redshift z~6 (Fan et al. 2001; Willot 2007; Mortlock et al. 2011; De Rosa et al. 2014) arises the question about the origin of such objects. Different studies favor the scenario where they are the manifestation of MBHs formed from very massive seeds of order ~104-6 Msun at z~10 (Lodato & Natarajan 2006; Volonteri et al. 2008; Tanaka & Haiman 2009). In this context, models of unstable super massive quasi-stars can produce MBH seeds of order ~104-6 Msun inside ACH (Loeb & Rasio 1994; Oh & Haiman 2002; Lodato & Natarajan 2006; Begelman et al. 2006, Begelman et al. 2008): a model of MBH formation by direct collapse. The gravitational waves emitted in the final collapse of such super massive quasi-stars onto a MBH will be detectable by eLISA (Shibata et. al 2016 and references therein), directly testing this direct collapse model.

However, the model presented above requires some special conditions to end up with the desired MBH seed, namely the gas should develop a fast mass accretion rate above ~0.1 Msun/yr (Begelman 2010; Hosokawa et al. 2013; Schleicher 2013; Ferrara et al. 2014; Latif & Volonteri 2015); it should efficiently redistribute the gas AM (Choi et al. 2015) and the primordial gas should be warm ~104 K in order to have a large Jeans mass and thus avoid fragmentation, this maximize the available accreted mass onto the central region (e.g. Omukai 2001; Bromm & Loeb 2003; Shang et al. 2010; Johnson et al. 2013).

The non-fragmentation condition is the most restrictive assumption of this model and as mentioned above, it has been claimed as a necessary condition to form MBHs seeds. Despite of that, there are some studies showing that the gas fragmentation around a central massive object does not stop its mass accretion rate significantly (Escala 2007; Inayoshi & Haiman 2014) and furthermore, migration of fragments could help the growth of the central object (Ceverino et al. 2010) even in the presence of strong SNe and AGN feedback (Prieto & Escala 2016, Prieto, Escala et al. 2017). Such findings open a window to study these systems relaxing the assumption of warm ~104 K primordial gas.

Our plan is to perform state-of-art MBH seeds formation and evolution simulations using the Adaptive Mesh Refinement technique (AMR; RAMSES code, Teyssier 2002) as part of the degree work of the U. Chile graduate student Matias Suazo. This set of simulations will include non-equilibrium thermo-chemistry and an external uniform UV radiation background with variable intensity. We will include these physical ingredients using the KROME package (Grassi et al. 2014; being the CoI one of the co-authors). This package allows us to include non-equilibrium thermo-chemical processes in 3D cosmological-hydrodynamic simulations in order to follow in a more realistic way the chemo-thermal evolution of the baryonic component in any desired system. Our aim will be to follow the gas dynamics inside a ~5×107 Msun DM halo at redshift ~10 under different UV radiation conditions. As mentioned above, one of the conditions to create MBH seeds is to keep the primordial gas warm (T~104 K), this can only be done by suppressing the molecular H abundances in such primordial environment. Depending on the Lyman-Werner UV radiation (and IR radiation) field strength, the amount of hydrogen molecules will vary inside those haloes. We will study how the gas fragmentation, triggered by a low UV radiation field, alters the MBH seeds mass accretion rate as in Latif et al. (2016,2014a,b), but following its evolution for several dynamical times using the sink particle technique and for a higher number of haloes. Then we could know if the gas fragmentation stopped (or not) the MBH growth process in its early evolutionary stages, as is generally assumed. Besides the external radiation field variations, in this study we will take into account different spin parameter for the DM haloes in order quantify its effect on the sink’s mass accretion rate (see Prieto et al. 2015; González et al. 2017; Di Matteo et al. 2017).

Objective 2: How the biggest MBHs were fed inside the galaxies in the first billion of years of our universe?

Observation of very bright quasars at z~6 with luminosity above ~1013 Lsun (Fan et al. 2001; Willot 2007; Mortlock et al. 2011; De Rosa et al. 2014) suggests the existence of MBHs with masses of the order of ~109 Msun when the Universe was about 1 Gyr. To understand how these objects reached such high masses already at z~6-7 is one of the remaining challenges in astrophysical research.

Recent big volume (~ few 100 Mpc of box side) cosmological simulations (Schaye et al. 2015; Sijacki et al. 2015; Dubois et al. 2016 and Feng et al. 2016) have reached the not negligible resolution (in relation with the simulated box volume) of < kpc to few 100pc scale to study the galaxy formation process from cosmological scales to galactic scales including gas, stars and MBH physics. After a calibration procedure, such simulations are able to reproduce statistical features (at least at lower redshifts), like MBH -σbulge relation, galaxies luminosity functions and MBH mass function. Despite of these notable results, this kind of simulations lack of the appropriate resolution (sub-pc scales) to resolve the internal dynamical processes governing the mass transport and angular momentum re-distribution in high redshift galaxies.

Beside the large volume simulations, there is another group of numerical experiments focused in individual objects instead of a whole population of objects and these are the zoom-in cosmological simulations (e.g. Abel et al. 2002; Greif et al. 2008). From cosmological initial conditions, Dubois et al. (2015) studied the evolution of a galaxy with a central MBH inside a ~1012 Msun DM halo at redshift ~2. They found that super novae (SNe) reduced the BH mass accretion rate with mergers boosting the BH growth. Despite of that, they did not explore in detail the nature of the processes involved in the mass transport in the galactic disc.

In Prieto & Escala (2016), was explored the effect of SNe feedback on the mass transport in galactic discs and its consequences on the central MBH growth. We focused on a relatively small DM halo of ~1010 Msun at redshift ~6. It was found that the gas can flow from the edge of the galaxy to the BH vicinity due to the combined effect of channelized filamentary large-scale accretion, and gravitational and pressure gradients torques acting in the galactic disc. In these relatively small systems, the mass accretion rate in the disc associated to mergers and smooth accretion through filaments can reach the ~1 Msun/yr but it is dramatically reduced in the BH vicinity due to the effect of SNe explosions. The previous work was extended in Prieto, Escala et al. (2017), by including the effect of BH feedback in the same galaxy. They confirmed the interplay between filamentary accretion, pressure gradients and gravity torques as mechanisms to transport matter in the galactic disc, and they also found a merger – BH mass boost relation as in Dubois et al (2015). Furthermore, their cosmological simulations showed that the combined effect of SNe and AGN feedback is very efficient quenching the BH growth in these small high redshift galaxies.

Our plan is to extend the previous work of the PI and CoI in the field of MBHs growth in redshift ~6 galaxies, by performing high-resolution cosmological-hydrodynamic simulations with the RAMSES code. In Prieto & Escala (2016) and Prieto, Escala et al. (2017) the authors explore the dynamical evolution of a relatively small system of ~1010 Msun in DM. It is know that the biggest BH at z~6 associated with the most luminous observed quasars are in the center of the most massive halos at such redshift: ~1012 Msun DM halo (e.g. Dubois et al. 2013a,b). This is a clear motivation to study more massive systems with un-precedent high spatial resolution (below pc scales) and try to answer the questions: what processes are involved in the mass transport in high redshift massive galaxies? How the angular momentum is redistributed in such objects? Do the MBH need to accrete at super-Eddington rates to explain the presence of the most luminous quasars at redshift above 6? These kinds of questions can be addressed performing simulations including different AGN feedback recipes. Furthermore, these experiments will be complemented with smaller scale radiative hydro-dynamical simulations to explore in a more realistic way the effect of AGN feedback on the MBH growth at high redshift. This smaller scale simulation will be performed with the radiative transfer module of the RAMSES code: RAMSES-rt (Rosdahl et al, 2013).

Objective 3: What are the mechanisms associated with light up of active galactic nucleus in observed galaxy mergers?

Galaxy mergers are believed to be not just common events in the universe, but also fundamental pieces in the evolution of galaxies since they trigger bursts of star formation (Larson & Tinsley 1978, Sanders & Mirabel 1996) and they are a key ingredient in the formation Elliptical Galaxies and Bulges (Toomre & Toomre 1972, Mihos & Hernquist 1996; Kazantzidis et al. 2005; Di Matteo et al. 2007).

The triggering of active galactic nuclei (AGN) in galaxy mergers is crucial for our understanding about the MBHs growth. In fact, it is believed that a merger of galaxies is one of the main mechanisms to activate black hole growth by gas accretion and the last phase of mergers, it has been suggested to be associated to quasar activity (Stockton 1982; Sanders et al. 1988; Alexander & Hickox 2012). Therefore, it is critical in our understanding of the growth of MBHs to determine the physical mechanisms that trigger the gas inflow from large scales towards the vicinity of the MBHs. Moreover, since it is believed that feedback from AGNs can play a critical role in the regulation of star formation (Hopkins et al. 2006; Menci et al., 2006, Croton et al., 2006; Hopkins & Quataert 2010; Thacker et al. 2014; Esquej et al. 2014; Volonteri et al. 2015; Gabor et al. 2015), a good understanding of AGN triggering is also critical for our understanding of galaxy formation.

Despite the efforts already done to study the MBHs evolution in galaxy mergers (e.g. del Valle & Escala 2015, 2016; Volonteri et al. 2015; Gabor et al. 2015), it is notable that only few of these simulations have been based on observed systems. The work of Teyssier et al. (2010) and Renaud et al. (2015) are examples of these kind of simulations. Their experiments were based on observations of the Antenae galaxy merger and include realistic baryonic physics but without MBHs. The lack of such studies is likely due to the difficulties getting the orbital parameters of observed systems. In a recent work Privon et al. (2013) –the first author is a collaborator in this project- have developed a tool to get accurate orbital parameters of galaxy mergers based on their tidal features: Identikit. Using Identikit, now it is possible to get fast and reliable orbital parameter in dozens of observed galaxy mergers and use it in more complex and realistic hydro-dynamical numerical simulations that also include MBH physics. Due to the complexity of these full hydro-simulations, to use them directly to determine the orbital parameters would take prohibitory numbers of cpu-hours, for that reason is needed to complement them with Identikit or another equivalent software.

In order to study the physical processes that trigger AGN activity, we will perform simulations of galaxy mergers with the RAMSES code, which allow us to theoretically constrain the presence of AGN at different stages of merging for real systems. Current computational facilities allows to perform galaxy mergers simulations that can resolve down to scales comparable to the MBH’s influence radius (Rinf ~ 1 – 50 pc; Mayer, Kazantzidis, Escala & Callegari 2010, Hopkins & Quataert 2010, Chapon et al. 2011, Gabor 2015), which is the resolution needed to study how gas at large scales flows down to where the black hole dominates the local dynamics (the BH’s influence radius). Coupling these kinds of simulations with the initial conditions obtained with Identikit (Privon et al. 2013) it will be possible to study real merging systems using the state-of-art numerical simulations. We already have experience coupling these two codes (RAMSES + Identikit) to explore the dynamic of the merging system NGC 2623, with successful results.

Our main focus, compared with the previous works, will be to study the global torques onto the gas that is responsible for the mass inflows from large scales to the vicinity of the MBHs. Analysis like that have been applied by Prieto & Escala (2016) and Prieto, Escala, et al. (2017) in a cosmological context. Our plan is to correlate peaks of large-scale inflows with the orbital evolution of the galaxy merger. Also, since we will include physically motivated prescriptions for feedback processes from SNe and MBH accretion, we will also study the effect of feedback on the in-falling material onto the MBH and the (possible) temporary fueling shutoff, by its own feedback.

Our simulations will be contrasted directly against multi-wavelength observations (Chandra, NuSTAR, ALMA), because our collaborators (George Privon and Ezequiel Treister at Pontificia Universidad Católica de Chile) perform systematic multi-wavelength study of dual AGN. The team is in a privileged position to lead these studies, because Chilean astronomers have the largest fraction of ALMA time per capita in the world. Since the hydro calculations can be directly contrasted against ALMA data, our simulations will be the perfect match to these observations that will effectively constrain models and be able to readily interpret the observational results.

Our approach of combining both simulations and observations will set direct constrains on the fueling processes onto dual AGNs, their characteristic growth and final MBHs masses. In addition, it will give direct constraint on the torques suffered by the MBHs, since in this kind of systems those torques are dominated by the gaseous component (Escala et al 2004, 2005; Dotti et al 2006; del Valle & Escala 2015, 2016). Therefore, it will give a better understanding on the characteristic migration and (possible) coalescence timescales for MBHs in galaxy mergers. To accurately determine both the characteristic coalescence timescale and final (pre-merger) MBHs masses, are crucial for the expectations in the future eLISA mission, since binary MBHs mergers are one of their main targets that will be observable by eLISA up to z~20, if they exist (Amaro-Seoane et a. 2013).

In summary, to advance in our understanding of these three objectives, will be important steps in the understanding of the formation and evolution of MBHs. To determine the typical seed masses (objective 1), how much MBHs can grow in the early universe (objective 2) and in their final stages before merging (objective 3), will have direct predictions that will be testable by eLISA. For that reason, this project is also on an excellent timing, a decade before the launching of the eLISA mission that will directly map the gravitational universe up to high redshift, leading to definite constrains in the formation and evolution of MBHs.

HYPOTHESES:

Objective 1:

How the seeds of the first massive black holes (MBHs) were formed at redshift z~10 in our universe?

How does the primordial gas fragmentation affect the mass of the first MBH seeds in the early universe?

Objective 2:

How the biggest massive black holes were fed inside proto-galaxies to create the extremely luminous observed quasars above z~6?

Objective 3:

What are the mechanisms associated with the light up of active galactic nucleus in observed galaxy mergers?

GOALS:

Objective 1:

Determine how the primordial gas fragmentation around the seeds of the first MBHs affects their growth rate.

Determine how this process depends on the intensity of the external UV radiation background.

Objective 2:

Determine the different processes that affect the growth of the MBHs in the early Universe.

Determine how fast the MBHs can accrete the surrounding gas above redshift z~6 and how this process depend on the injected energy by the MBHs.

Objective 3:

Based on constrains from observations, determine theoretically when during a galaxy merger it is expected the peak of AGN activity and MBH growth.

Determine the future evolutionary stages of observed galaxy mergers in terms of star formation rate, MBHs growth rate and MBHs migration timescales.

METHODOLOGY

Due to the inherent three-dimensional (3D) nature of most astrophysical phenomena, the large dynamical range involved in the problems we want to study and the different physical processes associated to the multi-phase ISM, cosmological-hydrodynamic simulations in 3D are the best approach to get insights about the questions we want to answer. Fortunately, in the last two decades appeared a number of codes designed to study 3D astrophysical systems using different numerical algorithms (e.g. ART, Kravtsov 1997; ENZO, Bryan et al. 2014; RAMSES, Teyssier 2002; GADGET, Sringel et al. 2001, 2005; AREPO, Springel 2010; GASOLINE, Wadsley, Stadel & Quinn 2004, among others).
In this project, we will work with the widely used and tested N-body adaptive mesh refinement (AMR) code RAMSES: this code has been written to study hydrodynamic and cosmological structure formation with high spatial resolution using the AMR technique, with a tree-based data structure. The AMR approach is suitable for systems with a large dynamical range where huge volumes have low mass density and interesting small volumes concentrate most of the matter as in a galaxy merger or in cosmological simulations. The AMR technique resolves the interesting regions with high spatial resolution whereas the less-interesting low-density regions keep a low level of refinement, saving computational time. The code solves the Euler equations with a gravitational term in an expanding universe using the second-order Godunov method (Piecewise Linear Method). Although there are several codes to study cosmological-hydrodynamic systems that could be used to carry out these investigations, the election of this particular code is based on the previous experience of the authors running RAMSES for different scientific purposes.

Regarding the initial conditions (ICs) for cosmological simulations. Our objective 1 and 2 will need the creation of cosmological ICs to study the MBH seeds formation and the growth process of the high redshift MBHs. For this two projects, we will use the MUSIC code (Hahn & Abel, 2011). This code allows us to create a Gaussian matter density field using the Planck results (Planck Collaboration, 2014) for the cosmological parameters. The code creates ICs for different cosmological box sizes at a given initial redshift and it can create ICs to run zoom-in experiments and study individual objects, suitable for our purposes.

Regarding objective 1. The first step is to generate ICs inside a box of 1 Mpc side, enough to find a few interesting DM haloes at the required final redshift, using the MUSIC code. Those ICs will be the starting point for a number of DM-only simulations to select one DM halo of ~5×107 Msun at z~10, i.e. an ACH. After selecting the halo of interest, we will re-center the ICs in the halo position at z~10 to use the re-centered ICs as our starting point for the high resolution cosmological-hydrodynamic simulation, including all the needed gas physics.

In this kind of simulations is crucial to follow the chemo-thermal evolution of primordial gas. We will be able to compute the changes in abundances of a gas composed by H, He, molecular H and their ions. Furthermore, we will be able to study the effect of an external uniform UV radiation field on the components of this gas, i.e. photo-ionization, photo-dissociation, etc. The KROME package (Grassi et al. 2014; with the CoI part of the co-authors) is a non-equilibrium chemo-thermal code which with a given initial chemical composition, temperature and density is able to compute the new temperature and new chemical composition after a given time interval inside a gas element. The CoI has included (and successfully tested, see Grassi et al. 2014) the non-equilibrium chemo-thermal evolution to the RAMSES code in order to work in primordial environments, suitable for our purpose.

Because we are interested in following the MBH seed formation and evolution inside ACHs it is crucial to model the massive object properly. In order to do that we will include sink particles to model their creation and growth in time. Due to the inherent resolution limitations in hydrodynamic simulations, when it is not possible to follow the gas evolution in the highest resolution regions it is useful to include non-zero mass particles which are able to accrete matter around them and if desired, can inject energy to the media: the so-called sink particles. Bleuler & Teyssier (2014) developed a new algorithm to form sink particles in hydrodynamic simulations, they have included this method to the RAMSES code and then it is possible to follow the MBH formation and its evolution in our cosmological simulations. The expected limit resolution is below ~0.01 pc ~ 2000 AU and we will follow the particles for several dynamical times in order to improve on previous works (e.g. Latif & Volonteri 2015).

The main goal of this numerical experiment will be to study how important is the fragmentation process on the MBH seed formation: is the primordial gas fragmentation stopping the MBH growth process? Starting from cosmological conditions, we will follow the behavior of primordial gas (including H molecule) inside an ACH until z~10. We will set different UV (Lyman-Werner band: 11.2-13.6 eV) and IR (energy band ~1-2 eV) background intensities in order to gradually dissociate the molecular H and detach H-, and then quantify how fast is the MBH growth under these different radiation conditions (such radiation background could came from low or high mass primordial stars). Based on recent results showing that the environment of DM haloes is connected with their spin and related to the BH mass accretion rate (e.g. Prieto et al. 2015; González et al. 2017; Di Matteo et al. 2017) we will study the evolution of haloes with different spin parameter to quantify its effect on the SMBH formation and evolution. The full treatment of this problem should include an on-the-fly radiative transfer computation (to model the super-star stage needed for the SMBH seed formation) and to solve the MHD equations (to study the gas cloud collapse and the evolution of the accretion disk around the sink). However, such approach is beyond the scope of this proposal due to its extremely high computational price. Despite of that, the project proposed here will contribute notoriously to our current understanding of the problem.

Regarding objective 2. As in the first step of objective 1 we will use the MUSIC code to create our ICs. However, due to the different size of our interesting DM haloes we will use different box sizes. We will create two sets of ICs. One inside a 20 Mpc box side to look for a DM halo of ~1011 Msun at z~6, and other inside a 40 Mpc box side to look for ~1012 Msun at the same redshift. Such ICs will allow us to study the MBH growth with un-precedent high resolution below the ~pc scales.

The RAMSES code has a number of sub-routines to include sub-grid gas physics. The code creates stellar populations at a given density threshold with a given efficiency, suitable to study the galaxy formation process. Through the stellar lifetime, the stars inject energy and momentum to the surrounding gas to model the stellar feedback in the galaxy. A fraction of these stellar populations will explode as SNe, after a given time injecting energy (which heat up the gas) and new chemical elements to the ISM (which will accelerate the cooling process in the media). Furthermore, as mentioned above the code can include sink particles to model MBH formation and evolution in the center of galaxies. The MBH can accrete matter (following different accretion models) and it also can inject energy to the ISM media mimicking the effect of MBHs feedback in high redshift galaxies.

Following Prieto & Escala (2016) and Prieto, Escala et al. (2017), the idea is to study all different processes involved in the mass transport in these high redshift massive galaxies. The mass transport will be studied from large scales associated to the DM filamentary structure around the DM haloes to the galactic scales on the disc. This analysis at different scales will allow us to associate the mass transport with the mass accretion rate onto the MBH. In particular, we will be able to resolve how gas clumps, formed by gravitational instabilities, can migrate from the galactic disc to the BH vicinity and feed the central massive object. Furthermore, we will study how the super-Eddington accretion affect the MBH evolution in order to elucidate if such a high accretion rate is necessary to create the high redshift quasars. The inclusion of the mentioned physical ingredients will allow us to study why and how the SMBHs observed above z~6 grew so fast in the first billion of year of history in our Universe.

The final and ambitious goal in this topic will be to run fully 3D radiative-transfer cosmological hydrodynamic simulations. Rosdahl et al. (2013) have developed the radiative transfer version of the RAMSES code: RAMSES-RT. This code solves the radiative transfer equations using moments method, i.e. instead of to follow photon beams, this method averages the photons crossing a given surface treating them as a “fluid” of photons. This method is called flux limited diffusion (FLD) approximation. The code can discretize the frequency of photons to study the effect of sources with different spectra energy distributions on the ISM. Using the same ICs obtained for the experiments presented above, we will explore the mass transport process in high redshift massive galaxies including stellar radiation and observationally motivated quasars spectra.

Regarding objective 3. Besides the cosmological environment in the RAMSES code, it is also possible to run hydrodynamic simulations of galaxy mergers. In these kinds of simulations, it is possible to include all the physical ingredients mentioned in the above lines, i.e. star formation, stellar feedback, SNe energy-chemical feedback, MBH formation and MBH feedback.

As mentioned in previous lines, Privon et al (2013) developed the Identikit code. This code can find the most likely orbital parameters of an observed merger based on their large-scale tidal features. These orbital parameters can be given to the ZENO package (freely provided by Joshua Barnes, see the bibliography) and run simple and fast N-body simulations including DM, gas and stars particles. Such approach allows us to get a series of snapshots of the merger process at different times, i.e. particle positions and particle velocities for our 3 particle types. Finally, one of these snapshots will be used as the starting point of our high-resolution AMR simulation with the RAMSES code, ensuring that the large-scale tidal features will be reproduced at the observed time.

The idea is to study the processes that trigger the AGN activity based on constrains from observed systems. For this purpose, we will run merger simulations based on observed systems at very high resolution, below ~pc scales. We will compute the torques acting on the gas component of the systems at each time step to follow its evolution (as already done in Prieto & Escala, 2016, for instance). Furthermore, we will compute the mass transport at different distances from the MBHs to investigate the torques-mass transport relation throughout the merger process as a function of the MBHs distance. Because we will include MBH feedback in our simulations, such an approach will allow us to quantify the MBH activity as a function of the merger stages and will be possible to correlate the star formation rate (SFR) with the MBH feedback activity.

The simulations described above are numerically very expensive in terms of CPU hours and the considerable amount of data output requires considerable RAM memory. We will run our simulations in the Leftraru cluster at the Centro de Modelamiento Matematico (CMM) at Universidad de Chile. This cluster has 2640 cores in 132 nodes. The analysis of our data will be done in the Geryon2 cluster at Universidad Catolica (PUC) that is shared by the whole astronomy community in Chile. The machine hosted at PUC, has 752 cores in 18 nodes. Our team has access to these computational resources, being used periodically.

Some of the simulations proposed in this project, require very long runs of approximately several months. These very long runs are complex to be performed in the shared clusters described above (have time limits of the order of a month) and for that reason, is required the improved (~ several hundred of cores) exclusive access cluster that we expect to be funded by this proposal. Only with access to these clusters, that are the fastest machines in the country, this project will be realizable within the four years of duration.

PRIOR WORK IN THE SUBJECT

Both the PI and CoI of this proposal have extensive previous experience in cosmological-hydrodynamic simulations, on problems that study the formation and evolution of the first black holes and the dynamics of massive black holes in merger of galaxies. Problems previously studied include gas-induced mergers of MBHs in galactic nuclei (Escala et al 2004, 2005), galactic-scale gas fueling onto MBHs (Escala 2006, 2007), MBH formation in galaxy mergers (Mayer, Kazantzidis, Escala & Callegari 2010), relativistic effects on the tidal disruption of a star by a MBH (Dai, Escala & Coppi 2013), the formation of the most massive stellar clusters (Escala & Larson 2008), gas fragmentation in galaxy mergers (Escala et al. 2013), the effect on gas cooling in the first proto-galaxies mergers (Prieto et al 2012, 2014), environmental-angular momentum connection in the first galaxies (Prieto et al. 2015), the environmental conditions to form MBHs (Prieto et al 2013) and the SNe-AGN effect on the growth of first MBHs in the first proto-galaxies (Prieto & Escala 2016; Prieto, Escala et al. 2017).

In a cosmological context, Prieto et al. (2013) simulated the gas in-fall from large scales onto the central region of a number of atomic cooling haloes (with DM haloes with masses above ~5×107 Msun) showing that it is likely that the most MBHs seeds were formed inside knots of the cosmic web, i.e. in isolated symmetric over-densities surrounded by a number of filaments were the gas angular momentum is canceled in the central galactic regions (Prieto et al. 2015). The top left figure below shows the DM structure in the position of a MBH seed. These kinds of objects are modeled as H-He systems where the only coolants are the atomic lines transition. We can perform this kind of modeling due to the chemo-thermal code KROME (Grassi et al. 2014).

In a more recent research, Prieto & Escala (2016) and Prieto, Escala et al. (2017) have shown how important are the channelized gas inflows and the gravitational and pressure gradients torques in the MBH’s growth inside small galaxies at redshift ~6. These two processes work together to move material from the external galaxy edge to the BH vicinity allowing an efficient BH growth. The top right figure below shows the gas distribution of our galaxy at z=6. These kinds of galaxies are not the host of the most massive BHs in the universe but their conditions give us some clues about the processes working in the most massive galaxies at the same redshift.

Recently, we have studied the interaction of a MBH binary with a circum-binary disk (del Valle & Escala 2012, 2014), focused on the torques that the binary produces on the disk and if it can drive the formation of a gap on it (if the opening timescale is shorter than the closing one). Using SPH simulations (see the bottom left figure) we showed that the formation of a gap in the disk depends on two parameters: i) the ratio between the disk’s scale height and the binary separation ii) the mass ratio between the mass enclosed by the orbit of the binary and the mass of the binary. Using this criterion, we were able to found for comparable mass binaries, an analogous behavior between the close (open) gap simulations and the fast Type I (slow Type II) migration that is observed in simulations of planet-disk interaction (binaries with extreme mass ratios). We tested the ubiquity of those gaps applying the criterion in gas-rich galaxy mergers simulations (del Valle & Escala 2015, 2016), finding that its occurrence is unlikely (see the bottom right figure). Therefore, the MBHs in gas-rich galaxy mergers are likely to have a fast migration and coalescence, being possible sources for the future eLiSA mission.

AVAILABLE RESOURCES:

The following resources are available for this proposal, provided by our host institution:

-) Internet access.

-) Journal subscriptions for most relevant journals in Astrophysics: ApJ, AJ, MNRAS, A&A, Nature, Science, etc.

-) Office space.

-) Power and refrigeration of the HPC cluster.

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