Dark Matter Halo Merger Trees Research Articles

Super-Eddington accretion in high-redshift black holes and the emergence of jetted AGN

Abstract In this work we study the co-evolution of central black holes (BHs) and host galaxies by utilizing an advanced iteration of the DELPHI semi-analytical model of galaxy formation and evolution. Based on dark matter halo merger trees spanning the redshift range from z = 20 to z = 4, it now incorporates essential components such as gas heating and cooling, cold and hot BH accretion, jet and radiative AGN feedback. We show how different BH growth models impact quasar and galaxy observables at z ≥ 5, providing predictions that will help discriminate between super-Eddington and Eddington-limited accretion models: despite being both consistent with observed properties of SMBHs and their host galaxies at z ∼ 5 − 7, they become very clearly distinguishable at higher redshift and in the intermediate mass regime. We find that the super-Eddington model, unlike the Eddington-limited scenario, predicts a gap in the BH mass function corresponding to the intermediate-mass range 104 M⊙ < Mbh < 106 M⊙. Additionally, it predicts black holes up to two orders of magnitude more massive for the same stellar mass at z = 9. The resulting velocity dispersion – BH mass relation at z ≥ 5 is consistent with local measurements, suggesting that its slope and normalisation are independent of redshift. Depending on the Eddington ratio, we also model the emergence of AGN jets, predicting their duty cycle across as a function of BH mass and their potential impact on the observed number density distribution of high-redshift AGN in the hard X-ray band.

ACACIA: a new method to produce on-the-fly merger trees in the ramses code

ABSTRACT The implementation of ACACIA, a new algorithm to generate dark matter halo merger trees with the Adaptive Mesh Refinement code RAMSES, is presented. The algorithm is fully parallel and based on the Message Passing Interface. As opposed to most available merger tree tools, it works on the fly during the course of the N-body simulation. It can track dark matter substructures individually using the index of the most bound particle in the clump. Once a halo (or a sub-halo) merges into another one, the algorithm still tracks it through the last identified most bound particle in the clump, allowing to check at later snapshots whether the merging event was definitive, or whether it was only temporary, with the clump only traversing another one. The same technique can be used to track orphan galaxies that are not assigned to a parent clump anymore because the clump dissolved due to numerical overmerging. We study in detail the impact of various parameters on the resulting halo catalogues and corresponding merger histories. We then compare the performance of our method using standard validation diagnostics, demonstrating that we reach a quality similar to the best available and commonly used merger tree tools. As a proof of concept, we use our merger tree algorithm together with a parametrized stellar-mass-to-halo-mass relation and generate a mock galaxy catalogue that shows good agreement with observational data.

SatGen: a semi-analytical satellite galaxy generator – I. The model and its application to Local-Group satellite statistics

ABSTRACT We present a semi-analytical model of satellite galaxies, SatGen, which can generate large statistical samples of satellite populations for a host halo of desired mass, redshift, and assembly history. The model combines dark matter (DM) halo merger trees, empirical relations for the galaxy–halo connection, and analytical prescriptions for tidal effects, dynamical friction, and ram-pressure stripping. SatGen emulates cosmological zoom-in hydrosimulations in certain aspects. Satellites can reside in cored or cuspy DM subhaloes, depending on the halo response to baryonic physics that can be formulated from hydrosimulations and physical modelling. The subhalo profile and the stellar mass and size of a satellite evolve depending on its tidal mass-loss and initial structure. The host galaxy can include a baryonic disc and a stellar bulge, each described by a density profile that allows analytic satellite orbit integration. SatGen complements simulations by propagating the effect of halo response found in simulated field galaxies to satellites (not properly resolved in simulations) and outperforms simulations by sampling the halo-to-halo variance of satellite statistics and overcoming artificial disruption due to insufficient resolution. As a first application, we use the model to study satellites of Milky Way (MW)- and M31-sized hosts, making it emulate simulations of bursty star formation and of smooth star formation, respectively, and to experiment with a disc potential in the host halo. We find that our model reproduces the observed satellite statistics reasonably well. Different physical recipes make a difference in satellite abundance and spatial distribution at the 25 per cent level, not large enough to be distinguished by current observations given the halo-to-halo variance. The MW/M31 disc depletes satellites by ${\sim } 20{{\ \rm per\ cent}}$ and has a subtle effect of diversifying the internal structure of satellites, which is important for alleviating certain small-scale problems. We discuss the conditions for a massive satellite to survive in MW/M31.

Self-consistent Semianalytic Modeling of Feedback during Primordial Star Formation and Reionization

Abstract We present a new semianalytic model of the formation of the first stars. Our method takes dark matter halo merger trees (including three-dimensional spatial information) from cosmological N-body simulations as input and applies analytic prescriptions to compute both the Population III and metal-enriched star formation histories. We have developed a novel method to accurately compute the major feedback processes affecting Population III star formation: H2 photodissociation from Lyman–Werner (LW) radiation, suppression of star formation due to inhomogeneous reionization, and metal enrichment via supernova winds. Our method utilizes a grid-based approach relying on fast Fourier transforms to rapidly track the LW intensity, ionization fraction, and metallicity in three dimensions throughout the simulation box. We present simulations for a wide range of astrophysical model parameters from z ≈ 30 to 6. Initially long-range LW feedback and local metal enrichment and reionization feedback dominate. However, for z ≲ 15 we find that the star formation rate density (SFRD) of Population III stars is impacted by the combination of external metal enrichment (metals from one halo polluting other pristine halos) and inhomogeneous reionization. We find that the interplay of these processes is particularly important for the Population III SFRD at z ≲ 10. Reionization feedback delays star formation long enough for metal bubbles to reach halos that would otherwise form Population III stars. Including these effects can lead to more than an order-of-magnitude decrease in the Population III SFRD at z = 6 compared to LW feedback alone.

Formation of globular cluster systems – II. Impact of the cut-off of the cluster initial mass function

Observations of young star clusters reveal that the high-mass end of the cluster initial mass function (CIMF) deviates from a pure power-law and instead truncates exponentially. We investigate the effects of this truncation on the formation of globular cluster (GC) systems by updating our analytic model for cluster formation and evolution, which is based on dark matter halo merger trees coupled to empirical galactic scaling relations, and has been shown in previous work to match a wide array of observational data. The cutoff masses of $M_c=10^{6.5} M_{\odot}$ or $10^{7}M_{\odot}$ match many scaling relations: between the GC system mass and host halo mass, between the average metallicity of the GC system and host halo mass, and the distribution of cluster masses. This range of $M_c$ agrees with indirect measurements from extragalactic GC systems. Models with $M_c<10^{6.5}M_{\odot}$ cannot reproduce the observed GC metallicity and mass distributions in massive galaxies. The slope of the mass-metallicity relation for metal-poor clusters (blue tilt) for all $M_c$ models is consistent with observations within their errors, when measured using the same method. We introduce an alternative, more robust fitting method, which reveals a trend of increasing tilt slope for lower $M_c$. In our model the blue tilt arises because the metal-poor clusters form in relatively low-mass galaxies which lack sufficient cold gas to sample the CIMF at highest masses. Massive blue clusters form in progressively more massive galaxies and inherit their higher metallicity. The metal-rich clusters do not exhibit such a tilt because they form in significantly more massive galaxies, which have enough cold gas to fully sample the CIMF.

Descendants of the first stars: the distinct chemical signature of second-generation stars

Extremely metal-poor (EMP) stars in the Milky Way (MW) allow us to infer the properties of their progenitors by comparing their chemical composition to the metal yields of the first supernovae. This method is most powerful when applied to mono-enriched stars, i.e. stars that formed from gas that was enriched by only one previous supernova. We present a novel diagnostic to identify this subclass of EMP stars. We model the first generations of star formation semi-analytically, based on dark matter halo merger trees that yield MW-like halos at the present day. Radiative and chemical feedback are included self-consistently and we trace all elements up to zinc. Mono-enriched stars account for only $\sim 1\%$ of second generation stars in our fiducial model and we provide an analytical formula for this probability. We also present a novel analytical diagnostic to identify mono-enriched stars, based on the metal yields of the first supernovae. This new diagnostic allows us to derive our main results independently from the specific assumptions made regarding Pop III star formation, and we apply it to a set of observed EMP stars to demonstrate its strengths and limitations. Our results may provide selection criteria for current and future surveys and therefore contribute to a deeper understanding of EMP stars and their progenitors.

Exploring the cosmic evolution of habitability with galaxy merger trees

We combine inferred galaxy properties from a semi-analytic galaxy evolution model incorporating dark matter halo merger trees with new estimates of supernova and gamma ray burst rates as a function of metallicity from stellar population synthesis models incorporating binary interactions. We use these to explore the stellar mass fraction of galaxies irradiated by energetic astrophysical transients and its evolution over cosmic time, and thus the fraction which is potentially habitable by life like our own. We find that 18 per cent of the stellar mass in the Universe is likely to have been irradiated within the last 260 Myr, with GRBs dominating that fraction. We do not see a strong dependence of irradiated stellar mass fraction on stellar mass or richness of the galaxy environment. We consider a representative merger tree as a Local Group analogue, and find that there are galaxies at all masses which have retained a high habitable fraction (>40 per cent) over the last 6 Gyr, but also that there are galaxies at all masses where the merger history and associated star formation have rendered galaxies effectively uninhabitable. This illustrates the need to consider detailed merger trees when evaluating the cosmic evolution of habitability.

The globular cluster-dark matter halo connection.

I present a simple phenomenological model for the observed linear scaling of the stellar mass in old globular clusters (GCs) with z = 0 halo mass in which the stellar mass in GCs scales linearly with progenitor halo mass at z = 6 above a minimum halo mass for GC formation. This model reproduces the observed M GCs-M halo relation at z = 0 and results in a prediction for the minimum halo mass at z = 6 required for hosting one GC: M min(z = 6) = 1.07 × 109 M⊙. Translated to z = 0, the mean threshold mass is M halo(z = 0) ≈ 2 × 1010 M⊙. I explore the observability of GCs in the reionization era and their contribution to cosmic reionization, both of which depend sensitively on the (unknown) ratio of GC birth mass to present-day stellar mass, ξ. Based on current detections of z ≳ 6 objects with M 1500<-17, values of ξ > 10 are strongly disfavoured; this, in turn, has potentially important implications for GC formation scenarios. Even for low values of ξ, some observed high-z galaxies may actually be GCs, complicating estimates of reionization-era galaxy ultraviolet luminosity functions and constraints on dark matter models. GCs are likely important reionization sources if 5 ≲ ξ ≲ 10. I also explore predictions for the fraction of accreted versus in situ GCs in the local Universe and for descendants of systems at the halo mass threshold of GC formation (dwarf galaxies). An appealing feature of the model presented here is the ability to make predictions for GC properties based solely on dark matter halo merger trees.

The segregation of baryons and dark matter during halo assembly

The standard galaxy formation theory assumes that baryons and dark matter are initially well mixed before becoming segregated due to radiative cooling. We use non-radiative hydrodynamical simulations to explicitly examine this assumption and find that baryons and dark matter can also be segregated due to different characteristics of gas and dark matter during the buildup of the halo. As a result, baryons in many haloes do not originate from the same Lagrangian region as the dark matter. When using the fraction of corresponding dark matter and gas particles in the initial conditions (the ‘paired fraction’) as a proxy of the dark matter and gas segregation strength of a halo, on average about 25 per cent of the baryonic and dark matter of the final halo are segregated in the initial conditions. This is at odds with the assumption of the standard galaxy formation model. A consequence of this effect is that the baryons and dark matter of the same halo initially experience different tidal torques and thus their angular momentum vectors are often misaligned. The degree of the misalignment is largely preserved during later halo assembly and can be understood with the tidal torque theory. The result challenges the precision of some semi-analytical approaches that utilize dark matter halo merger trees to infer properties of gas associated with dark matter haloes.

EFFECTS OF LARGE-SCALE ENVIRONMENT ON THE ASSEMBLY HISTORY OF CENTRAL GALAXIES

We examine whether large-scale environment affects the mass assembly history of their central galaxies. To facilitate this, we constructed dark matter halo merger trees from a cosmological N-body simulation and calculated the formation and evolution of galaxies using a semi-analytic method. We confirm earlier results that smaller halos show a notable difference in formation time with a mild dependence on large-scale environment. However, using a semi-analytic model, we found that on average the growth rate of the stellar mass of central galaxies is largely insensitive to large-scale environment. Although our results show that the star formation rate (SFR) and the stellar mass of central galaxies in smaller halos are slightly affected by the assembly bias of halos, those galaxies are faint, and the difference in the SFR is minute, and therefore it is challenging to detect it in real galaxies given the current observational accuracy. Future galaxy surveys, such as the BigBOSS experiment and the Large Synoptic Survey Telescope, which are expected to provide observational data for fainter objects, will provide a chance to test our model predictions.

On the scatter in the relation between stellar mass and halo mass: random or halo formation time dependent?

The empirical HOD model of Wang et al. 2006 fits, by construction, both the stellar mass function and correlation function of galaxies in the local Universe. In contrast, the semi-analytical models of De Lucia & Blazoit 2007 (DLB07) and Guo et al. 2011 (Guo11), built on the same dark matter halo merger trees than the empirical model, still have difficulties in reproducing these observational data simultaneously. We compare the relations between the stellar mass of galaxies and their host halo mass in the three models, and find that they are different. When the relations are rescaled to have the same median values and the same scatter as in Wang et al., the rescaled DLB07 model can fit both the measured galaxy stellar mass function and the correlation function measured in different galaxy stellar mass bins. In contrast, the rescaled Guo11 model still over-predicts the clustering of low-mass galaxies. This indicates that the detail of how galaxies populate the scatter in the stellar mass -- halo mass relation does play an important role in determining the correlation functions of galaxies. While the stellar mass of galaxies in the Wang et al. model depends only on halo mass and is randomly distributed within the scatter, galaxy stellar mass depends also on the halo formation time in semi-analytical models. At fixed value of infall mass, galaxies that lie above the median stellar mass -- halo mass relation reside in haloes that formed earlier, while galaxies that lie below the median relation reside in haloes that formed later. This effect is much stronger in Guo11 than in DLB07, which explains the over-clustering of low mass galaxies in Guo11. Our results illustrate that the assumption of random scatter in the relation between stellar and halo mass as employed by current HOD and abundance matching models may be problematic in case a significant assembly bias exists in the real Universe.

Convergence of galaxy properties with merger tree temporal resolution

Dark matter halo merger trees are now routinely extracted from cosmological simulations of structure formation. These trees are frequently used as inputs to semi-analytic models of galaxy formation to provide the backbone within which galaxy formation takes place. By necessity, these merger trees are constructed from a finite set of discrete "snapshots" of the N-body simulation and so have a limited temporal resolution. To date, there has been little consideration of how this temporal resolution affects the properties of galaxies formed within these trees. In particular, the question of how many snapshots are needed to achieve convergence in galaxy properties has not be answered. Therefore, we study the convergence in the stellar and total baryonic masses of galaxies, distribution of merger times, stellar mass functions and star formation rates in the Galacticus model of galaxy formation as a function of the number of "snapshot" times used to represent dark matter halo merger trees. When utilizing snapshots between z=20 and z=0, we find that at least 128 snapshots are required to achieve convergence to within 5% for galaxy masses. This convergence is obtained for mean quantities averaged over large samples of galaxies - significant variance for individual galaxies remains even when using very large numbers of snapshots. We find only weak dependence of the rate of convergence on the distribution of snapshots in time - snapshots spaced uniformly in the expansion factor, uniformly in the logarithm of expansion factor or uniformly in the logarithm of critical overdensity for collapse work equally well in almost all cases. We provide input parameters to Galacticus which allow this type of convergence study to be tuned to other simulations and to be carried out for other galaxy properties.

THE NON-CAUSAL ORIGIN OF THE BLACK-HOLE-GALAXY SCALING RELATIONS

We show that the MBH–Mbulge scaling relations observed from the local to the high-z universe can be largely or even entirely explained by a non-causal origin, i.e., they do not imply the need for any physically coupled growth of black hole (BH) and bulge mass, for example, through feedback by active galactic nuclei (AGNs). Provided some physics for the absolute normalization, the creation of the scaling relations can be fully explained by the hierarchical assembly of BH and stellar mass through galaxy merging, from an initially uncorrelated distribution of BH and stellar masses in the early universe. We show this with a suite of dark matter halo merger trees for which we make assumptions about (uncorrelated) BH and stellar mass values at early cosmic times. We then follow the halos in the presence of global star formation and BH accretion recipes that (1) work without any coupling of the two properties per individual galaxy and (2) correctly reproduce the observed star formation and BH accretion rate density in the universe. With disk-to-bulge conversion in mergers included, our simulations even create the observed slope of ∼1.1 for the MBH–Mbulge relation at z = 0. This also implies that AGN feedback is not a required (though still a possible) ingredient in galaxy evolution. In light of this, other mechanisms that can be invoked to truncate star formation in massive galaxies are equally justified.

The atomic-to-molecular transition and its relation to the scaling properties of galaxy discs in the local Universe

We extend existing semi-analytic models of galaxy formation to track atomic and molecular gas in disk galaxies. Simple recipes for processes such as cooling, star formation, supernova feedback, and chemical enrichment of the stars and gas are grafted on to dark matter halo merger trees derived from the Millennium Simulation. Each galactic disk is represented by a series of concentric rings. We assume that surface density profile of infalling gas in a dark matter halo is exponential, with scale radius r_d that is proportional to the virial radius of the halo times its spin parameter $\lambda$. As the dark matter haloes grow through mergers and accretion, disk galaxies assemble from the inside out. We include two simple prescriptions for molecular gas formation processes in our models: one is based on the analytic calculations by Krumholz, McKee & Tumlinson (2008), and the other is a prescription where the H_2 fraction is determined by the kinematic pressure of the ISM. Motivated by the observational results of Leroy et al. (2008), we adopt a star formation law in which $\Sigma_{SFR}\propto\Sigma_{H_2}$ in the regime where the molecular gas dominates the total gas surface density, and $\Sigma_{SFR}\propto \Sigma_{gas}^2$ where atomic hydrogen dominates. We then fit these models to the radial surface density profiles of stars, HI and H_2 drawn from recent high resolution surveys of stars and gas in nearby galaxies. We explore how the ratios of atomic gas, molecular gas and stellar mass vary as a function of global galaxy scale parameters, including stellar mass, stellar surface density, and gas surface density. We elucidate how the trends can be understood in terms of three variables that determine the partition of baryons in disks: the mass of the dark matter halo, the spin parameter of the halo, and the amount of gas recently accreted from the external environment.

Cosmic queuing: galaxy satellites, building blocks and the hierarchical clustering paradigm

Abstract We study the properties of building blocks (BBs; i.e. accreted satellites) and surviving satellites of present-day galaxies using the semi-analytic model of galaxy formation SAG (‚semi-analytic galaxies’) in the context of a concordance Λ cold dark matter (ΛCDM) cosmology. We consider large number of dark matter (DM) halo merger trees spanning a wide range of masses (∼1 × 1010–2.14 × 1015 M⊙). We find higher metallicities for BBs with respect to surviving satellites, an effect produced by the same processes behind the build up of the mass–metallicity relation. We prove that these metallicity differences arise from the higher peak height in the density fluctuation field occupied by BBs and central galaxies which have collapsed into a single object earlier than surviving satellites. BBs start to form stars earlier, during the peak of the merger activity in ΛCDM, and build up half of their final stellar mass (measured at the moment of disruption) up to four times faster than surviving satellites. Surviving satellites keep increasing their stellar masses rather quiescently down to z≃ 1. The difference between the metallicities of satellites, BBs and central galaxies depends on the host DM halo mass, in a way that can be used as a further test for the concordance cosmology.

THE ASSEMBLY OF SUPERMASSIVE BLACK HOLES AT HIGH REDSHIFTS

The supermassive black holes (SMBHs) massive enough to power the bright redshift ~6 quasars observed in the Sloan Digital Sky Survey (SDSS) are thought to have assembled by mergers and/or gas accretion from less massive "seed" BHs. If the seeds are the ~100 Msol remnant BHs from the first generation of stars, they must be in place well before redshift z=6, and must avoid being ejected from their parent proto-galaxies by the large (few hundred km/s) kicks they suffer from gravitational-radiation induced recoil during mergers with other BHs. We simulate the SMBH mass function at redshift z=6 using dark matter (DM) halo merger trees, coupled with a prescription for the halo occupation fraction, accretion histories, and radial recoil trajectories of the growing BHs. Our purpose is (i) to map out plausible scenarios for successful assembly of the z~6 quasar BHs by exploring a wide region of parameter space, and (ii) to predict the rate of low-frequency gravitational wave events detectable by the Laser Interferometer Space Antenna (LISA) for each such scenario. Our main findings are as follows: (1) ~100 Msol seed BHs can grow into the SDSS quasar BHs without super--Eddington accretion, but only if they form in minihalos by z~30 and subsequently accrete ~60% of the time; (2) the scenarios with optimistic assumptions required to explain the SDSS quasar BHs overproduce the mass density in lower--mass (10^5 to 10^7 Msol) SMBHs by a factor of 100-1000, unless seeds stop forming, or accrete at a severely diminished rates or duty cycles (e.g. due to feedback), at z < 20-30. We also present several successful assembly models and their LISA detection rates, including a "maximal" model that gives the highest rate (~30/yr at z~6) without overproducing the total SMBH density.

Generating dark matter halo merger trees

We present a new Monte-Carlo algorithm to generate merger trees describing the formation history of dark matter halos. The algorithm is a modification of the algorithm of Cole et al (2000) used in the GALFORM semi-analytic galaxy formation model. As such, it is based on the Extended Press-Schechter theory and so should be applicable to hierarchical models with a wide range of power spectra and cosmological models. It is tuned to be in accurate agreement with the conditional mass functions found in the analysis of merger trees extracted from the LCDM Millennium N-body simulation. We present a comparison of its predictions not only with these conditional mass functions, but also with additional statistics of the Millennium Simulation halo merger histories. In all cases we find it to be in good agreement with the Millennium Simulation and thus it should prove to be a very useful tool for semi-analytic models of galaxy formation and for modelling hierarchical structure formation in general. We have made our merger tree generation code and code to navigate the trees available at this http URL .

The statistical properties of Λ cold dark matter halo formation

We present a comparison of the statistical properties of dark matter halo merger trees extracted from the Millennium Simulation with Extended Press–Schechter (EPS) formalism and the related galform Monte Carlo method for generating ensembles of merger trees. The volume, mass resolution and output frequency make the Millennium Simulation a unique resource for the study of the hierarchical growth of structure. We construct the merger trees of present-day friends-of-friends groups and calculate a variety of statistics that quantify the masses of their progenitors as a function of redshift, accretion rates, and the redshift distribution of their most recent major merger. We also look in the forward direction and quantify the present-day mass distribution of haloes into which high-redshift progenitors of a specific mass become incorporated. We find that the EPS formalism and its Monte Carlo extension capture the qualitative behaviour of all these statistics, but as redshift increases they systematically underestimate the masses of the most massive progenitors. This shortcoming is worst for the Monte Carlo algorithm. We present a fitting function to a scaled version of the progenitor mass distribution and show how it can be used to make more accurate predictions of both progenitor and final halo mass distributions.