We study the properties of black holes and their host galaxies across cosmic time in the Illustris simulation. Illustris is a large scale cosmological hydrodynamical simulation which resolves a (106.5 Mpc)^3 volume with more than 12 billion resolutio
n elements and includes state-of-the-art physical models relevant for galaxy formation. We find that the black hole mass density for redshifts z = 0 - 5 and the black hole mass function at z = 0 predicted by Illustris are in very good agreement with the most recent observational constraints. We show that the bolometric and hard X-ray luminosity functions of AGN at z = 0 and 1 reproduce observational data very well over the full dynamic range probed. Unless the bolometric corrections are largely underestimated, this requires radiative efficiencies to be on average low, epsilon_r <= 0.1, noting however that in our model radiative efficiencies are degenerate with black hole feedback efficiencies. Cosmic downsizing of the AGN population is in broad agreement with the findings from X-ray surveys, but we predict a larger number density of faint AGN at high redshifts than currently inferred. We also study black hole -- host galaxy scaling relations as a function of galaxy morphology, colour and specific star formation rate. We find that black holes and galaxies co-evolve at the massive end, but for low mass, blue and star-forming galaxies there is no tight relation with either their central black hole masses or the nuclear AGN activity.
A discontinuous Galerkin (DG) method suitable for large-scale astrophysical simulations on Cartesian meshes as well as arbitrary static and moving Voronoi meshes is presented. Most major astrophysical fluid dynamics codes use a finite volume (FV) app
roach. We demonstrate that the DG technique offers distinct advantages over FV formulations on both static and moving meshes. The DG method is also easily generalized to higher than second-order accuracy without requiring the use of extended stencils to estimate derivatives (thereby making the scheme highly parallelizable). We implement the technique in the AREPO code for solving the fluid and the magnetohydrodynamic (MHD) equations. By examining various test problems, we show that our new formulation provides improved accuracy over FV approaches of the same order, and reduces post-shock oscillations and artificial diffusion of angular momentum. In addition, the DG method makes it possible to represent magnetic fields in a locally divergence-free way, improving the stability of MHD simulations and moderating global divergence errors, and is a viable alternative for solving the MHD equations on meshes where Constrained-Transport (CT) cannot be applied. We find that the DG procedure on a moving mesh is more sensitive to the choice of slope limiter than is its FV method counterpart. Therefore, future work to improve the performance of the DG scheme even further will likely involve the design of optimal slope limiters. As presently constructed, our technique offers the potential of improved accuracy in astrophysical simulations using the moving mesh AREPO code as well as those employing adaptive mesh refinement (AMR).
We present a new comprehensive model of the physics of galaxy formation designed for large-scale hydrodynamical simulations of structure formation using the moving mesh code AREPO. Our model includes primordial and metal line cooling with self-shield
ing corrections, stellar evolution and feedback processes, gas recycling, chemical enrichment, a novel subgrid model for the metal loading of outflows, black hole (BH) seeding, BH growth and merging procedures, quasar- and radio-mode feedback, and a prescription for radiative electro-magnetic (EM) feedback from active galactic nuclei (AGN). The metal mass loading of outflows can be adjusted independently of the wind mass loading. This is required to simultaneously reproduce the stellar mass content of low mass haloes and their gas oxygen abundances. Radiative EM AGN feedback is implemented assuming an average spectral energy distribution and a luminosity-dependent scaling of obscuration effects. This form of feedback suppresses star formation more efficiently than continuous thermal quasar-mode feedback alone, but is less efficient than mechanical radio-mode feedback in regulating star formation in massive haloes. We contrast simulation predictions for different variants of our galaxy formation model with key observations. Our best match model reproduces, among other things, the cosmic star formation history, the stellar mass function, the stellar mass - halo mass relation, g-, r-, i-, z-band SDSS galaxy luminosity functions, and the Tully-Fisher relation. We can achieve this success only if we invoke very strong forms of stellar and AGN feedback such that star formation is adequately reduced in both low and high mass systems. In particular, the strength of radio-mode feedback needs to be increased significantly compared to previous studies to suppress efficient cooling in massive, metal-enriched haloes.
We compare the structural properties of galaxies formed in cosmological simulations using the smoothed particle hydrodynamics (SPH) code GADGET with those using the moving-mesh code AREPO. Both codes employ identical gravity solvers and the same sub-
resolution physics but use very different methods to track the hydrodynamic evolution of gas. This permits us to isolate the effects of the hydro solver on the formation and evolution of galactic gas disks in GADGET and AREPO haloes with comparable numerical resolution. In a matching sample of GADGET and AREPO haloes we fit simulated gas disks with exponential profiles. We find that the cold gas disks formed using the moving mesh approach have systematically larger disk scale lengths and higher specific angular momenta than their GADGET counterparts across a wide range in halo masses. For low mass galaxies differences between the properties of the simulated galaxy disks are caused by an insufficient number of resolution elements which lead to the artificial angular momentum transfer in our SPH calculation. We however find that galactic disks formed in massive halos, resolved with 10^6 particles/cells, are still systematically smaller in the GADGET run by a factor of ~2. The reasons for this are: 1) The excessive heating of haloes close to the cooling radius due to spurious dissipation of the subsonic turbulence in GADGET; and 2) The efficient delivery of low angular momentum gaseous blobs to the bottom of the potential well. While this large population of gaseous blobs in GADGET originates from the filaments which are pressure confined and fragment due to the SPH surface tension while infalling into hot halo atmospheres, it is essentially absent in the moving mesh calculation, clearly indicating numerical rather than physical origin of the blob material.
We discuss cosmological hydrodynamic simulations of galaxy formation performed with the new moving-mesh code AREPO, which promises higher accuracy compared with the traditional SPH technique that has been widely employed for this problem. We use an i
dentical set of physics in corresponding simulations carried out with the well-tested SPH code GADGET, adopting also the same high-resolution gravity solver. We are thus able to compare both simulation sets on an object-by-object basis, allowing us to cleanly isolate the impact of different hydrodynamical methods on galaxy and halo properties. In accompanying papers, we focus on an analysis of the global baryonic statistics predicted by the simulation codes, (Vogelsberger et al. 2011) and complementary idealized simulations that highlight the differences between the hydrodynamical schemes (Sijacki et al. 2011). Here we investigate their influence on the baryonic properties of simulated galaxies and their surrounding haloes. We find that AREPO leads to significantly higher star formation rates for galaxies in massive haloes and to more extended gaseous disks in galaxies, which also feature a thinner and smoother morphology than their GADGET counterparts. Consequently, galaxies formed in AREPO have larger sizes and higher specific angular momentum than their SPH correspondents. The more efficient cooling flows in AREPO yield higher densities and lower entropies in halo centers (and the opposite trend in halo outskirts) leading to higher star formation rates of massive galaxies. While both codes agree to acceptable accuracy on a number of baryonic properties of cosmic structures, our results clearly demonstrate that galaxy formation simulations greatly benefit from the use of more accurate hydrodynamical techniques such as AREPO.
We present a detailed comparison between the well-known SPH code GADGET and the new moving-mesh code AREPO on a number of hydrodynamical test problems. Through a variety of numerical experiments we establish a clear link between test problems and sys
tematic numerical effects seen in cosmological simulations of galaxy formation. Our tests demonstrate deficiencies of the SPH method in several sectors. These accuracy problems not only manifest themselves in idealized hydrodynamical tests, but also propagate to more realistic simulation setups of galaxy formation, ultimately affecting gas properties in the full cosmological framework, as highlighted in papers by Vogelsberger et al. (2011) and Keres et al. (2011). We find that an inadequate treatment of fluid instabilities in GADGET suppresses entropy generation by mixing, underestimates vorticity generation in curved shocks and prevents efficient gas stripping from infalling substructures. In idealized tests of inside-out disk formation, the convergence rate of gas disk sizes is much slower in GADGET due to spurious angular momentum transport. In simulations where we follow the interaction between a forming central disk and orbiting substructures in a halo, the final disk morphology is strikingly different. In AREPO, gas from infalling substructures is readily depleted and incorporated into the host halo atmosphere, facilitating the formation of an extended central disk. Conversely, gaseous sub-clumps are more coherent in GADGET simulations, morphologically transforming the disk as they impact it. The numerical artefacts of the SPH solver are particularly severe for poorly resolved flows, and thus inevitably affect cosmological simulations due to their hierarchical nature. Our numerical experiments clearly demonstrate that AREPO delivers a physically more reliable solution.
We study the evolution of gravitationally recoiled supermassive black holes (BHs) in massive gas-rich galaxies by means of high-resolution hydrodynamical simulations. We find that the presence of a massive gaseous disc allows recoiled BHs to return t
o the centre on a much shorter timescale than for purely stellar discs. Also, BH accretion and feedback can strongly modify the orbit of recoiled BHs and hence their return timescale, besides affecting the distribution of gas and stars in the galactic centre. However, the dynamical interaction of kicked BHs with the surrounding medium is in general complex and can facilitate both a fast return to the centre as well as a significant delay. The Bondi-Hoyle-Lyttleton accretion rates of the recoiling BHs in our simulated galaxies are favourably high for the detection of off-centred AGN if kicked within gas-rich discs -- up to a few per cent of the Eddington accretion rate -- and are highly variable on timescales of a few 10^7 yrs. In major merger simulations of gas-rich galaxies, we find that gravitational recoils increase the scatter in the BH mass -- host galaxy relationships compared to simulations without kicks, with the BH mass being more sensitive to recoil kicks than the bulge mass. A generic result of our numerical models is that the clumpy massive discs suggested by recent high-redshift observations, as well as the remnants of gas-rich mergers, exhibit a gravitational potential that falls steeply in the central regions, due to the dissipative concentration of baryons. As a result, supermassive BHs should only rarely be able to escape from massive galaxies at high redshifts, which is the epoch where the bulk of BH recoils is expected to occur.[Abridged]
We employ cosmological hydrodynamical simulations to study the growth of massive black holes (BHs) at high redshifts subject to BH merger recoils from gravitational wave emission. We select the most massive dark matter halo at z=6 from the Millennium
simulation, and resimulate its formation at much higher resolution including gas physics and a model for BH seeding, growth and feedback. Assuming that the initial BH seeds are relatively massive, of the order of 10^5 Msun, and that seeding occurs around z~15 in dark matter haloes of mass 10^9-10^10 Msun, we find that it is possible to build up supermassive BHs (SMBHs) by z=6 that assemble most of their mass during extended Eddington-limited accretion periods. The properties of the simulated SMBHs are consistent with observations of z=6 quasars in terms of the estimated BH masses and bolometric luminosities, the amount of star formation occurring within the host halo, and the presence of highly enriched gas in the innermost regions of the host galaxy. After a peak in the BH accretion rate at z=6, the most massive BH has become sufficiently massive for the growth to enter into a much slower phase of feedback-regulated accretion. We explore the full range of expected recoils and radiative efficiencies, and also consider models with spinning BHs. In the most `pessimistic case where BH spins are initially high, we find that the growth of the SMBHs can be potentially hampered if they grow mostly in isolation and experience only a small number of mergers. Whereas BH kicks can expel a substantial fraction of low mass BHs, they do not significantly affect the build up of the SMBHs. On the contrary, a large number of BH mergers has beneficial consequences for the growth of the SMBHs by considerably reducing their spin. [Abridged]
We discuss a numerical model for black hole growth and its associated feedback processes that for the first time allows cosmological simulations of structure formation to self-consistently follow the build up of the cosmic population of galaxies and
active galactic nuclei. Our model assumes that seed black holes are present at early cosmic epochs at the centres of forming halos. We then track their growth from gas accretion and mergers with other black holes in the course of cosmic time. For black holes that are active, we distinguish between two distinct modes of feedback, depending on the black hole accretion rate itself. Black holes that accrete at high rates are assumed to be in a `quasar regime, where we model their feedback by thermally coupling a small fraction of their bolometric luminosity to the surrounding gas. For black holes with low accretion rates, we conjecture that most of their feedback occurs in mechanical form, where AGN-driven bubbles are injected into a gaseous environment. Using our new model, we carry out TreeSPH cosmological simulations on the scales of individual galaxies to those of massive galaxy clusters, both for isolated systems and for cosmological boxes. We demonstrate that our model produces results for the black hole and stellar mass densities in broad agreement with observational constraints. We find that the black holes significantly influence the evolution of their host galaxies, changing their star formation history, their amount of cold gas, and their colours. Also, the properties of intracluster gas are affected strongly by the presence of massive black holes in the cores of galaxy clusters, leading to shallower metallicity and entropy profiles, and to a suppression of strong cooling flows. [Abridged]
