Michael Boylan-Kolchin

From dwarf spheroidals to cD galaxies: simulating the galaxy population in a ΛCDM cosmology

We have updated and extended our semi-analytic galaxy formation modelling capabilities and applied them simultaneously to the stored halo/subhalo merger trees of the Millennium and Millennium-II simulations. These differ by a factor of 125 in mass resolution, allowing explicit testing of resolution effects on predicted galaxy properties. We have revised the treatments of the transition between the rapid infall and cooling flow regimes of gas accretion, of the sizes of bulges and of gaseous and stellar disks, of supernova feedback, of the transition between central and satellite status as galaxies fall into larger systems, and of gas and star stripping once they become satellites. Plausible values of efficiency and scaling parameters yield an excellent fit not only to the observed abundance of low-redshift galaxies over 5 orders of magnitude in stellar mass and 9 magnitudes in luminosity, but also to the observed abundance of Milky Way satellites. This suggests that reionisation effects may not be needed to solve the “missing satellite” problem except, perhaps, for the faintest objects. The same model matches the observed large-scale clustering of galaxies as a function of stellar mass and colour. The fit remains excellent down to � 30 kpc for massive galaxies. For M∗ < 6×10 10 M⊙, however, the model overpredicts clustering at scales below � 1 Mpc, suggesting that the assumed fluctuation amplitude, σ8 = 0.9, is too high. The observed difference in clustering between active and passive galaxies is matched quite well for all masses. Galaxy distributions within rich clusters agree between the simulations and match those observed, but only if galaxies without dark matter subhalos (so-called orphans) are included. Even at MS-II resolution, schemes which assign galaxies only to resolved dark matter subhalos cannot match observed clusters. Our model predicts a larger passive fraction among low-mass galaxies than is observed, as well as an overabundance of � 10 10 M⊙ galaxies beyond z � 0.6. (The abundance of � 10 11 M⊙ galaxies is matched out to z � 3.) These discrepancies appear to reflect deficiencies in the way star-formation rates are modelled.

How do galaxies populate dark matter haloes

For any assumed standard stellar initial mass function, the Sloan Digital Sky Survey (SDSS) gives a precise determination of the abundance of galaxies as a function of their stellar mass over the full stellar mass range 108 M(circle dot) < M(*) < 1012 M(circle dot). Within the concordance Lambda cold dark matter (Lambda CDM) cosmology, the Millennium Simulations give precise halo abundances as a function of mass and redshift for all haloes within which galaxies can form. Under the plausible hypothesis that the stellar mass of a galaxy is an increasing function of the maximum mass ever attained by its halo, these results combine to give halo mass as a function of stellar mass. The result agrees quite well with observational estimates of mean halo mass as a function of stellar mass from stacking analyses of the gravitational lensing signal and the satellite dynamics of SDSS galaxies. For M(*) similar to 5.5 x 1010 M(circle dot), the stellar mass usually assumed for the Milky Way (MW), the implied halo mass is similar to 2 x 1012 M(circle dot), consistent with most recent direct estimates and inferences from the MW/M31 timing argument. The fraction of the baryons associated with each halo which are present as stars in its central galaxy reaches a maximum of 20 per cent at masses somewhat below that of the MW and falls rapidly at both higher and lower masses. These conversion efficiencies are lower than in almost all recent high-resolution simulations of galaxy formation, showing that these are not yet viable models for the formation of typical members of the galaxy population. When inserted in the Millennium-II Simulation, our derived relation between stellar mass and halo mass predicts a stellar mass autocorrelation function in excellent agreement with that measured directly in the SDSS. The implied Tully-Fisher relation also appears consistent with observation, suggesting that galaxy luminosity functions and Tully-Fisher relations can be reproduced simultaneously in a Lambda CDM cosmology.

Too big to fail? The puzzling darkness of massive Milky Way subhaloes

ABSTRACT We show that dissipationless CDM simulations predict that the majority of themost massive subhalos of the Milky Way are too dense to host any of its brightsatellites (L V > 10 5 L ). These dark subhalos have circular velocities at infall ofV infall = 30 1070kms 1 and infall masses of [0:2 4] 10 M . Unless the Milky Way isa statistical anomaly, this implies that galaxy formation becomes e ectively stochasticat these masses. This is in marked contrast to the well-established monotonic relationbetween galaxy luminosity and halo circular velocity (or halo mass) for more massivehalos. We show that at least two (and typically four) of these massive dark subhalosare expected to produce a larger dark matter annihilation ux than Draco. It maybe possible to circumvent these conclusions if baryonic feedback in dwarf satellites ordi erent dark matter physics can reduce the central densities of massive subhalos byorder unity on a scale of 0.3 { 1 kpc.Key words: Galaxy: halo { galaxies: abundances { dark matter { cosmology: theory

The merger rates and mass assembly histories of dark matter haloes in the two Millennium simulations

We construct merger trees of dark matter haloes and quantify their merger rates and mass growth rates using the joint data set from the Millennium and Millennium-II simulations. The finer resolution of the Millennium-II simulation has allowed us to extend our earlier analysis of halo merger statistics to an unprecedentedly wide range of descendant halo mass (10 10 ≲ M 0 ≲ 10 15 M ⊙ ), progenitor mass ratio (10 -5 ≲ ξ ≤ 1) and redshift (0 ≤ z ≲ 15). We update our earlier fitting form for the mean merger rate per halo as a function of M 0 , ξ and z. The overall behaviour of this quantity is unchanged: the rate per unit redshift is nearly independent of z out to z ~ 15; the dependence on halo mass is weak (∝ Mg 0.13 0 ); and it is nearly a power law in the progenitor mass ratio (∝ ξ -2 ). We also present a simple and accurate fitting formula for the mean mass growth rate of haloes as a function of mass and redshift. This mean rate is 46 M ⊙ yr -1 for 10 12 M ⊙ haloes at z = 0, and it increases with mass as ∝ M 1.1 and with redshift as (1 + z) 2.5 (for z ≳ 1). When the fit for the mean mass growth rate is integrated over a halos history, we find excellent match to the mean mass assembly histories of the simulated haloes. By combining merger rates and mass assembly histories, we present results for the number of mergers over a halos history and the statistics of the redshift of the last major merger.

Dynamical friction and galaxy merging time‐scales

The time-scale for galaxies within merging dark matter haloes to merge with each other is an important ingredient in galaxy formation models. Accurate estimates of merging time-scales are required for predictions of astrophysical quantities such as black hole binary merger rates, the build-up of stellar mass in central galaxies and the statistical properties of satellite galaxies within dark matter haloes. In this paper, we study the merging time-scales of extended dark matter haloes using N-body simulations. We compare these results to standard estimates based on the Chandrasekhar theory of dynamical friction. We find that these standard predictions for merging time-scales, which are often used in semi-analytic galaxy formation models, are systematically shorter than those found in simulations. The discrepancy is approximately a factor of 1.7 for M sat /M host ≈ 0.1 and becomes larger for more disparate satellite-to-host mass ratios, reaching a factor of ∼3.3 for M sat /M host ≈ 0.01. Based on our simulations, we propose a new, easily implementable fitting formula that accurately predicts the time-scale for an extended satellite to sink from the virial radius of a host halo down to the halos centre for a wide range of M sat /M host and orbits. Including a central bulge in each galaxy changes the merging time-scale by ≤10 per cent. To highlight one concrete application of our results, we show that merging time-scales often used in the literature overestimate the growth of stellar mass by satellite accretion by ≈40 per cent, with the extra mass gained in low mass ratio mergers.

Galaxy formation in WMAP1 and WMAP7 cosmologies

Using the technique of Angulo & White (2010) we scale the Millennium and Millennium-II simulations of structure growth in aCDM universe from the cosmo- logical parameters with which they were carried out (based on first-year results from the Wilkinson Microwave Anisotropy Probe, WMAP1) to parameters consistent with the seven-year WMAP data (WMAP7). We implement semi-analytic galaxy formation modelling on both simulations in both cosmologies to investigate how the formation, evolution and clustering of galaxies are predicted to vary with cosmological parame- ters. The increased matter density m and decreased linear fluctuation amplitude σ8 in WMAP7 have compensating effects, so that the abundance and clustering of dark halos are predicted to be very similar to those in WMAP1 for z 6 3. As a result, local galaxy properties can be reproduced equally well in the two cosmologies by slightly altering galaxy formation parameters. The evolution of the galaxy populations is then also similar. In WMAP7, structure forms slightly later. This shifts the peak in cosmic star formation rate to lower redshift, resulting in slightly bluer galaxies at z = 0. Nev- ertheless, the model still predicts more passive low-mass galaxies than are observed. For rp 1 galaxies are predicted to be more strongly clustered for WMAP7. Differences in galaxy properties, including, clustering, in these two cosmologies are rather small out to z � 3. Given that there are still considerable residual uncertainties in galaxy formation models, it is very difficult to distinguish WMAP1 from WMAP7 through observations of galaxy properties or their evolution.

Red mergers and the assembly of massive elliptical galaxies: the fundamental plane and its projections

Several recent observations suggest that gas-poor (dissipationless) mergers of elliptical galaxies contribute significantly to the build-up of the massive end of the red sequence at z? 1. We perform a series of major merger simulations to investigate the spatial and velocity structure of the remnants of such mergers. Regardless of orbital energy or angular momentum, we find that the stellar remnants lie on the fundamental plane defined by their progenitors, a result of virial equilibrium with a small tilt due to an increasing central dark matter fraction. However, the locations of merger remnants in the projections of the fundamental plane - the Faber-Jackson and R e -M * relations - depend strongly on the merger orbit, and the relations steepen significantly from the canonical scalings (L ∝ σ 4 e and R e ∝ M 0.6 * ) for mergers on radial orbits. This steepening arises because stellar bulges on orbits with lower angular momentum lose less energy via dynamical friction on the dark matter haloes than do bulges on orbits with substantial angular momentum. This results in a less tightly bound remnant bulge with a smaller velocity dispersion and a larger effective radius. Our results imply that the projections of the fundamental plane - but not necessarily the plane itself - provide a powerful way of investigating the assembly history of massive elliptical galaxies, including the brightest cluster galaxies at or near the centres of galaxy clusters. We argue that most massive ellipticals are formed by anisotropic merging and that their fundamental plane projections should thus differ noticeably from those of lower mass ellipticals even though they should lie on the same fundamental plane. Current observations are consistent with this conclusion. The steepening in the L-σ e relation for luminous ellipticals may also be reflected in a corresponding steepening in the M BH-σe relation for massive black holes.

There's no place like home? Statistics of Milky Way‐mass dark matter haloes

We present an analysis of the distribution of structural properties for Milky Way-mass haloes in the Millennium-II Simulation (MS-II). This simulation of structure formation within the standard ACDM cosmology contains thousands of Milky Way-mass haloes and has sufficient resolution to properly resolve many subhaloes per host. It thus provides a major improvement in the statistical power available to explore the distribution of internal structure for haloes of this mass. In addition, the MS-II contains lower-resolution versions of the Aquarius Project haloes, allowing us to compare our results to simulations of six haloes at a much higher resolution. We study the distributions of mass assembly histories, of subhalo mass functions and accretion times and of merger and stripping histories for subhaloes capable of impacting discs at the centres of haloes. We show that subhalo abundances are not well described by Poisson statistics at low mass, but rather are dominated by intrinsic scatter. Using the masses of subhaloes at infall and the abundance-matching assumption, there is less than a 10 per cent chance that a Milky Way halo with M vir = 10 12 M ⊙ will host two galaxies as bright as the Magellanic Clouds. This probability rises to ∼25 per cent for a halo with M vir = 2.5 × 10 12 M ⊙ . The statistics relevant for disc heating are very sensitive to the mass range that is considered relevant. Mergers with infall mass: redshift zero virial mass greater than 1:30 could well impact a central galactic disc and are a near inevitability since z = 2, whereas only half of all haloes have had a merger with infall mass: redshift zero virial mass greater than 1:10 over this same period.

Forged in fire: cusps, cores and baryons in low-mass dwarf galaxies

We present multiple ultrahigh resolution cosmological hydrodynamic simulations of M_★ ≃ 10^(4–6.3) M_⊙ dwarf galaxies that form within two M_(vir) = 10^(9.5–10) M_⊙ dark matter halo initial conditions. Our simulations rely on the Feedback in Realistic Environments (FIRE) implementation of star formation feedback and were run with high enough force and mass resolution to directly resolve structure on the ∼200 pc scales. The resultant galaxies sit on the M_★ versus M_(vir) relation required to match the Local Group stellar mass function via abundance matching. They have bursty star formation histories and also form with half-light radii and metallicities that broadly match those observed for local dwarfs at the same stellar mass. We demonstrate that it is possible to create a large (∼1 kpc) constant-density dark matter core in a cosmological simulation of an M_★ ≃ 10^(6.3) M_⊙ dwarf galaxy within a typical M_(vir) = 10^(10) M_⊙ halo – precisely the scale of interest for resolving the ‘too big to fail’ problem. However, these large cores are not ubiquitous and appear to correlate closely with the star formation histories of the dwarfs: dark matter cores are largest in systems that form their stars late (z ≲ 2), after the early epoch of cusp building mergers has ended. Our M_★ ≃ 10^4 M_⊙ dwarf retains a cuspy dark matter halo density profile that matches that of a dark-matter-only run of the same system. Though ancient, most of the stars in our ultrafaint form after reionization; the ultraviolet field acts mainly to suppress fresh gas accretion, not to boil away gas that is already present in the protodwarf.

Dissipationless mergers of elliptical galaxies and the evolution of the fundamental plane

We carry out numerical simulations of dissipationless major mergers of elliptical galaxies using initial galaxy models that consist of a dark matter halo and a stellar bulge with properties consistent with the observed fundamental plane. By varying the density profile of the dark matter halo [standard Navarro, Frenk & White (NFW) profile versus adiabatically contracted NFW profile], the global stellar to dark matter mass ratio and the orbit of the merging galaxies, we are able to assess the impact of each of these factors on the structure of the merger remnant. Our results indicate that the properties of the remnant bulge depend primarily on the angular momentum and energy of the orbit; for a cosmologically motivated orbit, the effective radius and velocity dispersion of the remnant bulge remain approximately on the fundamental plane. This indicates that the observed properties of elliptical galaxies are consistent with significant growth via late dissipationless mergers. We also find that the dark matter fraction within the effective radius of our remnants increases after the merger, consistent with the hypothesis that the tilt of the fundamental plane from the virial theorem is due to a varying dark matter fraction as a function of galaxy mass. Ke yw ords: methods: N-body simulations ‐ galaxies: evolution ‐ galaxies: fundamental parameters ‐ galaxies: structure ‐ dark matter.