We use a complete and uniform sample of almost half a million galaxies from the Sloan Digital Sky Survey to characterize the distribution of stellar mass in the low-redshift Universe. Galaxy ...abundances are well determined over almost four orders of magnitude in stellar mass and are reasonably but not perfectly fit by a Schechter function with characteristic stellar mass m*= 6.7 × 1010 M⊙ and with faint-end slope α=−1.155. For a standard cosmology and a standard stellar initial mass function, only 3.5 per cent of the baryons in the low-redshift Universe are locked up in stars. The projected autocorrelation function of stellar mass is robustly and precisely determined for rp < 30 h−1 Mpc. Over the range 10 h−1 kpc < rp < 10 h−1 Mpc, it is extremely well represented by a power law. The corresponding three-dimensional autocorrelation function is ξ*(r) = (r/6.1 h−1 Mpc)−1.84. Relative to the dark matter, the bias of the stellar mass distribution is approximately constant on large scales, but varies by a factor of 5 for rp < 1 h−1 Mpc. This behaviour is approximately but not perfectly reproduced by current models for galaxy formation in the concordance Λcold dark matter cosmology. Detailed comparison suggests that a fluctuation amplitude σ8∼ 0.8 is preferred to the somewhat larger value adopted in the Millennium Simulation models with which we compare our data. This comparison also suggests that observations of stellar mass autocorrelations as a function of redshift might provide a powerful test for the nature of Dark Energy.
We present a new statistical method to determine the relationship between the stellar masses of galaxies and the masses of their host dark matter haloes over the entire cosmic history from z ∼ 4 to ...the present. This multi-epoch abundance matching (MEAM) model self-consistently takes into account that satellite galaxies first become satellites at times earlier than they are observed. We employ a redshift-dependent parametrization of the stellar-to-halo-mass relation to populate haloes and subhaloes in the Millennium simulations with galaxies, requiring that the observed stellar mass functions at several redshifts are reproduced simultaneously. We show that physically meaningful growth of massive galaxies is consistent with these data only if observational mass errors are taken into account. Using merger trees extracted from the dark matter simulations in combination with MEAM, we predict the average assembly histories of galaxies, separating into star formation within the galaxies (in situ) and accretion of stars (ex situ). Our main results are the peak star formation efficiency decreases with redshift from 23 per cent at z = 0 to 9 per cent at z =4 while the corresponding halo mass increases from 1011.8 to 1012.5 M. The star formation rate of central galaxies peaks at a redshift which depends on halo mass; for massive haloes this peak is at early cosmic times while for low-mass galaxies the peak has not been reached yet. In haloes similar to that of the Milky Way about half of the central stellar mass is assembled after z = 0.7. In low-mass haloes, the accretion of satellites contributes little to the assembly of their central galaxies, while in massive haloes more than half of the central stellar mass is formed ex situ with significant accretion of satellites at z < 2. We find that our method implies a cosmic star formation history and an evolution of specific star formation rates which are consistent with those inferred directly. We present convenient fitting functions for stellar masses, star formation rates and accretion rates as functions of halo mass and redshift.
We study the mass, velocity dispersion and anisotropy profiles of Λ cold dark matter (ΛCDM) haloes using a suite of N-body simulations of unprecedented numerical resolution. The Aquarius Project ...follows the formation of six different galaxy-sized haloes simulated several times at varying numerical resolution, allowing numerical convergence to be assessed directly. The highest resolution simulation represents a single dark matter halo using 4.4 billion particles, of which 1.1 billion end up within the virial radius. Our analysis confirms a number of results claimed by earlier work, and clarifies a few issues where conflicting claims may be found in the recent literature. The mass profile of ΛCDM haloes deviates slightly but systematically from the form proposed by Navarro, Frenk & White. The spherically averaged density profile becomes progressively shallower inwards and, at the innermost resolved radius, the logarithmic slope is γ≡− d ln ρ/d ln r≲ 1. Asymptotic inner slopes as steep as the recently claimed ρ∝r−1.2 are clearly ruled out. The radial dependence of γ is well approximated by a power law, γ∝rα (the Einasto profile). The shape parameter, α, varies slightly but significantly from halo to halo, implying that the mass profiles of ΛCDM haloes are not strictly universal: different haloes cannot, in general, be rescaled to look identical. Departures from similarity are also seen in velocity dispersion profiles and correlate with those in density profiles so as to preserve a power-law form for the spherically averaged pseudo-phase-space density, ρ/σ3∝r−1.875. The index here is identical to that of Bertschinger's similarity solution for self-similar infall on to a point mass from an otherwise uniform Einstein–de Sitter universe. The origin of this striking behaviour is unclear, but its robustness suggests that it reflects a fundamental structural property of ΛCDM haloes. Our conclusions are reliable down to radii below 0.4 per cent of the virial radius, providing well-defined predictions for halo structure when baryonic effects are neglected, and thus an instructive theoretical template against which the modifications induced by the baryonic components of real galaxies can be judged.
Abstract
We use publicly available data for the Millennium Simulation to explore the implications of the recent detection of assembly bias and splashback signatures in a large sample of galaxy ...clusters. These were identified in the Sloan Digital Sky Survey/Data Release 8 (SDSS/DR8) photometric data by the redMaPPer algorithm and split into high- and low-concentration subsamples based on the projected positions of cluster members. We use simplified versions of these procedures to build cluster samples of similar size from the simulation data. These match the observed samples quite well and show similar assembly bias and splashback signals. Previous theoretical work has found the logarithmic slope of halo density profiles to have a well-defined minimum whose depth decreases and whose radius increases with halo concentration. Projected profiles for the observed and simulated cluster samples show trends with concentration which are opposite to these predictions. In addition, for high-concentration clusters the minimum slope occurs at significantly smaller radius than predicted. We show that these discrepancies all reflect confusion between splashback features and features imposed on the profiles by the cluster identification and concentration estimation procedures. The strong apparent assembly bias is not reflected in the three-dimensional distribution of matter around clusters. Rather it is a consequence of the preferential contamination of low-concentration clusters by foreground or background groups.
We present an update to the multiphase smoothed particle hydrodynamics galaxy formation code by Scannapieco et al. We include a more elaborate treatment of the production of metals, cooling rates ...based on individual element abundances and a scheme for the turbulent diffusion of metals. Our supernova feedback model now transfers energy to the interstellar medium (ISM) in kinetic and thermal form, and we include a prescription for the effects of radiation pressure from massive young stars on the ISM. We calibrate our new code on the well-studied Aquarius haloes and then use it to simulate a sample of 16 galaxies with halo masses between 1 × 1011 and 3 × 1012 M. In general, the stellar masses of the sample agree well with the stellar mass to halo mass relation inferred from abundance matching techniques for redshifts z = 0-4. There is however a tendency to overproduce stars at z > 4 and to underproduce them at z < 0.5 in the least massive haloes. Overly high star formation rates (SFRs) at z < 1 for the most massive haloes are likely connected to the lack of active galactic nuclei feedback in our model. The simulated sample also shows reasonable agreement with observed SFRs, sizes, gas fractions and gas-phase metallicities at z = 0-3. Remaining discrepancies can be connected to deviations from predictions for star formation histories from abundance matching. At z = 0, the model galaxies show realistic morphologies, stellar surface density profiles, circular velocity curves and stellar metallicities, but overly flat metallicity gradients. 15 out of 16 of our galaxies contain disc components with kinematic disc fraction ranging between 15 and 65 per cent. The disc fraction depends on the time of the last destructive merger or misaligned infall event. Considering the remaining shortcomings of our simulations we conclude that even higher kinematic disc fractions may be possible for Λ cold dark matter haloes with quiet merger histories, such as the Aquarius haloes.
We present the Millennium-II Simulation (MS-II), a very large N-body simulation of dark matter evolution in the concordance Λ cold dark matter (ΛCDM) cosmology. The MS-II assumes the same ...cosmological parameters and uses the same particle number and output data structure as the original Millennium Simulation (MS), but was carried out in a periodic cube one-fifth the size (100 h−1 Mpc) with five times better spatial resolution (a Plummer equivalent softening of 1.0 h−1 kpc) and with 125 times better mass resolution (a particle mass of 6.9 × 106 h−1 M⊙). By comparing results at MS and MS-II resolution, we demonstrate excellent convergence in dark matter statistics such as the halo mass function, the subhalo abundance distribution, the mass dependence of halo formation times, the linear and non-linear autocorrelations and power spectra, and halo assembly bias. Together, the two simulations provide precise results for such statistics over an unprecedented range of scales, from haloes similar to those hosting Local Group dwarf spheroidal galaxies to haloes corresponding to the richest galaxy clusters. The ‘Milky Way’ haloes of the Aquarius Project were selected from a lower resolution version of the MS-II and were then resimulated at much higher resolution. As a result, they are present in the MS-II along with thousands of other similar mass haloes. A comparison of their assembly histories in the MS-II and in resimulations of 1000 times better resolution shows detailed agreement over a factor of 100 in mass growth. We publicly release halo catalogues and assembly trees for the MS-II in the same format within the same archive as those already released for the MS.
We present results from 13 cosmological simulations that explore the parameter space of the ‘Evolution and Assembly of GaLaxies and their Environments’ (EAGLE) simulation project. Four of the ...simulations follow the evolution of a periodic cube L = 50 cMpc on a side, and each employs a different subgrid model of the energetic feedback associated with star formation. The relevant parameters were adjusted so that the simulations each reproduce the observed galaxy
stellar mass function at z = 0.1. Three of the simulations fail to form disc galaxies as extended as observed, and we show analytically that this is a consequence of numerical radiative losses that reduce the efficiency of stellar feedback in high-density gas. Such losses are greatly reduced in the fourth simulation – the EAGLE reference model – by injecting more energy in higher density gas. This model produces galaxies with the observed size distribution, and also reproduces many galaxy scaling relations. In the remaining nine simulations, a single parameter or process of the reference model was varied at a time. We find that the properties of galaxies with stellar mass ≲ M
⋆ (the ‘knee’ of the galaxy stellar mass function) are largely governed by feedback associated with star formation, while those of more massive galaxies are also controlled by feedback from accretion on to their central black holes. Both processes must be efficient in order to reproduce the observed galaxy population. In general, simulations that have been calibrated to reproduce the low-redshift galaxy stellar mass function will still not form realistic galaxies, but the additional requirement that galaxy sizes be acceptable leads to agreement with a large range of observables.
We have updated the Munich galaxy formation model to the Planck first-year cosmology, while modifying the treatment of baryonic processes to reproduce recent data on the abundance and passive ...fractions of galaxies from z = 3 down to z = 0. Matching these more extensive and more precise observational results requires us to delay the reincorporation of wind ejecta, to lower the surface density threshold for turning cold gas into stars, to eliminate ram-pressure stripping in haloes less massive than
${\sim }10^{14}{\rm \, M_{{\odot }}}$
, and to modify our model for radio mode feedback. These changes cure the most obvious failings of our previous models, namely the overly early formation of low-mass galaxies and the overly large fraction of them that are passive at late times. The new model is calibrated to reproduce the observed evolution both of the stellar mass function and of the distribution of star formation rate at each stellar mass. Massive galaxies (log M
⋆/M⊙ ≥ 11.0) assemble most of their mass before z = 1 and are predominantly old and passive at z = 0, while lower mass galaxies assemble later and, for log M
⋆/M⊙ ≤ 9.5, are still predominantly blue and star forming at z = 0. This phenomenological but physically based model allows the observations to be interpreted in terms of the efficiency of the various processes that control the formation and evolution of galaxies as a function of their stellar mass, gas content, environment and time.
The Local Group galaxies offer some of the most discriminating tests of models of cosmic structure formation. For example, observations of the Milky Way (MW) and Andromeda satellite populations ...appear to be in disagreement with N-body simulations of the ‘lambda cold dark matter’ (ΛCDM) model: there are far fewer satellite galaxies than substructures in CDM haloes (the ‘missing satellites’ problem); dwarf galaxies seem to avoid the most massive substructures (the ‘too-big-to-fail’ problem); and the brightest satellites appear to orbit their host galaxies on a thin plane (the ‘planes of satellites’ problem). Here we present results from apostle (A Project Of Simulating The Local Environment), a suite of cosmological hydrodynamic simulations of 12 volumes selected to match the kinematics of the Local Group (LG) members. Applying the eagle code to the LG environment, we find that our simulations match the observed abundance of LG galaxies, including the satellite galaxies of the MW and Andromeda. Due to changes to the structure of haloes and the evolution in the LG environment, the simulations reproduce the observed relation between stellar mass and velocity dispersion of individual dwarf spheroidal galaxies without necessitating the formation of cores in their dark matter profiles. Satellite systems form with a range of spatial anisotropies, including one similar to the MWs, confirming that such a configuration is not unexpected in ΛCDM. Finally, based on the observed velocity dispersion, size, and stellar mass, we provide estimates of the maximum circular velocity for the haloes of nine MW dwarf spheroidals.
We examine the circular velocity profiles of galaxies in Λ cold dark matter (CDM) cosmological hydrodynamical simulations from the EAGLE and LOCAL GROUPS projects and compare them with a compilation ...of observed rotation curves of galaxies spanning a wide range in mass. The shape of the circular velocity profiles of simulated galaxies varies systematically as a function of galaxy mass, but shows remarkably little variation at fixed maximum circular velocity. This is especially true for low-mass dark-matter-dominated systems, reflecting the expected similarity of the underlying CDM haloes. This is at odds with observed dwarf galaxies, which show a large diversity of rotation curve shapes, even at fixed maximum rotation speed. Some dwarfs have rotation curves that agree well with simulations, others do not. The latter are systems where the inferred mass enclosed in the inner regions is much lower than expected for CDM haloes and include many galaxies where previous work claims the presence of a constant density ‘core’. The ‘cusp versus core’ issue is thus better characterized as an ‘inner mass deficit’ problem than as a density slope mismatch. For several galaxies, the magnitude of this inner mass deficit is well in excess of that reported in recent simulations where cores result from baryon-induced fluctuations in the gravitational potential. We conclude that one or more of the following statements must be true: (i) the dark matter is more complex than envisaged by any current model; (ii) current simulations fail to reproduce the diversity in the effects of baryons on the inner regions of dwarf galaxies; and/or (iii) the mass profiles of ‘inner mass deficit’ galaxies inferred from kinematic data are incorrect.
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