Stefan Gottlöber

Toward a halo mass function for precision cosmology: The Limits of universality

We measure the mass function of dark matter halos in a large set of collisionless cosmological simulations of flat ΛCDM cosmology and investigate its evolution at -->z 2. Halos are identified as isolated density peaks, and their masses are measured within a series of radii enclosing specific overdensities. We argue that these spherical overdensity masses are more directly linked to cluster observables than masses measured using the friends-of-friends algorithm (FOF), and are therefore preferable for accurate forecasts of halo abundances. Our simulation set allows us to calibrate the mass function at -->z = 0 for virial masses in the range -->1011 h−1 M☉ ≤ M≤ 1015 h−1 M☉ to 5%, improving on previous results by a factor of 2-3. We derive fitting functions for the halo mass function in this mass range for a wide range of overdensities, both at -->z = 0 and earlier epochs. Earlier studies have sought to calibrate a universal mass function, in the sense that the same functional form and parameters can be used for different cosmologies and redshifts when expressed in appropriate variables. In addition to our fitting formulae, our main finding is that the mass function cannot be represented by a universal function at this level or accuracy. The amplitude of the universal function decreases monotonically by 20%-50%, depending on the mass definition, from -->z = 0 to 2.5. We also find evidence for redshift evolution in the overall shape of the mass function.

Galaxies in N-Body Simulations: Overcoming the Overmerging Problem

We present analysis of the evolution of dark matter halos in dense environments of groups and clusters in dissipationless cosmological simulations. The premature destruction of halos in such environments, known as the overmerging, reduces the predictive power of N-body simulations and makes difficult any comparison between models and observations. We analyze the possible processes that cause the overmerging and assess the extent to which this problem can be cured with current computer resources and codes. Using both analytic estimates and high-resolution numerical simulations, we argue that the overmerging is mainly due to the lack of numerical resolution. We find that the force and mass resolution required for a simulated halo to survive in galaxy groups and clusters is extremely high and was almost never reached before: ~1-3 kpc and 108-109 M☉, respectively. We use the high-resolution Adaptive Refinement Tree (ART) N-body code to run cosmological simulations with particle mass ≈2 × 108 h-1 M☉ and spatial resolution ≈1-2 h-1 kpc and show that in these simulations the halos do survive in regions that would appear overmerged with lower force resolution. Nevertheless, the halo identification in very dense environments remains a challenge even with resolution this high. We present two new halo-finding algorithms developed to identify both isolated and satellite halos that are stable (existed at previous moments) and gravitationally bound. To illustrate the use of the satellite halos that survive the overmerging, we present a series of halo statistics, which can be compared with those of observed galaxies. Particularly, we find that, on average, halos in groups have the same velocity dispersion as the dark matter particles; i.e., they do not exhibit significant velocity bias. The small-scale (100 kpc to 1 Mpc) halo correlation function in both models is well described by the power law ξ r-1.7 and is in good agreement with observations. It is slightly antibiased (b≈0.7-0.9) relative to the dark matter. To test other galaxy statistics, we use the maximum of the halo rotation velocity and the Tully-Fisher relation to assign luminosity to the halos. For two cosmological models, a flat model with the cosmological constant and Ω0=1-ΩΛ=0.3,h=0.7 and a model with a mixture of cold and hot dark matter and Ω0=1.0,Ων=0.2,h=0.5, we construct luminosity functions and evaluate mass-to-light ratios in groups. Both models produce luminosity functions and mass-to-light ratios ( ~200-400) that are in reasonable agreement with observations. The latter implies that the mass-to-light ratio in galaxy groups (at least for Mvir 3 × 1013 h-1 M☉ analyzed here) is not a good indicator of Ω0.

The large-scale bias of dark matter halos: numerical calibration and model tests

We measure the clustering of dark matter halos in a large set of collisionless cosmological simulations of the flatCDM cosmology. Halos are identified using the spherical over density algorithm, which finds the mass around isolated peaks in the density field such that the m ean density istimes the background. We calibrate fitting functions for the large scale bias that are adaptable to any value ofwe examine. We find a � 6% scatter about our best fit bias relation. Our fitting functi ons couple to the halo mass functions of Tinker et. al. (2008) such that bias of all dark matter is normalized to unity. We demonstrate that the bias of massive, rare halos is higher than that predicted in the modified ellip soidal collapse model of Sheth, Mo, & Tormen (2001), and approaches the predictions of the spherical collapse model for the rarest halos. Halo bias results based on friends-of-friends halos identified with linking l ength 0.2 are systematically lower than for halos with the canonical � = 200 overdensity by � 10%. In contrast to our previous results on the mass function, we find that the universal bias function evolves very weakly with redshift, if at all. We use our numerical results, both for the mass function and the bias relation, to test the peak- background split model for halo bias. We find that the peak-background split achieves a reasonable agreement with the numerical results, but � 20% residuals remain, both at high and low masses. Subject headings:cosmology:theory — methods:numerical — large scale structure of the universe

Haloes gone MAD: The Halo-Finder Comparison Project

We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends, spherical-overdensity and phase-space-based algorithms. We

MultiDark simulations: the story of dark matter halo concentrations and density profiles

Accurately predicting structural properties of dark matter halos is one of the fundamental goals of modern cosmology. We use the new suite of MultiDark cosmological simulations to study the evolution of dark matter halo density profiles, concentrations, and velocity anisotropies. The MultiDark simulations cover a large range of masses 1e10-1e15Msun and volumes upto 50Gpc**3. The total number of dark matter halos in all the simulations exceeds 60 billion. We find that in order to understand the structure of dark matter halos and to make ~1% accurate predictions for density profiles, one needs to realize that halo concentration is more complex than the traditional ratio of the virial radius to the core radius in the NFW profile. For massive halos the averge density profile is far from the NFW shape and the concentration is defined by both the core radius and the shape parameter alpha in the Einasto approximation. Combining results from different redshifts, masses and cosmologies, we show that halos progress through three stages of evolution. (1) They start as rare density peaks that experience very fast and nearly radial infall. This radial infall brings mass closer to the center producing a high concentrated halo. Here, the halo concentration increases with the increasing halo mass and the concentration is defined by the alpha parameter with nearly constant core radius. Later halos slide into (2) the plateau regime where the accretion becomes less radial, but frequent mergers still affect even the central region. Now the concentration does not depend on halo mass. (3) Once the rate of accretion slows down, halos move into the domain of declining concentration-mass relation because new accretion piles up mass close to the virial radius while the core radius is staying constant. We provide accurate analytical fits to the numerical results for halo density profiles and concentrations.

The structure of voids

Using high resolution N-body simulations we address the problem of emptiness of giant � 20h −1 Mpc–diameter voids found in the distribution of bright galaxies. Are the voids filled by dwarf galaxies? Do cosmological models predict too many small dark matter haloes inside the voids? Can the problems of cosmological models on small scales be addressed by studying the abundance of dwarf galaxies inside voids? We find that voids in the distribution of 10 12 h −1 M⊙ haloes (expected galactic magnitudes � M∗) are almost the same as the voids in 10 11 h −1 M⊙ haloes. Yet, much smaller haloes with masses 10 9 h −1 M⊙ and circular velocities vcirc � 20 km/s readily fill the voids: there should be almost 1000 of these haloes in a 20h −1 Mpc–diameter void. A typical void of diameter 20h −1 Mpc contains about 50 haloes with vcirc > 50 km/s. The haloes are arranged in a pattern, which looks like a miniature Universe: it has the same structural elements as the large-scale structure of the galactic distribution of the Universe. There are filaments and voids; larger haloes are at the intersections of filaments. The only difference is that all masses are four orders of magnitude smaller. There is severe (anti)bias in the distribution of haloes, which depends on halo mass and on the distance from the centre of the void. Large haloes are more antibiased and have a tendency to form close to void boundaries. The mass function of haloes in voids is different from the “normal” mass function. It is much steeper for high masses resulting in very few M33-type galaxies (vcirc � 100 km/s). We present an analytical approximation for the mass function of haloes in voids.

Merging History as a Function of Halo Environment

According to the hierarchical scenario, galaxies form via merging and accretion of small objects. Using N-body simulations, we study the frequency of merging events in the history of the halos. We find that at z 2 the merging rate of the overall halo population can be described by a simple power law, (1 + z)3. The main emphasis of this paper is on the effects of environment of halos at the present epoch (z = 0). We find that the halos located inside clusters have formed earlier (Δz ≈ 1) than isolated halos of the same mass. At low redshifts (z < 1), the merger rate of cluster halos is 3 times lower than that of isolated halos and twice as low as that of halos that end up in groups by z = 0. At higher redshifts (z ~ 1-4), progenitors of cluster and group halos have 3-5 times higher merger rates than isolated halos. We briefly discuss the implications of our results for galaxy evolution in different environments.

Density Profiles of ΛCDM Clusters

We analyze the mass accretion histories (MAHs) and density profiles of cluster-size halos with virial masses of 0.6 - 2.5 × 10 14 h -1 M⊙ in a flatCDM cosmology. We find that most MAHs have a similar shape: an early, merger-dominated mass increase followed by a more gradual, accretion-dominated growth. For some clusters the intense merger activity and rapid mass growth continue until the present-day epoch. In agreement with previous studies, we find that the concentration of the density distri bution is tightly correlated with the halos MAH and with its formation redshift. During the period of fast mass growth the concentration remains approximately constant and low cv ≈ 3 - 4, while during the slow accretion stages the concentration increases with decreasing redshift as cv ∝ (1 + z) -1 . We consider fits of three widely discussed analytic density profiles to the simulated clusters focusing on the most relaxed inner regions. We find that there is no unique best fit analytic profile for all the systems. At the same time, if a cluster is best fit by a particul ar analytic profile at z = 0, the same is usually true at earlier epochs out to z ∼ 1 - 2. The local logarithmic slope of the density profiles at 3% of the virial radius ranges from -1.2 to -2.0, a remarkable diversity for the relatively narrow mass range of our cluster sample. Interestingly, for all the studied clusters the logarithmic slope becomes s hallower with decreasing radius without reaching an asymptotic value down to the smallest resolved scale (. 1% of the virial radius). We do not find a clear correlation of the inner slope with the formation redshift or the shape of the halos MAH. We do find, however, that during the period of rapid mass growth the density profiles can be wel l described by a single power law �(r) ∝ r - with ∼ 1.5 - 2. The relatively shallow power law slopes result in low concentrations at these stages of evolution, as the scale radius where the density profiles reaches the slo pe of -2 is at large radii. This indicates that the inner power law like density distribution of halos is built u p during the periods of rapid mass accretion and active merging, while outer steeper profile is formed when the mass a ccretion slows down. To check the convergence and robustness of our conclusions, we resimulate one of our clusters using eight times more particles and twice better force resolution. We find good agreement between the t wo simulations in all of the results discussed in our study. Subject headings: cosmology: theory - dark matter - clusters: formation - clusters - structure methods: numerical

THE VELOCITY FUNCTION IN THE LOCAL ENVIRONMENT FROM ΛCDM AND ΛWDM CONSTRAINED SIMULATIONS

Using constrained simulations of the local universe for generic cold dark matter (CDM) and for 1 keV warm dark matter (WDM), we investigate the difference in the abundance of dark matter halos in the local environment. We find that the mass function (MF) within 20 h –1 Mpc of the Local Group is ~2 times larger than the universal MF in the 109-1013 h –1 M ☉ mass range. Imposing the field of view of the ongoing H I blind survey Arecibo Legacy Fast ALFA (ALFALFA) in our simulations, we predict that the velocity function (VF) in the Virgo-direction region (VdR) exceeds the universal VF by a factor of 3. Furthermore, employing a scheme to translate the halo VF into a galaxy VF, we compare the simulation results with a sample of galaxies from the early catalog release of ALFALFA. We find that our simulations are able to reproduce the VF in the 80-300 km s-1 velocity range, having a value ~10 times larger than the universal VF in the VdR. In the low-velocity regime, 35-80 km s-1, the WDM simulation reproduces the observed flattening of the VF. In contrast, the simulation with CDM predicts a steep rise in the VF toward lower velocities; for V max = 35 km s-1, it forecasts ~10 times more sources than the ones observed. If confirmed by the complete ALFALFA survey, our results indicate a potential problem for the CDM paradigm or for the conventional assumptions about energetic feedback in dwarf galaxies.

The Aspen–Amsterdam void finder comparison project

Despite a history that dates back at least a quarter of a century studies of voids in the large–scale structure of the Universe are bedevilled by a major problem: there exist a large number of quite different void–finding algorithms, a fact that has so far got in the way of groups comparing their results without worrying about whether such a comparison in fact makes sense. Because of the recent increased interest in voids, both in very large galaxy surveys and in detailed simulations of cosmic structure formation, this situation is very unfortunate. We here present the first systematic comparison study of thirteen different void finders constructed using particles, haloes, and semi– analytical model galaxies extracted from a subvolume of the Millennium simulation. The study includes many groups that have studied voids over the past decade. We show their results and discuss their differences and agreements. As it turns out, the basic results of the various methods agree very well with each other in that they all locate a major void near the centre of our volume. Voids have very underdense centres, reaching below 10 percent of the mean cosmic density. In addition, those void finders that allow for void galaxies show that those galaxies follow similar trends. For example, the overdensity of void galaxies brighter than mB = 20 is found to be smaller than about 0.8 by all our void finding algorithms.