Halo mass function

Abstract: High resolution N-body simulations show that the density profiles of dark matter halos formed in the standard CDM cosmogony can be fit accurately by scaling a simple “universal” profile. Regardless of their mass, halos are nearly isothermal over a large range in radius, but significantly shallower than r -2 near the center and steeper than r -2 in the outer regions. The characteristic overdensity of a halo correlates strongly with halo mass in a manner consistent with the mass dependence of the epoch of halo formation. Matching the shape of the rotation curves of disk galaxies with this halo structure requires (i) disk mass-to-light ratios to increase systematically with luminosity, (ii) halo circular velocities to be systematically lower than the disk rotation speed, and (iii) that the masses of halos surrounding bright galaxies depend only weakly on galaxy luminosity. This offers an attractive explanation for the puzzling lack of correlation between luminosity and dynamics in observed samples of binary galaxies and of satellite companions of bright spiral galaxies, suggesting that the structure of dark matter halos surrounding bright spirals is similar to that of cold dark matter halos.

Abstract: The results of numerical simulations of nonlinear gravitational clustering in universes dominated by weakly interacting, 'cold' dark matter are presented. The numerical methods used and the way in which initial conditions were generated are described, and the simulations performed are catalogued. The evolution of the fundamental statistical properties of the models is described and their comparability with observation is discussed. Graphical comparisons of these open models with the observed galaxy distribution in a large redshift survey are made. It is concluded that a model with a cosmological density parameter omega equal to one is quite unacceptable if galaxies trace the mass distribution, and that models with omega of roughly two, while better, still do not provide a fully acceptable match with observation. Finally, a situation in which galaxy formation is suppressed except in sufficiently dense regions is modelled which leads to models which can agree with observation quite well even for omega equal to one.

Abstract: Dark matter haloes are biased tracers of the underlying dark matter distribution. We use a simple model to provide a relation between the abundance of dark matter haloes and their spatial distribution on large scales. Our model shows that knowledge of the unconditional mass function alone is sufficient to provide an accurate estimate of the large-scale bias factor. We then use the mass function measured in numerical simulations of SCDM, OCDM and ΛCDM to compute this bias. Comparison with these simulations shows that this simple way of estimating the bias relation and its evolution is accurate for less massive haloes as well as massive ones. In particular, we show that haloes that are less/more massive than typical M* haloes at the time they form are more/less strongly clustered than is predicted by formulae based on the standard Press–Schechter mass function.

Abstract: We present an analytical description of the merging of virialized haloes which is applicable to any hierarchical model in which structure grows via gravitational instability. The formulae are an extension of the Press-Schechter model. The dependence of the merger rate on halo mass, epoch, the spectrum of initial density fluctuations and the density parameter Ω0 is explicitly quantified. We calculate the distribution of halo formation times and survival times. We also describe a Monte Carlo method for constructing representative histories of merger events leading to formation of haloes of a prescribed mass. Applying these results to the age distribution of rich clusters of galaxies, we infer that a high value of the density parameter (Ω0 ≳ 0.5) is required to reproduce the substantial fraction of rich clusters that exhibit significant substructure, if such substructure only persists for a time 0.2t0 after a merger, where t0 is the present age of the universe. We also investigate the rate of infall of satellite galaxies into galactic discs, by combining our Monte Carlo technique for halo mergers with an estimate of the time required for dynamical friction to erode the orbits of the baryonic cores of the accreted galaxies. We find that, even for Ω0 = 1, the infall rate is low (provided that the satellite orbits are not too eccentric), and that we would expect only a modest fraction of stellar discs to be thickened or disrupted by this process.