The universality of the virial halo mass function and models for non-universality of other halo definitions

Abstract

The abundance of galaxy clusters can constrain both the geometry and growth of structure in our Universe. However, this probe could be significantly complicated by recent claims of nonuniversality -non-trivial dependences with respect to the cosmological model and redshift. In this work we analyse the dependance of the mass function on the way haloes are identified and establish if this can cause departures from universality. In order to explore this dependance, we use a set of different N-body cosmological simulations (Le SBARBINE simulations), with the latest cosmological parameters from the Planck collaboration; this first suite of simulations is followed by a lower resolution set, carried out with different cosmological parameters. We identify dark matter haloes using a Spherical Overdensity algorithm with varying overdensity thresholds (virial, 2000ρ c , 1000ρ c , 500ρ c , 200ρ c and 200ρ b ) at all redshifts. We notice that, when expressed in term of the rescaled variable ν, the mass function for virial haloes is a nearly universal as a function of redshift and cosmology, while this is clearly not the case for the other overdensities we considered. We provide fitting functions for the halo mass function parameters as a function of overdensity, that allow to predict, to within a few percent accuracy, the halo mass function for a wide range of halo definitions, redshifts and cosmological models. We then show how the departures from universality associated with other halo definitions can be derived by combining the universality of the virial definition with the expected shape of the density profile of halos.

The mass function of unprocessed dark matter haloes and merger tree branching rates

“…Table 1 lists the parameters of the best fit Sheth & Tormen (2002) mass function at z = 0, for cases where backsplash halos are included and excluded (along with results for other redshifts, and for cases where the N-body halo mass error distribution is not accounted for). For the case with backsplash halos included the best fit parameters we find are close to, but significantly different from, those found by Despali et al (2015).…”

“…ν as defined in §1) we expect them to be mostly independent of the choice of cosmological parameters (e.g. Despali et al 2015).…”

“…This parametric form was also used by Despali et al (2015). To find the optimal values of the parameters (a, p, A) we perform a Markov Chain Monte Carlo (MCMC) simulation in which these parameters are allowed to vary.…”

“…In the upper row we show mass functions measured from the MDPL simulation including backsplash halos (green points) and with backsplash halos removed (purple points). The solid blue line indicates the best fit mass function reported by Despali et al (2015), while the green and purple lines indicate the best fit mass functions to our measurements from the MDPL (with backsplash halos included and excluded respectively) using the fitting function of Sheth & Tormen (2002), convolved by the expected N-body halo mass error distribution. Transparent, shaded bands around each line indicate the expected Poisson errors in the N-body data.…”

“…Press & Schechter 1974). Recently, Despali et al (2015) have shown that this choice of density threshold should be preferred as it results in the most universal mass function when expressed in terms of the rescaled mass variable 1 , ν = δc/σ(M ), where δc is the 1 While this is good motivation for choosing a particular definition of halo (it is at least motivated by a simple physical model and, as Despali et al (2015) show, leads to the most universal mass function), it is highly idealized, and there is no notable physical distinction to this radius. It may be more robust therefore to critical linear theory overdensity for a halo to undergo gravitational collapse, and σ(M ) is the amplitude of fluctuations in spheres containing, on average, mass M in the linear density field at the present day.…”