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, 2000rho_c, 1000rho_c, 500rho_c, 200rho_c and 200rho_b) at all redshifts. We notice that, when expressed in term of the rescaled variable nu, the mass functionfor 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.
Highlights
In the Cold Dark Matter (CDM) model, structures – up to protogalactic scales – form through the amplification of small density fluctuations via gravitational instability (Longair 1998; Springel et al 2005; Mo et al 2010; Angulo et al 2012)
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
In this paper we analysed a set of cosmological simulations in order to study the halo mass function and its dependence on redshift, cosmology and the halo identification method
Summary
In the Cold Dark Matter (CDM) model, structures – up to protogalactic scales – form through the amplification of small density fluctuations via gravitational instability (Longair 1998; Springel et al 2005; Mo et al 2010; Angulo et al 2012). Our major result is that, if haloes are defined using the virial density, and the fitting formula includes a parameter which is related to this – as was done by Sheth & Tormen (1999) – the mass function can be considered universal to within a few percent. In this respect, our findings confirm those of Courtin et al (2011): departures from universality result from ignoring the redshift and cosmology dependance of these quantities. All logarithms where not explicitly stated in the text are in base ten
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