The virialized mass of dark matter haloes
Abstract
Virial mass is used as an estimator for the mass of a dark matter halo. However, the commonly used constant overdensity criterion does not reflect the dynamical structure of haloes. Here, we analyse dark matter cosmological simulations in order to obtain properties of haloes of different masses focusing on the size of the region with zero mean radial velocity. Dark matter inside this region is stationary, and thus the mass of this region is a much better approximation for the virial mass. We call this mass the static mass to distinguish from the commonly used constant overdensity mass. We also study the relation of this static mass with the traditional virial mass, and we find that the matter inside galaxysized haloes (M ~ 10^{12}M_{solar}) is underestimated by the virial mass by nearly a factor of 2. At z ~ 0, the virial mass is close to the static mass for clustersized haloes (M ~ 10^{14}M_{solar}). The same pattern  large haloes having M_{vir} > M_{static}  exists at all redshifts, but the transition mass M_{0} = M_{vir} = M_{static} decreases dramatically with increasing redshift: M_{0}(z) ~ 3 × 10^{15}h^{1}M_{solar} (1 + z)^{8.9}. When rescaled to the same M_{0} haloes clearly demonstrate a selfsimilar behaviour, which in a statistical sense gives a relation between the static and virial mass. To our surprise, we find that the abundance of haloes with a given static mass, i.e. the static mass function, is very accurately fitted by the Press & Schechter approximation at z = 0, but this approximation breaks at higher redshifts z ~= 1. Instead, the virial mass function is well fitted as usual by the Sheth & Tormen approximation even at z <~ 2. We find an explanation why the static radius can be two to three times larger as compared with the constant overdensity estimate. The traditional estimate is based on the tophat model, which assumes a constant density and no rms velocities for the matter before it collapses into a halo. Those assumptions fail for small haloes, which find themselves in an environment where density is falling off well outside the virial radius and random velocities grow due to other haloes. Applying the nonstationary Jeans equation, we find that the role of the pressure gradients is significantly larger for small haloes. At some moment, it gets too large and stops the accretion.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 2008
 DOI:
 10.1111/j.13652966.2008.13590.x
 arXiv:
 arXiv:0710.5520
 Bibcode:
 2008MNRAS.389..385C
 Keywords:

 methods: Nbody simulations;
 galaxies: haloes;
 cosmology: theory;
 dark matter;
 largescale structure of Universe;
 Astrophysics
 EPrint:
 14 pages, 16 figures, accepted for publication in MNRAS. v2: Evolution of static mass function and some other minor changes added to match the accepted version