On an Analytical Framework for Voids: Their abundances, density profiles
and local mass functions
(2004)cite arxiv:astro-ph/0407513
Comment: 14 pages, 7 figures, MNRAS in press.Abstract
We present a general analytical procedure for computing the number density of
voids with radius above a given value within the context of gravitational
formation of the large scale structure of the universe out of Gaussian initial
conditions. To this end we develop an accurate (under generally satisfied
conditions) extension of unconditional mass function to constrained
environments, which allowes us both to obtain the number density of collapsed
objects of certain mass at any distance from the center of the void, and to
derive the number density of voids defined by those collapsed objects. We have
made detailed calculations for the spherically averaged mass density and halo
number density profiles for individual voids. We also present a formal
expression for the number density of voids defined by galaxies of a given type
and luminosity. This expression contains the probability for a collapsed object
of certain mass to host a galaxy of that type and luminosity as a function of
the environmental density. We propose a procedure to infer this function, which
may provide useful clues as to the galaxy formation process, from the observed
void densities.
Description
On an Analytical Framework for Voids: Their abundances, density profiles
and local mass functions