Abstract
The abundance of cosmic voids can be described by an analogue of halo mass functions for galaxy clusters. In this work, we explore a number of void mass functions: from those based on excursion-set theory to new mass functions obtained by modifying halo mass functions. We show how different void mass functions vary in their predictions for the largest void expected in an observational volume, and compare those predictions to observational data. Our extreme-value formalism is shown to be a new practical tool for testing void theories against simulation and observation.
Highlights
Are very sensitive to the detail on the particular way that voids are defined and detected
The primary aim of this work was to explore analytic void mass-functions and compare their predictions for the largest void expected in a given observational volume
We proposed using void mass functions which are derived from halo mass functions such as those of Press-Schechter, Sheth-Tormen and Tinker et al
Summary
We summarise key concepts and equations in the exact extreme-value formalism for cosmic voids. From Eq (2.1), we can construct the probability density function (pdf) for voids with radius in the infinitesimal interval [R, R + dR], in the redshift bin centred z, width ∆z, as f (R, z) = fsky z+∆z/2 dV 1 dn dz. Consider N observations of voids drawn from the distribution with cdf F (R, z) from a bin centred at redshift z. [It should be understood that all our pdfs and cdfs are redshift dependent, so for convenience we will just write F (R) to mean F (R, z).] We ask: what is the probability that the largest void observed will have radius R∗? Starting with the void mass function, dn/dln R, one can derive the pdf of extreme voids (2.5). We discuss a range of multiplicity functions, f (ν), in equation (2.7)
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