Cosmic voids and biased galaxy formation

Using cosmological $N$-body simulations and the void probability function(VPF), we investigate the statistical properties of voids within a wide rangeof initially Gaussian models for the origin of large-scale structure. We payparticular attention to the ability of the VPF to diagnose `biased galaxyformation': the preferential formation of galaxies in regions of highbackground density and corresponding suppression of galaxy formation in regionsof low background density. Biased models have systematically higher VPFs thanunbiased models, but for a given biasing scheme the VPF is relativelyinsensitive to the value of the bias factor $b$. Thus, while the VPF candistinguish unbiased models from some biased models, it is probably not auseful way to constrain the bias factor; uncertainties in the appropriatechoice of biasing prescription overwhelm the mild dependence on $b$. We comparethe predictions of our models to the most extensive VPF observations publishedto date. These data do {\it not} require strong biasing; Gaussian models inwhich galaxies trace mass can reproduce the VPF data to within the errorsexpected from the current finite volume fluctuations. Models with the moderatebiasing predicted by cosmological simulations with gas dynamics yield aslightly better match to the data. Models in which galaxy formation is stronglysuppressed in low density regions produce an excess of large, empty voids.Comment: TeX + epsf, 36 pages incl. 11 eps figures, subm. to MNRA