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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 range of initially Gaussian models for the origin of large-scale structure. We pay particular attention to the ability of the VPF to diagnose `biased galaxy formation': the preferential formation of galaxies in regions of high background density and corresponding suppression of galaxy formation in regions of low background density. Biased models have systematically higher VPFs than unbiased models, but for a given biasing scheme the VPF is relatively insensitive to the value of the bias factor $b$. Thus, while the VPF can distinguish unbiased models from some biased models, it is probably not a useful way to constrain the bias factor; uncertainties in the appropriate choice of biasing prescription overwhelm the mild dependence on $b$. We compare the predictions of our models to the most extensive VPF observations published to date. These data do {\it not} require strong biasing; Gaussian models in which galaxies trace mass can reproduce the VPF data to within the errors expected from the current finite volume fluctuations. Models with the moderate biasing predicted by cosmological simulations with gas dynamics yield a slightly better match to the data. Models in which galaxy formation is strongly suppressed in low density regions produce an excess of large, empty voids.