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 study the dependence of the VPF on cosmological parameters, on the power spectrum of primordial fluctuations, and on assumptions about galaxy formation. 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. We find that the VPF is insensitive to the cosmic density parameter Ω0 and the cosmological constant λ0, provided that fluctuations are normalized to a fixed rms amplitude on scales | 8 h^-1| Mpc. In the absence of biasing, the VPF is also insensitive to the shape of the initial power spectrum. The VPF does depend on the prescription adopted for biased galaxy formation, in the obvious sense that a scheme that more efficiently suppresses galaxy formation in low-density regions leads to larger voids. 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, the ratio of rms galaxy fluctuations to rms mass fluctuations. 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 not require strong biasing; Gaussian models in which galaxies trace mass can reproduce the VPF data to within errors expected from the current finite volume fluctuations. Models with the moderate biasing predicted by cosmological simulations that incorporate 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.