Void Ellipticity Distribution as a Probe of Cosmology

Cosmic voids refer to the large empty regions in the Universe with a very low number density of galaxies. Voids are likely to be severely disturbed by the tidal effect from the surrounding dark matter. We derive a completely analytic model for the void ellipticity distribution from physical principles. We use the spatial distribution of galaxies in a void as a measure of its shape, tracking the trajectory of the void galaxies under the influence of the tidal field using Lagrangian perturbation theory. Our model implies that the void ellipticity distribution depends sensitively on the cosmological parameters. Testing our model against the high-resolution Millennium Run simulation, we find excellent quantitative agreements of the analytic predictions with the numerical results.

Figure 1

Probability density distributions of the void ellipticity predicted by our analytic model for the four different sets of cosmological parameters at two different smoothing scales: $R_L=5$ and $8{\mathrm{h}}^{-1}\mathrm{Mpc}$ in the upper and the lower panel, respectively. For each case, the void density contrast is set at ${\delta }_v=-0.9$.

Figure 2

Illustration of the four examples of the voids identified in the Millennium Run simulation. Each panel corresponds to the four bins. The shaded regions and the dots represent the areas of the voids and the positions of the void galaxies in them projected onto the two-dimensional plane.

Figure 3

The ellipticity distributions of the voids belonging to the four bins. In each panel the histogram represents the numerical data points from the Millennium Run simulation while the solid line corresponds to the analytic prediction. For the analytic results, the values of the Lagrangian scale radius $R_L$ are evaluated by the relation of $R_L=(1+{\overline{\delta }}_v{)}^{1/3}{\overline{R}}_E$.