Redshift-space distortions around voids

We have derived estimators for the linear growth rate of density fluctuations using the cross-correlation function (CCF) of voids and haloes in redshift space. In linear theory, this CCF contains only monopole and quadrupole terms. At scales greater than the void radius, linear theory is a good match to voids traced out by haloes; small-scale random velocities are unimportant at these radii, only tending to cause small and often negligible elongation of the CCF near its origin. By extracting the monopole and quadrupole from the CCF, we measure the linear growth rate without prior knowledge of the void profile or velocity dispersion. We recover the linear growth parameter β to 9 per cent precision from an effective volume of 3( h−1Gpc)3 using voids with radius >25 h−1Mpc. Smaller voids are predominantly sub-voids, which may be more sensitive to the random velocity dispersion; they introduce noise and do not help to improve measurements. Adding velocity dispersion as a free parameter allows us to use information at radii as small as half of the void radius. The precision on β is reduced to 5 per cent. Voids show diverse shapes in redshift space, and can appear either elongated or flattened along the line of sight. This can be explained by the competing amplitudes of the local density contrast, plus the radial velocity profile and its gradient. The distortion pattern is therefore determined solely by the void profile and is different for void-in-cloud and void-in-void. This diversity of redshift-space void morphology complicates measurements of the Alcock–Paczynski effect using voids.