Density and velocity profiles around cosmic voids
We study the evolution of the cross-correlation between voids and the mass density field - i.e. of void profiles. We show that approaches based on the spherical model alone miss an important contribution to the evolution on large scales of most interest to cosmology: they fail to capture the well-known fact that the large-scale bias factor of conserved tracers evolves. We also show that the operations of evolution and averaging do not commute, but this difference is only significant within about two effective radii. We show how to include a term which accounts for the evolution of bias, which is directly related to the fact that voids move. The void motions are approximately independent of void size, so they are more significant for smaller voids that are typically more numerous. This term also contributes to void-matter pairwise velocities: including it is necessary for modeling the typical outflow speeds around voids. It is, therefore, important for void redshift space distortions. Finally, we show that the excursion set peaks/troughs approach provides a useful, but not perfect framework for describing void profiles and their evolution.