Linear redshift space distortions for cosmic voids based on galaxies in redshift space

Abstract

Cosmic voids found in galaxy surveys are defined based on the galaxy distribution in redshift space. We show that the large scale distribution of voids in redshift space traces the fluctuations in the dark matter density field $\stackrel{^}{\ensuremath{\delta}}(\mathbit{k})$ (in Fourier space with $\ensuremath{\mu}$ being the line-of-sight projected $\mathbit{k}$ vector), ${\stackrel{^}{\ensuremath{\delta}}}_{\mathrm{v}}^{s}(\mathbit{k})=(1+{\ensuremath{\beta}}_{\mathrm{v}}{\ensuremath{\mu}}^{2}){b}_{\mathrm{v}}^{s}\stackrel{^}{\ensuremath{\delta}}(\mathbit{k})$, with a beta factor that will be, in general, different than the one describing the distribution of galaxies. Only if voids are assumed to be quasilocal transformations of the linear (Gaussian) galaxy redshift space field does one get equal beta factors ${\ensuremath{\beta}}_{\mathrm{v}}={\ensuremath{\beta}}_{\mathrm{g}}=f/{b}_{\mathrm{g}}$ with $f$ being the growth rate and ${b}_{\mathrm{g}}$, ${b}_{\mathrm{v}}^{s}$ being the galaxy and void bias on large scales defined in redshift space. Indeed, in our mock void catalogs, we measure void beta factors in good agreement with the galaxy one. Further work needs to be done to confirm the level of accuracy of the beta factor equality between voids and galaxies, but in general the void beta factor needs to be considered as a free parameter for linear RSD studies.