The impact of the redshift-dependent selection effect of halos on the redshift-space power spectrum

Abstract: In a wide-area spectroscopic survey of galaxies, it is nearly impossible to obtain a homogeneous sample of galaxies with respect to galaxy properties such as stellar mass and host halo mass across a range of redshifts. Despite the selection effect, theoretical templates in most analyses assume single tracers when compared with the measured clustering quantities. We demonstrate analytically that the selection effect inevitably introduces a bias in the redshift-space power spectrum on scales from linear to nonlinear scales. To quantitatively assess the impact of the selection effect, we construct mock galaxy catalogs from halos in N-body simulations by selecting halos above redshift-dependent mass thresholds such that the resulting redshift distribution of the halos, $n(z)$, matches that of SDSS-like galaxies. We find that the selection effect causes fractional changes of up to only 1% and 2% in the monopole and quadrupole moments of the redshift-space power spectrum at $k\lesssim 0.3~h{\rm{Mpc}}^{-1}$, respectively, compared to the moments for the single mass-threshold (therefore single tracer) sample, for $n_{\rm g}(z)$ of the SDSS-like galaxy samples. We also argue that the selection effect is unlikely to cause a significant bias in the estimation of cosmological parameters using the Fisher matrix method, provided that the redshift-dependent selection effect is modest.