Nonlinear Redshift-Space Distortions on the Full Sky

Abstract

We derive an analytic expression for the two-point correlation function in redshift space which (i) is nonlinear; (ii) is valid on the full sky, i.e. the distant-observer limit is not assumed; (iii) can account for the effect of magnification and evolution bias due to a non-uniform selection function; and (iv) respects the fact that observations are made on the past lightcone, so naturally yields unequal-time correlations. Our model is based on an exact treatment of the streaming model in the wide-angle regime. Within this general regime, we find that the redshift-space correlation function is essentially determined by a geometric average of its real-space counterpart. We show that the linear expression for the galaxy overdensity, accurate to subleading order, can be recovered from our nonlinear framework. This work is particularly relevant for the modeling of odd multipoles of the correlation function at small separations and low redshifts, where wide-angle effects, selection effects, and nonlinearities are expected to be equally important.