Wide angle effects for peculiar velocities

The line-of-sight peculiar velocities of galaxies contribute to their observed redshifts, breaking the translational invariance ofgalaxy clustering down to a rotational invariance around the observer. This becomes important when the line-of-sight directionvaries significantly across a survey, leading to what are known as ‘wide-angle’ effects in redshift-space distortions. Wide-angleeffects will also be present in measurements of the momentum field, i.e. the galaxy density-weighted velocity field, in upcomingpeculiar velocity surveys. In this work, we study how wide-angle effects modify the predicted correlation function and powerspectrum for momentum statistics, both in autocorrelation and in cross-correlation with the density field. Using both lineartheory and the Zel’dovich approximation, we find that deviations from the plane-parallel limit are large and could becomeimportant in data analysis for low-redshift surveys. We point out that even multipoles in the cross-correlation between densityand momentum are non-zero regardless of the choice of line of sight, and therefore contain new cosmological information thatcould be exploited. We discuss configuration space, Fourier space, and spherical analyses; providing exact expressions in eachcase rather than relying on an expansion in small angles. We hope these expressions will be of use in the analysis of upcomingsurveys for redshift-space distortions and peculiar velocities