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