Measuring cosmic velocities with 21cm intensity mapping and galaxy redshift survey cross-correlation dipoles

We investigate the feasibility of measuring the effects of peculiar velocities in large-scale structure using the dipole of the redshift-space cross-correlation function. We combine number counts of galaxies with brightness-temperature fluctuations from 21cm intensity mapping, demonstrating that the dipole may be measured at modest significance ($\lesssim 2\sigma$) by combining the upcoming radio survey CHIME with the future redshift surveys of DESI and Euclid. More significant measurements ($\lesssim~10\sigma$) will be possible by combining intensity maps from the SKA with these of DESI or Euclid, and an even higher significance measurement ($\lesssim 100\sigma$) may be made by combining observables completely internally to the SKA. We account for effects such as contamination by wide-angle terms, interferometer noise and beams in the intensity maps, non-linear enhancements to the power spectrum, stacking multiple populations, sensitivity to the magnification slope, and the possibility that number counts and intensity maps probe the same tracers. We also derive a new expression for the covariance matrix of multi-tracer redshift-space correlation function estimators with arbitrary orientation weights, which may be useful for upcoming surveys aiming at measuring redshift-space clustering with multiple tracers.