Redshift-space distortions from vector perturbations II: Anisotropic
  signal
  We study the impact on the galaxy correlation function of the presence of a
vector component in the tracers' peculiar velocities, in the case in which
statistical isotropy is violated. We present a general framework - based on the
bipolar spherical harmonics expansion - to study this effect in a model
independent way, without any hypothesis on the origin or the properties of
these vector modes. We construct six new observables, that can be directly
measured in galaxy catalogs in addition to the standard monopole, quadrupole
and hexadecapole, and we show that they completely describe any deviations from
isotropy. We then perform a Fisher analysis in order to quantify the
constraining power of future galaxy surveys. As an example, we show that the
SKA2 would be able to detect anisotropic rotational velocities with amplitudes
as low as 1% of that of the vorticity generated during shell-crossing in
standard dark matter scenarios.
