Optimal galaxy survey for detecting the dipole in the cross-correlation
  with 21 cm Intensity Mapping
  We investigate the future perspectives of the detection of the relativistic
dipole by cross-correlating the 21 cm emission in Intensity Mapping (IM) and
galaxy surveys at low redshift. We model the neutral hydrogen (HI) and the
galaxy population by means of the halo model to relate the parameters that
affect the dipole signal such as the biases of the two tracers and the
Poissonian noise. We investigate the behavior of the signal-to-noise as a
function of the galaxy and magnification biases, for two fixed models of the
neutral hydrogen. In both cases we found that the signal-to-noise does not grow
by increasing the difference between the biases of the two tracers, due to the
larger shot-noise yields by highly biased tracers. We also study and provide an
optimal luminosity-threshold galaxy catalogue to enhance the signal-to-noise
ratio of the relativistic dipole. Interestingly, we show that the maximum
magnitude provided by the survey does not lead to the maximum signal-to-noise
for detecting relativistic effects and we predict the optimal value for the
limiting magnitude. Our work suggests that an optimal analysis could increase
the signal-to-noise ratio up to a factor five compared to a standard one.
