Optimising the measurement of relativistic distortions in large-scale
  structure
  It has been shown recently that relativistic distortions generate a dipolar
modulation in the two-point correlation function of galaxies. To measure this
relativistic dipole it is necessary to cross-correlate different populations of
galaxies with for example different luminosities or colours. In this paper, we
construct an optimal estimator to measure the dipole with multiple populations.
We show that this estimator increases the signal-to-noise of the dipole by up
to 35 percent. Using 6 populations of galaxies, in a survey with halos and
number densities similar to those of the millennium simulation, we forecast a
cumulative signal-to-noise of 4.4. For the main galaxy sample of SDSS at low
redshift z<0.2 our optimal estimator predicts a cumulative signal-to-noise of
2.4. Finally we forecast a cumulative signal-to-noise of 7.4 in the upcoming
DESI survey. These forecasts indicate that with the appropriate choice of
estimator the relativistic dipole should be detectable in current and future
surveys.
