Redshift-space distortions from the cross-correlation of photometric
  populations
  Several papers have recently highlighted the possibility of measuring
redshift space distortions from angular auto-correlations of galaxies in
photometric redshift bins. In this work we extend this idea to include as
observables the cross-correlations between redshift bins, as an additional way
of measuring radial information. We show that this extra information allows to
reduce the recovered error in the growth rate index \gamma by a factor of ~2.
Although the final error in \gamma depends on the bias and the mean photometric
accuracy of the galaxy sample, the improvement from adding cross-correlations
is robust in different settings. Another factor of 2-3 improvement in the
determination of \gamma can be achieved by considering two galaxy populations
over the same photometric sky area but with different biases. This additional
gain is shown to be much larger than the one from the same populations when
observed over different areas of the sky (with twice the combined area). The
total improvement of ~5 implies that a photometric survey such as the Dark
Energy Survey should be able to recover \gamma at the 5-10% from the angular
clustering in linear scales of two different tracers. It can also constrain the
evolution of f(z)x\sigma_8(z) in few bins beyond z~0.8-0.9 at the 10-15% level
per-bin, compatible with recent constrains from lower-z spectroscopic surveys.
We also show how further improvement can be achieved by reducing the
photometric redshift error.
