Combining spectroscopic and photometric surveys using angular
  cross-correlations II: Parameter constraints from different physical effects
  Future spectroscopic and photometric surveys will measure accurate positions
and shapes of an increasing number of galaxies. In the previous paper of this
series we studied the effects of Redshift Space Distortions (RSD), baryon
acoustic oscillations (BAO) and Weak gravitational Lensing (WL) using angular
cross-correlation. Here, we provide a new forecast that explores the
contribution of including different observables, physical effects (galaxy bias,
WL, RSD, BAO) and approximations (non-linearities, Limber approximation,
covariance between probes). The radial information is included by using the
cross-correlation of separate narrow redshift bins. For the auto correlation
the separation of galaxy pairs is mostly transverse, while the
cross-correlations also includes a radial component. We study how this
information adds to our figure of merit (FoM), which includes the dark energy
equation of state $w(z)$ and the growth history, parameterized by $\gamma$. We
show that the Limber approximation and galaxy bias are the most critical
ingredients to the modelling of correlations. Adding WL increases our FoM by
4.8, RSD by 2.1 and BAO by 1.3. We also explore how overlapping surveys perform
under the different assumption and for different figures of merit. Our
qualitative conclusions depend on the survey choices and scales included, but
we find some clear tendencies that highlight the importance of combining
different probes and can be used to guide and optimise survey strategies.
