Combining spectroscopic and photometric surveys using angular cross-correlations - III. Galaxy bias and stochasticity

In the first paper of this series, we studied the effect of baryon acoustic oscillations (BAO), redshift space distortions (RSD), and weak lensing (WL) on measurements of angular cross-correlations in narrow redshift bins. The second paper presented a multi-tracer forecast as Figures of Merits (FoMs), combining a photometric and a spectroscopic stage-IV survey. The uncertainties from galaxy bias, the way light traces mass, is an important ingredient in the forecast. Fixing the bias would increase our main FoM equivalent to 3.3 times larger area for the combined constraints. This paper focuses on how modelling the galaxy bias affects the forecast. In the combined forecast, lensing both helps and benefits from the improved bias measurements in overlapping surveys after marginalizing over the cosmological parameters. Adding a second lens population in counts-shear does not have a large impact on bias error, but removing all counts-shear information increases the bias error in a significant way. We also discuss the relative impact of WL, magnification, RSD, and BAO, and how results change as a function of the bias amplitude, photo-z error, and sample density. Bias stochasticity, even when added as one new free parameter per bin, only produces moderate decrease in the FoM. In general, we find that the degradation in the figure of merit caused by the uncertainties in the knowledge of bias is significantly smaller for overlapping surveys.