CFHTLenS: Galaxy bias as function of scale, stellar mass, and colour. Conflicts with predictions by semi-analytic models

Galaxy models predict a tight relation between the clustering of galaxies and dark matter on cosmological scales, but predictions differ notably in the details. We used this opportunity and tested two semi-analytic models by the Munich and Durham groups with data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). For the test we measured the scale-dependent galaxy bias factor $b(k)$ and correlation factor $r(k)$ from linear to non-linear scales of $k\approx 10h\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$ at two redshifts $\bar{z}=0.35,0.51$ for galaxies with stellar mass between $5\times {10}^9$ and $3\times {10}^{11}{h}_{70}^{-2}{\mathrm{M}}_{\odot }$. Our improved gravitational lensing technique accounts for the intrinsic alignment of sources and the magnification of lens galaxies for better constraints for the galaxy-matter correlation $r(k)$. Galaxy bias in CFHTLenS increases with $k$ and stellar mass, it is colour-dependent, revealing the individual footprints of galaxy types. Despite a reasonable model agreement for the relative change with both scale and galaxy properties, there is a clear conflict for $b(k)$ with no model preference: the model galaxies are too weakly clustered. This may flag a model problem at $z\gtrsim 0.3$ for all stellar masses. As in the models, however, there is a high correlation $r(k)$ between matter and galaxy density on all scales, and galaxy bias is typically consistent with a deterministic bias on linear scales. Only our blue and low-mass galaxies of about $7\times {10}^9{h}_{70}^{-2}{\mathrm{M}}_{\odot }$ at $\bar{z}=0.51$ show, contrary to the models, a weak tendency towards a stochastic bias on linear scales where $r_{\mathrm{l}\mathrm{s}}=0.75\pm 0.14(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.06(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{.})$. This result is of interest for cosmological probes, such as $E_{\mathrm{G}}$, that rely on a deterministic galaxy bias.