The coevolution of supermassive black holes and galaxies in luminous AGN over a wide range of redshift

It is well known that supermassive black holes (SMBHs) and their host galaxies co-evolve. A manifestation of this co-evolution is the correlation that has been found between the SMBH mass, M${}_{BH}$, and the galaxy bulge or stellar mass, M${}_{\ast }$. The cosmic evolution of this relation, though, is still a matter of debate. In this work, we examine the M${}_{BH}-$M${}_{\ast }$ relation, using 687 X-ray luminous (median $\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{L}}_{\mathrm{X},2-10\mathrm{k}\mathrm{e}\mathrm{V}}(\mathrm{e}\mathrm{r}\mathrm{g}{\mathrm{s}}^{-1})]=44.3$), broad line AGN, at $0.2<\mathrm{z}<4.0$ (median $\mathrm{z}\approx 1.4$) that lie in the XMM-{\it{XXL}} field. Their M${}_{BH}$ and M${}_{\ast }$ range from $7.5<\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{M}}_{\mathrm{B}\mathrm{H}}({\mathrm{M}}_{\odot })]<9.5$ and $10<\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{M}}_{\ast }({\mathrm{M}}_{\odot })]<12$, respectively. Most of the AGN live in star-forming galaxies and their Eddington ratios range from 0.01 to 1, with a median value of 0.06. Our results show that M${}_{BH}$ and M${}_{\ast }$ are correlated ($\mathrm{r}=0.47\pm 0.21$, averaged over different redshift intervals). Our analysis also shows that the mean ratio of the M${}_{BH}$ and M${}_{\ast }$ does not evolve with redshift, at least up to $\mathrm{z}=2$ and has a value of $\mathrm{l}\mathrm{o}\mathrm{g}($M${}_{BH}\mathrm{/}$M${}_{\ast })=-2.44$. The majority of the AGN ($75\mathrm{\%}$) are in a SMBH mass growth dominant phase. In these systems, the M${}_{BH}-$M${}_{\ast }$ correlation is weaker and their M${}_{\ast }$ tends to be lower (for the same M${}_{BH}$) compared to systems that are in a galaxy mass growth phase. Our findings suggest that the growth of black hole mass occurs first, while the early stellar mass assembly may not be so efficient.