The miniJPAS survey: AGN & host galaxy co-evolution of X-ray selected sources

Studies indicate strong evidence of a scaling relation in the local Universe between the supermassive black hole mass (M_\rm{BH}) and the stellar mass of their host galaxies ($M_\star$). They even show similar histories across cosmic times of their differential terms: star formation rate (SFR) and black hole accretion rate (BHAR). However, a clear picture of this coevolution is far from being understood. We select an X-ray sample of active galactic nuclei (AGN) up to $z=2.5$ in the miniJPAS footprint. Their X-ray to infrared spectral energy distributions (SEDs) have been modeled with CIGALE, constraining the emission to 68 bands. For a final sample of 308 galaxies, we derive their physical properties (e.g., $M_\star$, $\rm{SFR}$, $\rm{SFH}$, and L_\rm{AGN}). We also fit their optical spectra for a subsample of 113 sources to estimate the M_\rm{BH}. We calculate the BHAR depending on two radiative efficiency regimes. We find that the Eddington ratios ($\lambda$) and its popular proxy (L_\rm{X}/$M_\star$) have 0.6 dex of difference, and a KS-test indicates that they come from different distributions. Our sources exhibit a considerable scatter on the M_\rm{BH}-$M_\star$ relation, which can explain the difference between $\lambda$ and its proxy. We also model three evolution scenarios to recover the integral properties at $z=0$. Using the SFR and BHAR, we show a notable diminution in the scattering between M_\rm{BH}-$M_\star$. For the last scenario, we consider the SFH and a simple energy budget for the AGN accretion, obtaining a relation similar to the local Universe. Our study covers $\sim 1$ deg$^2$ in the sky and is sensitive to biases in luminosity. Nevertheless, we show that, for bright sources, the link between SFR and BHAR, and their decoupling based on an energy limit is the key that leads to the local M_\rm{BH}-$M_\star$ scaling relation.