Studies indicate strong evidence of a scaling relation in the local Universe between the supermassive black hole mass (MBH) and the stellar mass
of their host galaxies (M?). They even show similar histories across cosmic times of their di erential terms: the star formation rate (SFR) and
black hole accretion rate (BHAR). However, a clear picture of this coevolution is far from being understood.We selected 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 the CIGALE code, constraining the emission to 68 bands, from which 54 are the narrow filters from the miniJPAS survey. For a final sample
of 308 galaxies, we derived their physical properties, such as their M?, SFR, star formation history (SFH), and the luminosity produced by the
accretion process of the central BH (LAGN). For a subsample of 113 sources, we also fit their optical spectra to obtain the gas velocity dispersion
from the broad emission lines and estimated the MBH. We calculated the BHAR in physical units depending on two radiative e ciency regimes.
We find that the Eddington ratios ( Edd) and its popular proxy (LX=M?) have a di erence of 0.6 dex, on average, and a KS test indicates that they
come from di erent distributions. Our sources exhibit a considerable scatter on the MBHM? scaling relation, which can explain the di erence
between Edd and its proxy. We also modeled three evolution scenarios for each source to recover the integral properties at z = 0. Using the SFR
and BHAR, we show a notable diminution in the scattering between MBHM?. For the last scenario, we considered the SFH and a simple energy
budget for the AGN accretion, and we retrieved a relation similar to the calibrations known for the local Universe. Our study covers 1 deg2 in
the sky and is sensitive to biases in luminosity. Nevertheless, we show that, for bright sources, the link between the di erential values (SFR and
BHAR) and their decoupling based on an energy limit is the key that leads to the local MBHM? scaling relation. In the future, we plan to extend
this methodology to a thousand degrees of the sky using JPAS with an X-ray selection from eROSITA, to obtain an unbiased distribution of BHAR
and Eddington ratios.
