The Galaxy Activity, Torus, and Outflow Survey (GATOS). Black hole mass estimation using machine learning

The detailed feeding and feedback mechanisms of Active Galactic Nuclei (AGN) are not yet well known. For low-luminosity and obscured AGN, as well as late-type galaxies, determining the central black hole (BH) masses is challenging. Our goal with the GATOS sample is to study circum-nuclear regions and better estimate BH masses with more precision than scaling relations offer. Using ALMA's high spatial resolution, we resolve CO(3-2) emissions within ~100 pc around the supermassive black hole (SMBH) in seven GATOS galaxies to estimate their BH masses when sufficient gas is present. We study seven bright ($L_{AGN}(14-150\mathrm{keV}) \geq 10^{42}\mathrm{erg/s}$), nearby (<28 Mpc) galaxies from the GATOS core sample. For comparison, we searched the literature for previous BH mass estimates and made additional calculations using the \mbh~ - $\sigma$ relation and the fundamental plane of BH activity. We developed a supervised machine learning method to estimate BH masses from position-velocity diagrams or first-moment maps using ALMA CO(3-2) observations. Numerical simulations with a wide range of parameters created the training, validation, and test sets. Seven galaxies provided enough gas for BH mass estimations: NGC4388, NGC5506, NGC5643, NGC6300, NGC7314, NGC7465, and NGC~7582. Our BH masses, ranging from 6.39 to 7.18 log$(M_{BH}/M_\odot)$, align with previous estimates. Additionally, our machine learning method provides robust error estimations with confidence intervals and offers greater potential than scaling relations. This work is a first step toward an automated \mbh estimation method using machine learning.