Predicting Supermassive Black Hole Mass with Machine Learning Methods

It is crucial to measure the mass of supermassive black holes (SMBHs) in understanding the co-evolution between the SMBHs and their host galaxies. Previous methods usually require spectral data which are expensive to obtain. We use the AGN catalog from the Sloan Digital Sky Survey project Data Release 7 (DR7) to investigate the correlations between SMBH mass and their host galaxy properties. We apply the machine learning algorithms, such as Lasso regression, to establish the correlation between the SMBH mass and various photometric properties of their host galaxies. We find an empirical formula that can predict the SMBH mass according to galaxy luminosity, colors, surface brightness, and concentration. The root-mean-square error is 0.5 dex, comparable to the intrinsic scatter in SMBH mass measurements. The 1 sigma scatter in the relation between the SMBH mass and the combined galaxy properties relation is 0.48 dex, smaller than the scatter in the SMBH mass versus galaxy stellar mass relation. This relation could be used to study the SMBH mass function and the AGN duty cycles in the future.