In-situ star formation in accretion disk and explanation for correlation between black hole mass and metallicity in AGNs

Recent observations show that the metallicity of the broad line region ($Z_{\mathrm{B}\mathrm{L}\mathrm{R}}$) in active galactic nuclei (AGNs) is solar-to-supersolar, which is positively correlated with the mass of supermassive black holes ($M_{\mathrm{B}\mathrm{H}}$) and does not evolve with redshift up to $z\sim 7$. We revisit the $M_{\mathrm{B}\mathrm{H}}-Z_{\mathrm{B}\mathrm{L}\mathrm{R}}$ correlation with more AGNs with $M_{\mathrm{B}\mathrm{H}}\sim {10}^{6-8}{M}_{\odot }$ and find that the positive correlation become flat in low-mass range. It is known that outer part of accretion disks is gravitationally unstable and can fragment into stars. Considering the star formation and supernovae (SNe) in the outer AGN disk, we calculate the metal enrichment and find that positive $M_{\mathrm{B}\mathrm{H}}-Z_{\mathrm{B}\mathrm{L}\mathrm{R}}$ correlation can be roughly reproduced if the stellar mass distribution is ``top-heavy". We find that the observed BLR size is more or less similar to the self-gravity radius of the AGN disk, which suggests that the BLR may be closely correlated with the underlying accretion process.