Constraining the Low-Mass End of the Black Hole Mass Function and the Active Fraction of the Intermediate-mass Black Holes

Abstract

We investigate the black hole mass function (BHMF) and the Eddington ratio distribution function (ERDF), focusing on the intermediate-mass black holes (IMBHs) with masses down to $M_{\bullet }\sim 10^4{M}_{\odot }$. Based on the active galactic nuclei (AGNs) with a detected broad H$\alpha$ emission line, we construct a sample of 14,242 AGNs at redshift $z<0.35$, including 243 IMBHs with $M_{\bullet }<10^6{M}_{\odot }$. By jointly modeling the BHMF and ERDF via the maximum posterior estimation, we find that the BHMF peaks at $\sim$$10^6{M}_{\odot }$ and exhibits a relatively constant value of $10^{-4}\mathrm{Mp}{\mathrm{c}}^{-3}\mathrm{de}{\mathrm{x}}^{-1}$ at the low-mass end. By comparing the derived BHMF of type 1 AGNs with the galaxy mass function based on the updated black hole mass--host galaxy stellar mass relation, we derive the active fraction. We also determine the active fraction for all AGNs using the upper and lower limit of the type 1 fraction. The active fraction decreases from 15%--40% for massive galaxies ($M_{\star }>10^{10}{M}_{\odot }$) to lower than $\sim$2% for dwarf galaxies with $M_{\star }\sim 10^8{M}_{\odot }$. These results suggest that the black hole occupation fraction is expected to be $\sim$50% for low-mass galaxies ($M_{\star }\sim 10^{8.5}$--$10^9{M}_{\odot }$) if the duty cycle is similar IMBHs and supermassive black holes.

arXiv comment18 pages, 10 figures

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• Emission Line Diagnostics for IMBHs in Dwarf Galaxies: Accounting for BH Seeding and ULX Excitation