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

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•~10⁴ M_. Based on the active galactic nuclei (AGNs) with a detected broad Hα emission line, we construct a sample of 14,242 AGNs at redshift $z<0.35$, including 243 IMBHs with M•<10⁶ M_. By jointly modeling the BHMF and ERDF via the maximum posterior estimation, we find that the BHMF peaks at ~10⁶ M_$ and exhibits a relatively constant value of $10⁻⁴\,{Mpc⁻³\,dex⁻¹}$ 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_>10¹⁰ M_) to lower than ~2% for dwarf galaxies with M_~10⁸ M_. These results suggest that the black hole occupation fraction is expected to be ~50% for low-mass galaxies (M_~108.5--10⁹ M_) if the duty cycle is similar IMBHs and supermassive black holes.