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 H emission line, we construct a sample of 14, 242 AGNs at redshift z10^10 M_) to lower than 2% for dwarf galaxies with M₁0⁸ M_. These results suggest that the black hole occupation fraction is expected to be 50% for low-mass galaxies (M₁0^8. 5--10⁹ M_) if the duty cycle is similar IMBHs and supermassive black holes.