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 • ∼ 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 between IMBHs and supermassive black holes.