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

TL;DR

This study constrains the low-mass end of the black hole mass function and active fraction of intermediate-mass black holes using a large AGN sample, revealing a peak at around 10^6 solar masses and low active fractions in dwarf galaxies.

Contribution

It provides the first detailed modeling of the black hole mass function down to 10^4 solar masses and estimates the active fraction across galaxy types, advancing understanding of IMBH demographics.

Findings

BHMF peaks at ~10^6 M_7

Active fraction drops below 2% in dwarf galaxies

Black hole occupation fraction is ~50% in low-mass galaxies

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 $M_{\bullet}\sim10^4 M_\odot$. 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 $10^{-4}\,\mathrm{Mpc^{-3}\,dex^{-1}}$ 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 ($M_\star>10^{10} M_\odot$) to lower than $\sim$2% for dwarf galaxies with $M_\star\sim10^8 M_\odot$. These results suggest that the black hole occupation fraction is expected to be $\sim$50% for low-mass galaxies ($M_\star\sim10^{8.5}$--$10^9 M_\odot$) if the duty cycle is similar IMBHs and supermassive black holes.