Multi-wavelength constraints on the local black hole occupation fraction

The fraction of dwarf galaxies hosting central, intermediate-mass black holes (IMBHs) at low redshifts is an important observational probe of black hole seeding at high redshift. Detections of nuclear accretion signatures in dwarf galaxies provides strong evidence for the presence of these IMBHs. We develop a Bayesian model to infer the black hole occupation fraction assuming a broken power law Eddington ratio distribution function. Our approach accounts for non-detections, incompleteness, and contamination from star-forming-related emission. We apply this model to galaxies with X-ray data from the Chandra Source Catalog at distances $<50$ Mpc, radio data from the VLA Sky Survey at $< 50$ Mpc, and optical variability data from the Palomar Transient Factory at $z<0.055$. We find a black hole occupation fraction of at least $90$ percent at stellar masses of $M_{\star}=10^8~M_{\odot}$ and at least $39$ percent at $M_{\star} = 10^7~M_{\odot}$ (95\% confidence intervals). We show the resulting black hole mass function. These constraints on the IMBH population have implications for the Laser Interferometer Space Antenna (LISA) mission and for cosmological models of black hole seeding and growth. We also constrain the extremely low luminosity end ($L_{\rm{bol}}\lesssim10^{40}$ erg s$^{-1}$) of the AGN luminosity functions at $z=0$. Our AGN luminosity functions are broadly consistent with an extrapolation of the shallow slope of the AGN luminosity functions from previous work.