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The black hole occupation fraction (focc) defines the fraction of galaxies that harbor central massive black holes (MBHs), irrespective of their accretion activity level. While it is widely accepted that focc is nearly 100% in local massive galaxies with stellar masses M⋆ ≳ 1010 M⊙, it is not yet clear whether MBHs are ubiquitous in less-massive galaxies. In this work, we present new constraints on focc based on over 20 yr of Chandra imaging data for 1606 galaxies within 50 Mpc. We employ a Bayesian model to simultaneously constrain focc and the specific accretion-rate distribution function, p(λ), where the specific accretion rate is defined as λ = LX/M⋆, where LX is the MBH accretion luminosity in the 2─10 keV range. Notably, we find that p(λ) peaks around 1028ergs−1M⊙−1 ; above this value, p(λ) decreases with increasing λ, following a power law that smoothly connects with the probability distribution of bona fide active galactic nuclei. We also find that the occupation fraction decreases dramatically with decreasing M⋆: in high-mass galaxies (M⋆ ≍ 1011−12 M⊙), the occupation fraction is >93% (a 2σ lower limit), and then declines to 66%−7%+8% (1σ errors) between M⋆ ≍ 109−10 M⊙, and to 33%−9%+13% in the dwarf galaxy regime between M⋆ ≍ 108−9 M⊙. Our results have significant implications for the normalization of the MBH mass function over the mass range most relevant for tidal disruption events, extreme mass ratio inspirals, and MBH merger rates that upcoming facilities are poised to explore. 

ABSTRACT We estimate the mass of the intermediate-mass black hole at the heart of the dwarf elliptical galaxy NGC 404 using Atacama Large Millimetre/submillimetre Array (ALMA) observations of the molecular interstellar medium at an unprecedented linear resolution of ≈0.5 pc, in combination with existing stellar kinematic information. These ALMA observations reveal a central disc/torus of molecular gas clearly rotating around the black hole. This disc is surrounded by a morphologically and kinematically complex flocculent distribution of molecular clouds, that we resolve in detail. Continuum emission is detected from the central parts of NGC 404, likely arising from the Rayleigh–Jeans tail of emission from dust around the nucleus, and potentially from dusty massive star-forming clumps at discrete locations in the disc. Several dynamical measurements of the black hole mass in this system have been made in the past, but they do not agree. We show here that both the observed molecular gas and stellar kinematics independently require a ≈5 × 105 M⊙ black hole once we include the contribution of the molecular gas to the potential. Our best estimate comes from the high-resolution molecular gas kinematics, suggesting the black hole mass of this system is 5.5$$^{+4.1}_{-3.8}\times 10^5$$ M⊙ (at the 99 per cent confidence level), in good agreement with our revised stellar kinematic measurement and broadly consistent with extrapolations from the black hole mass–velocity dispersion and black hole mass–bulge mass relations. This highlights the need to accurately determine the mass and distribution of each dynamically important component around intermediate-mass black holes when attempting to estimate their masses.