| Summary: | We complete the census of nuclear X-ray activity in 100 early-type Virgo galaxies observed by the Chandra X-ray Telescope as part of the AMUSE-Virgo survey, down to a (3σ) limiting luminosity of 3.7 × 10[superscript 38] erg s[superscript –1] over 0.5-7 keV. The stellar mass distribution of the targeted sample, which is mostly composed of formally "inactive" galaxies, peaks below 10[superscript 10] M ☉, a regime where the very existence of nuclear supermassive black holes (SMBHs) is debated. Out of 100 objects, 32 show a nuclear X-ray source, including 6 hybrid nuclei which also host a massive nuclear cluster as visible from archival Hubble Space Telescope images. After carefully accounting for contamination from nuclear low-mass X-ray binaries based on the shape and normalization of their X-ray luminosity function (XLF), we conclude that between 24% and 34% of the galaxies in our sample host an X-ray active SMBH (at the 95% confidence level). This sets a firm lower limit to the black hole (BH) occupation fraction in nearby bulges within a cluster environment. The differential logarithmic XLF of active SMBHs scales with the X-ray luminosity as L X [superscript –0.4±0.1] up to 10[superscript 42] erg s[superscript –1]. At face value, the active fraction—down to our luminosity limit—is found to increase with host stellar mass. However, taking into account selection effects, we find that the average Eddington-scaled X-ray luminosity scales with BH mass as M BH -0.62 +0.13[over]-0.12, with an intrinsic scatter of 0.46+0.08[subscript –0.06 dex]. This finding can be interpreted as observational evidence for "down-sizing" of BH accretion in local early types, that is, low-mass BHs shine relatively closer to their Eddington limit than higher mass objects. As a consequence, the fraction of active galaxies, defined as those above a fixed X-ray Eddington ratio, decreases with increasing BH mass.
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