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 ( 3 \sigma ) limiting luminosity of 3.7 \times 10 ^ { 38 } erg s ^ { -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 ^ { 10 } M _ { \odot } , a regime where the very existence of nuclear super-massive 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 , we conclude that between 24 - 34 \% of the galaxies in our sample host a X-ray active SMBH ( at the 95 \% C.L . ) .
This sets a firm lower limit to the black hole occupation fraction in nearby bulges within a cluster environment .
The differential logarithmic X-ray luminosity function of active SMBHs scales with the X-ray luminosity as L _ { X } ^ { -0.4 \pm 0.1 } up to 10 ^ { 42 } erg s ^ { -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 black hole mass as M _ { BH } ^ { -0.62 ^ { +0.13 } _ { -0.12 } } , with an intrinsic scatter of 0.46 ^ { +0.08 } _ { -0.06 } dex .
This finding can be interpreted as observational evidence for ‘ down-sizing ’ of black hole accretion in local early types , that is , low mass black holes 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 black hole mass .