Distinct seed formation mechanisms are imprinted upon the fraction of dwarf galaxies currently containing a central supermassive black hole .
Seeding by Pop III remnants is expected to produce a higher occupation fraction than is generated with direct gas collapse precursors . Chandra observations of nearby early-type galaxies can directly detect even low-level supermassive black hole activity , and the active fraction immediately provides a firm lower limit to the occupation fraction .
Here , we use the volume-limited AMUSE surveys of \sim 200 optically-selected early-type galaxies to characterize simultaneously , for the first time , the occupation fraction and the scaling of L _ { X } with M _ { star } , accounting for intrinsic scatter , measurement uncertainties , and X-ray limits .
For early-type galaxies with M _ { star } < 10 ^ { 10 } M _ { \odot } , we obtain a lower limit to the occupation fraction of > 20 % ( at 95 % confidence ) , but full occupation can not be excluded .
The preferred dependence of \log { L _ { X } } upon \log { M _ { star } } has a slope of \sim 0.7–0.8 , consistent with the “ downsizing ” trend previously identified from the AMUSE dataset , and a uniform Eddington efficiency is disfavored at \sim 2 \sigma .
We provide guidelines for the future precision with which these parameters may be refined with larger or more sensitive samples .