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X-ray constraints on the local supermassive black hole occupation fraction

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 ~200 optically-selected early-type galaxies to characterize simultaneously, for the first time, the occupation fraction and the scaling of nuclear X-ray luminosity with stellar mass, accounting for intrinsic scatter, measurement uncertainties, and X-ray limits. For early-type galaxies with log(M_star/M_sun)<10, we obtain a lower limit to the occupation fraction of >20% (at 95% confidence), but full occupation cannot be excluded. The preferred dependence of log(L_X) upon log(M_star) has a slope of about 0.7-0.8, consistent with the "downsizing" trend previously identified from the AMUSE dataset, and a uniform Eddington efficiency is disfavored at ~2 sigma. We provide guidelines for the future precision with which these parameters may be refined with larger or more sensitive samples.