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.
