Black Hole Blackbodies

Many black-hole sources emit a substantial fraction of their luminosities in blackbody-like spectral components. It is usual to assume that these are produced in regions at least comparable in size to the hole's Schwarzschild radius, so that a measure of the emitting area provides an estimate of the black hole mass M. However there is then no guarantee that the source luminosity (if isotropic) obeys the Eddington limit corresponding to M. We show that the apparent blackbody luminosity L_sph and temperature T must obey the inequality L_sph < 2.3 10^44 (T/100 eV)^-4 erg s^-1 for this to hold. Sources violating this limit include ultrasoft AGN and some of the ultraluminous X-ray sources (ULXs) observed in nearby galaxies. We discuss the possible consequences of this result, which imply either super-Eddington or anisotropic emission in both cases. We suggest that the ultrasoft AGN are the AGN analogues of the ULXs.