Tidal disruption Eddington envelopes around massive black holes

Optically-thick envelopes may form following the tidal disruption of a star by a massive black hole. Such envelopes would reprocess hard radiation from accretion close to the black hole into the UV and optical bands producing AGN-luminosity flares with duration ∼ 1 year. We show that due to relativistic effects, the envelopes are convective. If convection is efficient, then the structure of the envelopes is similar to that described in previous work; however, the photospheric radius is shown to be very sensitive to the luminosity at the envelope base, suggesting that either the envelope collapses or the envelope expands to a maximum radius at which point a wind may set in. For an envelope without winds, we find a maximum photospheric radius of ∼ 10¹⁶ cm (i.e. minimum effective temperature ∼ 6,000 K). The evolution of the envelopes is described based on simple energy arguments.