  Observations of luminous flares resulting from the possible tidal disruption
of stars by supermassive black holes have raised a number of puzzles.
Outstanding questions include the origin of the optical and ultraviolet (UV)
flux, the weakness of hydrogen lines in the spectrum, and the occasional
simultaneous observation of x-rays. Here we study the emission from tidal
disruption events (TDEs) produced as radiation from black hole accretion
propagates through an extended, optically thick envelope formed from stellar
debris. We analytically describe key physics controlling spectrum formation,
and present detailed radiative transfer calculations that model the spectral
energy distribution (SED) and optical line strengths of TDEs near peak
brightness. The steady-state transfer is coupled to a non local thermodynamic
equilibrium treatment of the excitation and ionization states of hydrogen,
helium and oxygen (as a representative metal). Our calculations show how an
extended envelope can reprocess a fraction of soft x-rays and produce the
observed optical fluxes of order 10^43 ergs per second. Variations in the mass
or size of the envelope may help explain how the optical flux changes over time
with roughly constant color. For high enough accretion luminosities, x-rays can
highly ionize the reprocessing region and escape to be observed simultaneously
with the optical flux, producing an SED not described by a single blackbody.
Due to optical depth effects, hydrogen Balmer line emission is often strongly
suppressed relative to helium line emission (with HeII-to-H line ratios of at
least 5:1 in some cases) even in the disruption of a solar-composition star. We
discuss the implications of our results to understanding the type of stars
destroyed in TDEs and the physical processes responsible for producing the
observed flares.
