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 and optical line strengths of TDEs near peak brightness. The steady-state transfer is coupled to a solver for the excitation and ionization states of hydrogen, helium, and oxygen (as a representative metal), without assuming local thermodynamic equilibrium. Our calculations show how an extended envelope can reprocess a fraction of soft X-rays and produce the observed optical fluxes of the order of 1043 erg s?1, with an optical/UV continuum that is not described by a single blackbody. 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 escape to be observed simultaneously with the optical flux. Due to optical depth effects, hydrogen Balmer line emission is often strongly suppressed relative to helium line emission (with He ii-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.
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