What Sets the Line Profiles in Tidal Disruption Events?

We investigate line formation in gas that is outflowing and optically thick to electron scattering, as may be expected following the tidal disruption of a star by a super-massive black hole. Using radiative transfer calculations, we show that the optical line profiles produced by expanding TDE outflows are most likely primarily emission features, rather than the P-Cygni profiles seen in most supernova spectra. This is a result of the high line excitation temperatures in the highly irradiated TDE gas. The outflow kinematics cause the emission peak to be blueshifted and to have an asymmetric red wing. Such features have been observed in some TDE spectra, and we propose that these may be signatures of outflows. We also show that non-coherent scattering off of hot electrons can broaden the emission lines by $\sim 10000$~km~s$^{-1}$, such that in some TDEs the line width may be set by the electron scattering optical depth rather than the gas kinematics. The scattering broadened line profiles produce distinct, wing-shaped profiles that are similar to those observed in some TDE spectra. The narrowing of the emission lines over time in these observed events may be related to a drop in density rather than a drop in line-of-sight velocity.