  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.
