  We used low-energy, momentum-resolved inelastic electron scattering to study
surface collective modes of the three-dimensional topological insulators
Bi$_2$Se$_3$ and Bi$_{0.5}$Sb$_{1.5}$Te$_{3-x}$Se$_{x}$. Our goal was to
identify the "spin plasmon" predicted by Raghu and co-workers [S. Raghu, et
al., Phys. Rev. Lett. 104, 116401 (2010)]. Instead, we found that the primary
collective mode is a surface plasmon arising from the bulk, free carrers in
these materials. This excitation dominates the spectral weight in the bosonic
function of the surface, $\chi "(\textbf{q},\omega)$, at THz energy scales, and
is the most likely origin of a quasiparticle dispersion kink observed in
previous photoemission experiments. Our study suggests that the spin plasmon
may mix with this other surface mode, calling for a more nuanced understanding
of optical experiments in which the spin plasmon is reported to play a role.
