  We characterize the topological insulator Bi$_2$Se$_3$ using time- and angle-
resolved photoemission spectroscopy. By employing two-photon photoemission, a
complete picture of the unoccupied electronic structure from the Fermi level up
to the vacuum level is obtained. We demonstrate that the unoccupied states host
a second, Dirac surface state which can be resonantly excited by 1.5 eV
photons. We then study the ultrafast relaxation processes following optical
excitation. We find that they culminate in a persistent non-equilibrium
population of the first Dirac surface state, which is maintained by a
meta-stable population of the bulk conduction band. Finally, we perform a
temperature-dependent study of the electron-phonon scattering processes in the
conduction band, and find the unexpected result that their rates decrease with
increasing sample temperature. We develop a model of phonon emission and
absorption from a population of electrons, and show that this counter-intuitive
trend is the natural consequence of fundamental electron-phonon scattering
processes. This analysis serves as an important reminder that the decay rates
extracted by time-resolved photoemission are not in general equal to single
electron scattering rates, but include contributions from filling and emptying
processes from a continuum of states.
