Secondary ionization and heating by fast electrons

We examine the fate of fast electrons (with energies E > 10 eV) in a thermal gas of primordial composition. To follow their interactions with the background gas, we construct a Monte Carlo model that includes: (1) electron-electron scattering (which transforms the electron kinetic energy into heat), (2) collisional ionization of hydrogen and helium (which produces secondary electrons that themselves scatter through the medium) and (3) collisional excitation (which produces secondary photons, whose fates we also follow approximately). For the last process, we explicitly include all transitions to upper levels n < 4, together with a well-motivated extrapolation to higher levels. In all cases, we use recent calculated cross-sections at E < 1 keV and the Bethe approximation to extrapolate to higher energies. We compute the fractions of energy deposited as heat, ionization (tracking H i and the helium species separately) and excitation (tracking H i Ly alpha separately) under a broad range of conditions appropriate to the intergalactic medium. The energy deposition fractions depend on both the background ionized fraction and the electron energy but are nearly independent of the background density. We find good agreement with some, but not all, previous calculations at high energies. Electronic tables of our results are available.