  We calculate nonequilibrium quasiparticle and phonon distributions for a
number of widely-used low transition temperature thin-film superconductors
under constant, uniform illumination by sub-gap probe and pair-breaking signal
photons simultaneously. From these distributions we calculate
material-characteristic parameters that allow rapid evaluation of an effective
quasiparticle temperature using a simple analytical expression, for all
materials studied (Mo, Al, Ta, Nb, and NbN) for all photon energies. We also
explore the temperature and energy-dependence of the low-energy quasiparticle
generation efficiency $\eta$ by pair-breaking signal photons finding $\eta
\approx 0.6$ in the limit of thick films at low bath temperatures that is
material-independent. Taking the energy distribution of excess quasiparticles
into account, we find $\eta \to 1$ as the bath temperature approaches the
transition temperature in agreement with the assumption of the two-temperature
model of the nonequilibrium response that is appropriate in that regime. The
behaviour of $\eta$ with signal frequency scaled by the superconducting energy
gap is also shown to be material-independent, and is in qualitative agreement
with recent experimental results. An enhancement of $\eta$ in the presence of
sub-gap (probe) photons is shown to be most significant at signal frequencies
near the superconducting gap frequency and arises due to multiple photon
absorption events that increase the average energy of excess quasiparticles
above that in the absence of the probe.
