  The response of superconducting pair-breaking detectors is dependent on the
details of the quasiparticle distribution. In Kinetic Inductance Detectors
(KIDs), where both pair breaking and non-pair breaking photons are absorbed
simultaneously, calculating the detector response therefore requires knowledge
of the often nonequilibrium distributions. The quasiparticle effective
temperature provides a good approximation to these nonequilibrium
distributions. We compare an analytical expression relating absorbed power and
the quasiparticle effective temperature in superconducting thin films to full
solutions for the nonequilibrium distributions, and find good agreement for a
range of materials, absorbed powers, photon frequencies and temperatures
typical of KIDs. This analytical expression allows inclusion of nonequilibrium
effects in device models without solving for the detailed distributions. We
also show our calculations of the frequency dependence of the detector response
are in agreement with recent experimental measurements of the response of Ta
KIDs at THz frequencies.
