  Understanding the detailed behaviour of superconducting pair breaking photon
detectors such as Kinetic Inductance Detectors requires knowledge of the
nonequilibrium quasiparticle energy distributions. We have previously
calculated the steady state distributions resulting from uniform absorption of
monochromatic sub gap and above gap frequency radiation by thin films. In this
work, we use the same methods to calculate the effect of illumination by
broadband sources, such as thermal radiation from astrophysical phenomena or
from the readout system. Absorption of photons at multiple above gap
frequencies is shown to not change the structure of the quasiparticle energy
distribution close to the superconducting gap. Hence for typical absorbed
powers, we find the effects of absorption of broadband pair breaking radiation
can simply be considered as the sum of the effects of absorption of many
monochromatic sources. Distribution averaged quantities, like quasiparticle
generation effciency $\eta$, match exactly a weighted average over the
bandwidth of the source of calculations assuming a monochromatic source. For
sub gap frequencies, however, distributing the absorbed power across multiple
frequencies does change the low energy quasiparticle distribution. For moderate
and high absorbed powers, this results in a significantly larger $\eta$ - a
higher number of excess quasiparticles for a broadband source compared to a
monochromatic source of equal total absorbed power. Typically in KIDs the
microwave power absorbed has a very narrow bandwidth, but in devices with broad
resonance characteristics (low quality factors), this increase in $\eta$ may be
measurable.
