  We have calculated the non-equilibrium quasiparticle and phonon distributions
$f(E)$, $n(\Omega)$, where $E$ and $\Omega$ are the quasiparticle and phonon
energies respectively, generated by the photons of the probe signal of a low
temperature superconducting resonator SR operating well-below its transition
temperature $T_c$ as the absorbed probe power per unit volume $P_{abs}$ was
changed. The calculations give insight into a rate equation estimate which
suggests that the quasiparticle distributions can be driven far from the
thermal equilibrium value for typical readout powers. From $f(E)$ the driven
quasiparticle number density $N_{qp}$ and lifetime $\tau_r$ were calculated.
Using $N_{qp}$ we defined an effective temperature $T_N^*$ to describe the
driven $f(E)$. The lifetime was compared to the distribution averaged thermal
lifetime at $T_N^*$ and good agreement was found typically within a few
percent. We used $f(E)$ to model a representative SR. The complex conductivity
and hence the frequency dependence of the experimentally measured forward
scattering parameter $S_{21}$ of the SR as a function of $P_{abs}$ were found.
The non-equilibrium $S_{21}$ cannot be accurately modeled by a thermal
distribution at an elevated temperature $T_{21}^*$ having a higher
quality-factor in all cases studied and for low $P_{abs}$ $T_{21}^*\sim T_N^*$.
  Using $\tau_r$ and $N_{qp}$ we determined the achievable Noise Equivalent
Power of the resonator used as a detector as a function of $P_{abs}$. Simpler
expressions for $T_N^*$ as a function of $P_{abs}$ were derived which give a
very good account of $T_N^*$ and also $N_{qp}$ and $\tau_r$. We conclude that
multiple photon absorption from the probe increases the quasiparticle number
above the thermal background and ultimately limits the achievable NEP of the
resonator.
