Inverse Compton reflection - Time-dependent theory

We consider time-dependent behavior in inverse Compton reflection, in which an external flux of soft photons is incident upon a hot, thermal plasma of large scattering depth and small absorption depth. Fluctuations are assumed to arised from variability in the input of solf photons. Our treatment is largely analytic. We calculate in detail the spectral evolution during a fluctuation and show how such observables as the frequency-dependent rise time and the spectral hardness ratio may be used to derive the plasma parameters and soft photon frequency, or perhaps rule out an inverse Compton model altogether. Some of the results are qualitatively applicable to inverse Compton processes in general. Such considerations may be relevant to models for rapidly fluctuating X-ray sources.