Partially coherent scattering in stellar chromospheres. V. Analytic approximations including background continuum absorption

The comoving-frame partially coherent scattering (CPCS) approximation is a heuristic approach to modeling partially coherent resonance-line scattering. It is analytic, conceptually motivated, and easy to apply, while generally maintaining roughly 20% accuracy. Here, it is extended to include the effects of continuum or dust absorption. As usual for resonance lines, a key process is Doppler diffusion, whereby photons created in the line core reach wing frequencies via the gradual accumulation of thermal Doppler shifts over many scatterings. This complex process can be idealized to yield semiquantitative results by using the " single longest excursion " escape model included in the CPCS approach, as described in earlier papers in this series. This paper extends the CPCS scheme by allowing the partial frequency redistribution to be truncated by continuous absorption during propagation. The result is a semianalytic approximation that reveals the mechanisms by which background opacity alters resonance-line formation and profile diagnostics. This is relevant for understanding shifts in the slope of the Wilson-Bappu effect, resonance-line profiles in quasar models, and resonance scattering in any highly opaque low-density environment with appreciable continuous absorption.