Angle-dependent emission from evolving accretion layers

Abstract

Photon propagation through an evolving atmosphere can change the angular distribution of emerging radiation even when its integrated optical column remains constant. We quantify this effect in an irradiated, internally heated, expanding plane-parallel layer using grey, special-relativistic similarity solutions. The full angular radiation field determines both the source function and the acceleration of a pressureless flow in prompt radiative balance. We compare each evolving solution with two frozen transport calculations on the same density and velocity profiles, holding the source fixed in one and allowing it to relax in the other. Heating produces the familiar transition from limb darkening to limb brightening, while the temporal correction to the angular contrast changes sign with optical column. For an upper boundary moving at $0.04c$, an injection speed of $0.06c$, and heating four times the reference incident flux, the intensity ratio between direction cosines $0.1$ and $1$ exceeds the frozen, fixed-source result by $18.8$ per cent at column $τ_0=0.15$, but is smaller by $2.53$ per cent at $τ_0=0.55$. Source relaxation preserves this reversal. The corresponding direct photon flight times are one third and three per cent of the flow age in the oblique and normal directions, respectively. These solutions provide a controlled local benchmark for temporal angular transfer in evolving disc atmospheres and reprocessing layers; application to a specific accreting system requires thermal, spectral, and geometrical physics beyond the present model.