The Effect of Coherent Scattering on Radiative Losses in the Solar CaiiK Line

Abstract

We investigate the influence of partial frequency redistribution (PRD) on radiative cooling due to the Ca II K line in a hydrostatic model of the quiet Sun, and in a series of 20 snapshots from a chromospheric radiation-hydrodynamics simulation. The net radiative rates in the K line were calculated through these models with three different frequency-redistribution formalisms: complete redistribution (CRD), angle-averaged PRD, and angle-dependent PRD. It is found that the approximation of CRD generally leads to an overestimate of the net radiative rates because of its neglect of coherent scattering. Compared to the more realistic full angle-dependent solution, angle-averaged PRD provides accurate emergent profiles and cooling rates in the hydrostatic model and also provides accurate instantaneous profiles in the dynamical snapshots, even when considerable macroscopic velocities are present. Instantaneous angle-averaged cooling rates in the dynamical snapshots may be different at times, but on average, cooling is very similar to the angle-dependent case. In the temperature minimum, the Ca II K line provides, on average, more cooling in the dynamic chromosphere at the same column mass than in the hydrostatic model. It provides less cooling in the chromosphere. Finally, we formulate an approximation for angle-averaged redistribution in a moving atmosphere, employing the unshifted redistribution function. This approximation is easy to implement in existing numerical codes and should provide an efficient method for PRD transfer solutions in dynamic models without loss of accuracy in emergent profiles and radiative cooling rates.