Coherent and Non-coherent Scattering in the Theory of Line Formation

Abstract

When the scattering of light is coherent, the exact solution of the problem of line formation in the Milne–Eddington model, with a linear Planck function |${B}_{\nu}\,=\,{{b}_{\nu}}^{(0)}\,+\,{{b}_{\nu}}^{(1)}\,{\tau}_{\nu}$| , has been given by Chandrasekhar. In Section 2 this solution is found by a new method, and in Sections 3–5 the method is used to solve the parallel problem when the scattering of light is completely non-coherent. This solution is exact when |${{b}_{\nu}}^{(0)}$| and |${k}_{\nu}\,{{b}_{v}}^{(1)}$| are independent of the frequency ν and the depth z , K v being the continuous absorption coefficient. The solution agrees with that found by Sobolev for the case |${k}_{\nu}={k},\,{{b}_{\nu}}^{(0)}=B,\,{{b}_{\nu}}^{(1)}=0$| . In Sections 6–8 the magnitudes of the terms appearing in the solution are discussed. Sobolev's assertion that the resulting central intensities of absorption lines are much lighter than those found on the hypothesis of coherent scattering is shown to be true for lines at the limb. No definite conclusions can be drawn for other lines until the H -functions involved have been computed, but the same result is likely to hold.