On the Intensities of Interlocked Multiplet Lines in the Milne-eddington Model

The equations of transfer in the Milne–Eddington model for multiplet lines with a common upper state are solved exactly. It is assumed that no redistribution in frequency takes place other than that due to interlocking, that the ratios of the line absorption coefficients to the continuous absorption . coefficient are independent of depth, and that the lower states of the lines are sharp. A linear approximation for the Planck function is used. The solution is found to depend on H -functions of a fairly simple type. The case of a doublet is considered in detail. Values for the H -functions are computed and the residual intensities of the two components are evaluated as functions of μ ( = cos θ ) for three distances from the centres of the lines. These are compared with the residual intensities for doublet lines when there is no interlocking. It is shown that interlocking causes a small reduction in the difference between the residual intensities of the two lines, the reduction being greater towards the limb. A solution for the doublet intensities based on Eddington's approximation is also considered and it is shown that the errors in the approximate solution are satisfactorily small for $$\mu \gt 0 \cdot 2$$ .