Eddington approximation

W.J. Wiscombe, The delta-Eddington approximation for a vertically inhomogeneous atmospherey NCAR Technical Note, NCAR/TN-121+STR, 1977, pp.1-66. 

Joseph, J.H., W.J. Wiscombe, and J.A. Weinman, The delta-Eddington approximation for radiative flux transfer. J Atmos Sci 33, 2452, 1976. 

J. Joseph, W. J. Wiscombe, and J. A. Weinman, The Delta-Eddington Approximation for Radiative Flux Transfer, Journal of Atmospheric Sciences, 33, p. 2452,1976. 

A form of the curve of growth more relevant to stellar (as opposed to interstellar) absorption lines is derived from work by E. A. Milne, A. S. Eddington, M. Min-naert, D. H. Menzel and A. Unsold. In the Milne-Eddington model of a stellar photosphere, the continuum source function (equated to the Planck function in the LTE approximation) increases linearly with continuum optical depth rA and there is a selective absorption i]K, in the line, where rj(Av), the ratio of selective to continuous absorption, is a constant independent of depth given by... 

However, the situation is not so simple when the heat transport is coupled with stellar structure. Here, I would give another example. It is a problem of X-ray bursting neutron star. The X-ray burst proceeds in tens of second and it might be much shorter as compared with the time scale of heat transport in the envelope of the neutron star. During the burst the X-ray luminosity of the neutron star becomes very close to the Eddington luminosity and the outer layers of the envelope are pushed up by the radiation coming from the interior. Then the neutron star is puffed up and the time scale of heat transport becomes shorter and shorter. Finally, the envelope solution with steady mass flow in thermal equilibrium becomes a good approximation and such situation is also observation-ally confirmed. Before this has become understood, a specialist tried to calculate such expansion of the envelope all the way as an initial value problem by means of stellar evolution code, but it was found impracticable. 

The evolution of a star formed from the merger of two helium white dwarfs considered a 0.4 M0 helium white dwarf accreting helium at approximately half the Eddington accretion rate (lO 5M0yr 1 [62]). Helium ignites at the core-envelope boundary when 0.067 M0 has been accreted and stars expands to become a yellow supergiant in 103 yr. The accretion is switched off artificially once a pre-selected final mass has been reached, whereupon the star evolves towards the helium main sequence as previously described (Sect. 14.5). 

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