On the radiative equilibrium of a stellar atmosphere

Chandrasekhar, S. (1944) On the radiative equilibrium of a stellar atmosphere Astrophysical Journal, 99 . pp. 180-190. ISSN 0004-637X

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Official URL: http://adsabs.harvard.edu/abs/1944ApJ....99..180C

Related URL: http://dx.doi.org/10.1086/144606


In this paper the equation of transfer μdI/dτ=I-I0; I0+1-1Idμ is solved by expanding I in terms of spherical harmonics in the form I(τ,μ)=Σl=0Il(τ)Pl(μ). It is shown how successively higher approximations to I can be obtained by retaining more and more terms in the foregoing expansion; thus, the first, second, and third approximations are obtained by retaining the first three, five, and seven terms, respectively, in the expansion. The first three approximations to I0(τ) are explicitly obtained, and the corresponding laws of darkening derived. The exact function describing the law of darkening and given by Hopf's. theory is also numerically evaluated. A comparison of this exact law with those derived on our second and third approximations indicates that the method described in this paper is sufficiently rapidly convergent.

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