Transfer of Radiation. III. Reflection Effect in Eclipsing Binaries.
Abstract
We have applied the method described in Ap. J., 110, 1,1949 (hereafter called "Paper I") to solve the Milne integrodifferential equation for diffuse radiation (I) in the plane-parallel atmosphere of a reflecting star: a I(r, ) =I(r, ) -B(r), where B(T) =51 f'I(r3 )d $ . The reflecting star is exposed to a parallel beam of radiation of flux 7rF per unit area normal to itself and incident at an angle p normal to the boundary of the atmosphere. We have assumed the following expansion for B (r): B(r) =a+ +2(r) -sec where K (T) is the exponential integral of the nth order, defined by K (r) = % ¼ dx and =1tcosP1n(tanP/2) The coefficients Aj can be evaluated from a system of linear equations involving the C,q's tabulated in Paper I. We have calculated the emergent intensity corresponding to the solution of four simultaneous equations and have compared our values with those obtained from the Chandrasekhar-Hopf formula (Ap. J., 106, 143,1947): I( ,jio) =-41F where H(M) is the solution of the functional equation H(M) = 1+ ( )f01 H )}i#' and = CoS P The two sets of values of the emergent intensity agree to within one part in a thousand, on the average, and somewhat less for p = 0 , on account of a singnlarity in the solution. The solution of more equations does not consistently improve the agreement. We believe that for higher accuracy we need to improve the trial function for B (r).
- Publication:
-
The Astrophysical Journal
- Pub Date:
- May 1951
- DOI:
- 10.1086/145419
- Bibcode:
- 1951ApJ...113..490M