Abstract
A general treatment of the transfer of polarized radiation in spectral lines assuming a Rayleigh phase function and a general law of frequency redistribution is derived. It is shown how nine families of coupled integral equations for the moments of the radiation field arise which are necessary to fully describe the state of polarization of the emergent radiation from a plane-parallel, semi-infinite atmosphere. The special case of angle independent redistribution functions is derived from the general formalism, and it is shown how the nine families of integral equations reduce to the six linearly independent integral equations derived by Collins (1972). To serve as a test of the formulation, solutions for isothermal atmospheres are given.
Similar content being viewed by others
References
Auer, L. H., Heasley, J. N. and House, L. L.: 1977,Astrophys. J. 216, 531.
Brown, J. C. and McLean, I. S.: 1977,Astron. Astrophys. 55, 347.
Brown, J. C., McLean, I. S. and Emslie, A. G.: 1978,Astron. Astrophys. 68, 415.
Buerger, P. F. and Collins, G. W.: 1970,Astrophys. J. 161, 1025.
Chandrasekhar, S.: 1960,Radiative Transfer, Dover, New York.
Collins, G. W., II: 1968a,Astrophys. J. 151, 217.
Collins, G. W., II: 1968b,Astrophys. J. 152, 847.
Collins, G. W., II: 1970a, in A. Slettebak (ed.),Stellar Rotation, D. Reidel Publ. Co., Dordrecht, Holland, 85.
Collins, G. W., II: 1970b,Astrophys. J. 159, 583.
Collins, G. W.: 1972,Astrophys. J. 175, 147.
Collins, G. W., II and Buerger, P. F.: 1974, in T. Gehrels (ed.),Planets, Stars, and Nebulae Studied with Photopolarimetry, Univ. Arizona Press.
Collins, G. W. and Harrington, J. P.: 1966,Astrophys. J. 146, 152.
Dumont, S., Omont, A., Pecker, J.-C. and Rees, E.: 1977,Astron. Astrophys. 54, 675.
Hardorp, J. and Strittmatter, P. A.: 1968,Astrophys. J. 153, 465.
Harrington, J. P.: 1970,Astrophys. Space Sci. 8, 227.
Harrington, J. P. and Collins, G. W., II: 1968,Astrophys. J. 151, 1051.
Hummer, D. G. and Rybicki, G.: 1967,Meth. Comp. Phys. 7, 53.
Landi Degl'Innocenti, E.: 1978,Astron. Astrophys. 66, 19.
McKenna, S. J.: 1978,Bull. Am. Astron. Soc. 10, 457.
McKenna, S. J.: 1980,Astrophys. J. 242, 283.
McKenna, S. J.: 1981, ‘The Transfer of Polarized Radiation in Spectral Lines from Rotationally Distorted Stars’, Dissertation, Ohio State University, Ohio, U.S.A.
McLean, I. S. and Brown, J. C.: 1978,Astron. Astrophys. 69, 291.
Mikhlin, S. G. and Smolitskiy, K. L.: 1967,Approximate Methods for Solution of Differential and Integral Equations, American Elsevier Publ. Comp. New York.
Milkey, R. W., Shine, R. A. and Mihalas, D.: 1975,Astrophys. J. 199, 718.
Pomraning, G. C.: 1973, ‘The Equations of Radiation Hydrodynamics’, Vol. 54, International Series on Monographs of Natural Philosophy, San Francisco, Pergamon Press, London.
Rees, D. E.: 1978,Publ. Astron. Soc. Japan 30, 455.
Slettebak, A., Kuzma, T. J. and Collins, G. W.: 1980,Astrophys. J. 242, 171.
Stenflo, J. O.: 1976,Astron. Astrophys. 46, 62.
Stenflo, J. O.: 1978,Astron. Astrophys. 86, 241.
Stenflo, J. O. and Stenholm, L.: 1976,Astron. Astrophys. 46, 69.
Whittaker, E. T. and Watson, G. N.: 1920,Modern Analysis, Cambridge Univ. Press, Cambridge.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
McKenna, S.J. The transfer of polarized radiation in spectral lines: Formalism and solutions in simple cases. Astrophys Space Sci 108, 31–66 (1985). https://doi.org/10.1007/BF00650118
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00650118