Advertisement

On some trends in the progress of astrophysical radiative transfer

  • Arthur G. Nikoghosian
Chapter
Part of the Springer Praxis Books book series (PRAXIS)

Abstract

The objective of this review is to provide some insight into trends in the development of one of the most important fields of theoretical astrophysics – the theory of radiative transfer. The foundation of the field goes back to the pioneering works of Schuster, Schwarzschild, Milne and Eddington appearing at the beginning of the last century in connection with modeling the stellar atmospheres. Since then the approaches proposed in these works have made rapid progress forming a theory usually referred to as ‘classical’. Parallel to this an alternative approach was offered by Ambartsumian with his methods based on the principle of invariance and the laws of addition of layers. With their deep physical content the methods have been extremely flexible in applications and efficient in numerical computations. Their major role in the theory is well-known. However, the modern fundamental results in this direction make expedient reviewing the most important of them to elucidate their place in existing theory and significance from the point of view of its further progress.

Keywords

Radiative Transfer Optical Depth Transfer Equation Optical Thickness Source Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Menzel, D., 1966: ed., Selected Papers on the Transfer of Radiation, New York: Dover.Google Scholar
  2. 2.
    Ambartsumian, V.A., 1943: On diffuse reflection of light by turbid medium, Dokl. Akad. Nauk SSSR, 38, 257–261,.Google Scholar
  3. 3.
    Ambartsumian, V.A., 1960: Scientific Papers, Vol. 1, Yerevan: Izd AN ArmSSR (in Russian).Google Scholar
  4. 4.
    Ambartsumian, V.A., 1980: On some trends in the development of astrophysics, Ann. Rev. Astron. Astrophys., 18, 1–13.CrossRefGoogle Scholar
  5. 5.
    Ambartsumian, V.A., 1980: Invariance principle and some of its applications, in: Proc. Symp. ‘The Invariance Principle and its Applications’, 9–17, Yerevan: Izd. AN ArmSSR (in Russian).Google Scholar
  6. 6.
    Nikoghossian, A.G., 1999: The variational formalism and bilinear relations of the radiative transfer theory, J. Quantit. Spectrosc. Radiat. Transfer, 61, 345–359.CrossRefGoogle Scholar
  7. 7.
    Ambartsumian, V.A., 1944: On one-dimensional case of the problem of the scattering and absorbing medium of finite optical thickness, Izv. AN ArmSSR, No. 1–2, 31–36.Google Scholar
  8. 8.
    Sobolev, V.V., 1963: A Treatise on Radiative Transfer, Princeton: Van Nostrand.Google Scholar
  9. 9.
    Chandrasekhar, S., 1960: Radiative Transfer, New York: Dover.Google Scholar
  10. 10.
    Yengibarian, N.B., and M.A. Mnatsakanian, 1974: On the linear transfer problems, Dokl. Akad. Nauk SSSR, 217, 533–535.Google Scholar
  11. 11.
    Ambartsumian, V.A., 1942: On reflection of light by atmospheres of planets, Astron. Zh., 19, 30 (see also [3], 206–222).Google Scholar
  12. 12.
    Ambartsumian, V.A., 1941: Light scattering and absorption in atmospheres of planets, Uch. Zap. LGU, No. 11 (see also [3], 181–205).Google Scholar
  13. 13.
    Ambartsumian, V.A., 1944: The diffusion of light through scattering medium of large optical thickness, Dokl. Akad. Nauk SSSR, 43, 106 (see also [3] 256–262).Google Scholar
  14. 14.
    Sobolev, V.V., 1958: On the theory of radiation transfer, Izv. AN ArmSSR, 11, 39–50.Google Scholar
  15. 15.
    Sobolev, V.V. 1959: On the theory of radiation transfer in stellar atmospheres, Astron. Zh., 36, 573–578.Google Scholar
  16. 16.
    Sobolev, V.V., 1985: Course in Theoretical Astrophysics (in Russian), Moscow, Nauka.Google Scholar
  17. 17.
    Ivanov, V.V., 1969: Radiative Transfer and the Spectra of Celestial Objects (in Russian), Moscow, Nauka.Google Scholar
  18. 18.
    Case, K.M., and P.F. Zweifel, 1967: Linear Transport Theory, Reading, MA: Addison-Wesley.Google Scholar
  19. 19.
    Minin, I.N., 1958: Dokl. Akad. Nauk SSSR, 120, 63.Google Scholar
  20. 20.
    Ambartsumian, V.A., 1943: On the problem of diffuse reflection, J. Exp. Teoret. Phys., 13, 323–334.Google Scholar
  21. 21.
    Ambartsumian, V.A., 1941: The light scattering and absorption in atmospheres of planets, Trudi Astron. Obs. LGU, 12, 64 (see also [3], 181–205).Google Scholar
  22. 22.
    Ambartsumian, V.A., 1942: New method for studying the light scattering in the foggy medium, Izv. AN SSSR, No.3, 97 (see also [3], 223–231).Google Scholar
  23. 23.
    Hummer, D.G., 1962: Non-coherent scattering: I. The redistribution function with Doppler broadening Mon. Notic. Roy Astron. Soc., 125, 21–37.Google Scholar
  24. 24.
    Mihalas, D., 1970: Stellar Atmospheres, San Francisco: Freeman and Co.Google Scholar
  25. 25.
    Nikoghossian, A.G., 1977: The problem of diffuse reflection for redistribution of radiation over frequencies and directions, Dokl. Akad. Nauk SSSR, 235, 786–789.Google Scholar
  26. 26.
    Nikoghossian, A.G., and H.A. Haruthyunian, 1978: The diffuse reflection of light for an arbitrary phase function, Astrophysics, 14, 223–230.CrossRefGoogle Scholar
  27. 27.
    Nikoghossian, A.G., and H.A. Haruthyunian, 1979: The radiation field in a semiinfinite atmosphere containing energy sources, Astrophys. Space Sci., 64, 285–299.CrossRefGoogle Scholar
  28. 28.
    Nikoghossian, A.G., and H.A. Haruthyunian, 1980: Application of the invariance principle to solution of various problems of non-coherent and non-isotropic scattering, in: Proc. Symp. ‘The Invariance Principle and its Applications’, 232–241. Yerevan: Izd. AN ArmSSR (in Russian).Google Scholar
  29. 29.
    Haruthyunian, H.A., and A.G. Nikoghossian, 1980: Application of the invariance principle to the compton scattering problem, in: Proc. Symp.The Invariance Principle and its Applications’ 431–439, Yerevan: Izd. AN ArmSSR (in Russian).Google Scholar
  30. 30.
    Nikoghossian, A.G., 2007: Diffuse reflection of the line-radiation from a semi-infinite turbulent atmosphere, Astrophysics, 50, 321–332.CrossRefGoogle Scholar
  31. 31.
    Nikoghossian, A.G., and H.A. Haruthyunian, 1976: Spectral lines formation for a general law of redistribution, Dokl. Akad. Nauk SSSR, 229, 583–586.Google Scholar
  32. 32.
    Haruthyunian, H.A., and A.G. Nikoghossian, 1976: Radiation scattering for a gen erallaw of frequency redistribution, J. Quantit. Spectrosc. Radiat. Transfer, 19, 135–148.CrossRefGoogle Scholar
  33. 33.
    Preisendorfer, R.W., 1976: Hydrologic Optics, Vol. IV, Honolulu, Hawaii: U.S. Department of Commerce.Google Scholar
  34. 34.
    Rybicki, G.B., 1977: Integrals of the transfer equations, I, Astrophys. J., 213, 165– 176.CrossRefGoogle Scholar
  35. 35.
    Ivanov, V.V., 1978: Nonlinear equations in linear problems of radiation transfer in plane atmospheres, Astron. Zh., 22, 612–618.Google Scholar
  36. 36.
    Nikoghossian, A.G., 1997: Invariance principle and bilinear relations of the radiative transfer theory, I, Astrophys. J., 483, 849–856.CrossRefGoogle Scholar
  37. 37.
    Hubeny, I., 1987a: Probabilistic interpretation of radiative transfer, I, Astron. Astrophys, 185, 332–335,Google Scholar
  38. 38.
    Hubeny, I., 1987b: Probabilistic interpretation of radiative transfer, II, Astron. Astrophys, 185, 336–342,Google Scholar
  39. 39.
    Krikorian, R.A., and A.G. Nikoghossian, 1996: On the lagrangian formalism in the radiative transfer theory, J. Quantit. Spectrosc. Radiat. Transfer, 56, 465–469.CrossRefGoogle Scholar
  40. 40.
    Vainberg, M.M., 1964: Variational Methods for the Study of Non-Linear Operators, San Francisco: Holden Day.Google Scholar
  41. 41.
    Gelfand, I.M., and S.V. Fomin, 1965: Calculus of Variation, Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  42. 42.
    Tavel, M., 1971: Application of Noether’s theorem to the transport equation, Transport Theory Statist Phys., 1, 271–285.CrossRefGoogle Scholar
  43. 43.
    Anderson, D., 1973: Variational principles for the radiative transfer equation of single scattering, J. Inst. Math. Applic., 12, 55–62.CrossRefGoogle Scholar
  44. 44.
    Nikoghossian, A.G., 2000: Non-linear relations for statistical mean quantities describing the multiple scattering process, Astrophysics, 43, 337–342.CrossRefGoogle Scholar
  45. 45.
    Nikoghossian, A.G., 2011: Bilinear integrals of the radiative transfer equation, Astrophysics, 54, 242–249.CrossRefGoogle Scholar
  46. 46.
    Yengibarian, N.B., 1972: On factorization of the symmetric integral operators, Dokl. Akad. Nauk SSSR, 203, 4.Google Scholar
  47. 47.
    Yengibarian, N.B., and A.G. Nikoghossian, 1973: Non-coherent scattering, J. Quantit. Spectrosc. Radiat. Transfer, 13, 787–811.CrossRefGoogle Scholar
  48. 48.
    Hubeny, I., 1992: in: Atmospheres of Early-type Stars, U. Huber, C.S. Jeffery, ed., Lecture Notes in Physics, No. 401, p. 377, Berlin: Springer.Google Scholar
  49. 49.
    Rybicki, G.B., 1984: Escape probability methods, in: Methods in Radiative Transf er,W. Kalkofen, ed., 21–64, Cambridge: Cambridge University press.Google Scholar
  50. 50.
    Sobolev, V.V., 1966: The number of scatterings during photon diffusion, I, Astrophysics, 2, 69–73.CrossRefGoogle Scholar
  51. 51.
    Sobolev, V.V., 1966: The number of scatterings during photon diffusion, II, Astrophysics, 2, 119–123.CrossRefGoogle Scholar
  52. 52.
    Sobolev, V.V., 1967: The number of scatterings during photon diffusion, III, Astrophysics, 3, 1–5.CrossRefGoogle Scholar
  53. 53.
    Haruthyunian, H.A.and A.G. Nikoghossian, 1983: The mean number of scatterings for radiative transfer with frequency redistribution, Dokl. Akad. Nauk SSSR, 268, 1342–1346.Google Scholar
  54. 54.
    Nikoghossian, A.G., 1984: Statistical description of radiation field on the basis of the invariance principle, I, Astrophysics, 21, 527–537.CrossRefGoogle Scholar
  55. 55.
    Nikoghossian, A.G., 1984: Statistical description of radiation field on the basis of the invariance principle, II, Astrophysics, 21, 685–693.CrossRefGoogle Scholar
  56. 56.
    Haruthyunian, H.A., and A.G. Nikoghossian, 1987: Statistical description of radiation field on the basis of the invariance principle, IV, Astrophysics, 27, 536–543.Google Scholar
  57. 57.
    Nikoghossian, A.G., 1986: Statistical description of radiation field on the basis of the invariance principle, III, Astrophysics, 24, 89–99.CrossRefGoogle Scholar
  58. 58.
    Irvine, W.M., 1964: The formation of absorption bands and the distribution of photon optical paths in a scattering atmosphere, Bull. Astron. Inst. Netherl., 17, 266– 279.Google Scholar
  59. 59.
    Irvine, W.M., 1966: The Distribution of photon optical paths in a scattering atmosphere, Astrophys. J., 144, 1140–1147.CrossRefGoogle Scholar
  60. 60.
    Ivanov, V.V., 1970: The mean free path of a photon in a scattering medium, Astrophysics, 6, 355–367.CrossRefGoogle Scholar
  61. 61.
    Hummer, D.G., and P.B. Kunasz, 1980: Energy loss by resonance line photons in an absorbing medium, Astrophys. J., 236, 609–618.CrossRefGoogle Scholar
  62. 62.
    Nikoghossian, A.G., 2006: Statistical description of the radiation field in a homogeneous medium of finite optical thickness, Astrophysics, 49, 229–239.CrossRefGoogle Scholar
  63. 63.
    Nikoghossian, A.G., 2000: Nonlinear equations for statistical averages describing process of multiple scattering, Astrophysics, 43, 337–342.CrossRefGoogle Scholar
  64. 64.
    Bellman, R., R. Kalaba, and M. Wing, 1960: Invariant imbedding and mathematical physics, I, Particle processes, J. Math. Phys., 1, 280–308.CrossRefGoogle Scholar
  65. 65.
    Bellman, R., R. Kalaba and M. Prestrud, 1963: Invariant imbedding and radiative transfer in slabs of finite thickness, New York: American Elsevier.Google Scholar
  66. 66.
    Yanovitskij, E.G., 1997: Light Scattering in Inhomogeneous Atmospheres, New York: Springer.Google Scholar
  67. 67.
    Van de Hulst, H.C., 1980: Multiple Light Scattering Tables, Formulas and Applications, Vol. 1, New York, Academic Press.Google Scholar
  68. 68.
    Nikoghossian, A.G., 2004: Radiative transfer in one-dimensional inhomogeneous atmospheres, Astron. Astrophys, 422, 1059–1066.Google Scholar
  69. 69.
    Redheffer, R., 1962: On the relation of transmission-line theory to scattering and transfer, J. Math. Phys., 41, 1–41.Google Scholar
  70. 70.
    Grant, I.P., and G.E. Hrant, 1968: Solution of radiative transfer problems using the invariant Sn method, Mon. Not. Roy. Astr. Soc., 141, 27–41.Google Scholar
  71. 71.
    Peraiah, A., 1999, Principles of invariance in radiative transfer, Sp. Sci. Rev., 87, 465–538.CrossRefGoogle Scholar
  72. 72.
    Jefferis J.T., and C. Lindsey, 1988: Radiative transfer in inhomogeneous atmospheres – A statistical approach, Astrophys. J., 335, 372–382.CrossRefGoogle Scholar
  73. 73.
    Gu, Y., C. Lindsey, and J.T. Jefferies, 1995: Radiative transfer in stochastic media, Astrophys. J., 450, 318–333.CrossRefGoogle Scholar
  74. 74.
    Cecchi-Pestellini, C., and L. Barletti, 2001: Radiative transfer in a stochastic universe, I, New Astron., 6, 151–163.CrossRefGoogle Scholar
  75. 75.
    Meinkohn, E., and S. Richling, 2002: Radiative transfer with finite elements, II, Lyalpha line transfer in moving media, Astron. Astrophys., 392, 827–839.CrossRefGoogle Scholar
  76. 76.
    Juvela, M., and P. Padovan, 2003: Dust emission from inhomogeneous interstellar clouds: Radiative transfer in 3D with transiently heated particles, Astron. Astrophys., 397, 201–212.CrossRefGoogle Scholar
  77. 77.
    Nikoghossian, A.G., S. Pojoga, and Z. Mouradian, 1997: On the radiative transfer in atmospheres with randomly distributed inhomogeneities, Astron. Astrophys., 325, 813–818.Google Scholar
  78. 78.
    Pojoga, S., A.G. Nikoghossian, and Z. Mouradian, 1998: A statistical approach to the investigation of fine structure of solar prominences, Astron. Astrophys., 332, 325–338.Google Scholar
  79. 79.
    Nikoghossian, A.G., S. Pojoga, and Z. Mouradian, 1999: Statistical characteristics of radiation formed in atmosphere with randomly distributed inhomogeneities, Astron. Astrophys., 342, 785–798.Google Scholar
  80. 80.
    Nikoghossian, A.G., and Z. Mouradian, 2000: Profiles of the spectral lines formed in stochastic multicomponent atmosphere, Astron. Astrophys., 360, 1086–1095.Google Scholar
  81. 81.
    Bellman, R., 1957: Functional equations in the theory of dynamic programming, VII, A partial differential equation for the Fredholm resolvent, Proc. Amer. Math. Soc., 8, 435–440.Google Scholar
  82. 82.
    Sobolev, V.V., 1957: Radiation diffusion in a semi-infinite medium, Dokl. Akad. Nauk SSSR, 116, 45–48.Google Scholar
  83. 83.
    Krein, M.G., 1955: On new method of solution of linear integral equations of the first and second kinds, Dokl. Akad. Nauk SSSR, 100, 413–416.Google Scholar
  84. 84.
    Casti, J., and R. Kalaba, 1976: Imbedding Methods in Applied Mathematics [Russian translation], Moscow: Mir.Google Scholar
  85. 85.
    Scott, M., 1973: Invariant Imbedding and its Applications to Ordinary Differential Equations. An Introduction, Reading, MA: Addison-Wesley.Google Scholar
  86. 86.
    Nikoghossian, A.G., 2004: Radiative transfer in inhomogeneous atmospheres, I, Astrophysics, 47, 104–116.CrossRefGoogle Scholar
  87. 87.
    Nikoghossian, A.G., 2004: Radiative transfer in inhomogeneous atmospheres, II, Astrophysics, 47, 248–259.CrossRefGoogle Scholar
  88. 88.
    Nikoghossian, A.G., 2004: Radiative transfer in inhomogeneous atmospheres, III, Astrophysics, 47, 412–421.CrossRefGoogle Scholar
  89. 89.
    Nikoghossian, A.G., 2011: Solution of linear radiation transfer problems in planeparallel atmosphere, I, Astrophysics, 54, 553–567.CrossRefGoogle Scholar
  90. 90.
    Magnus, W., 1954: On the exponential solution of differential equations for a linear operator, Comm. Pure and Appl. Math., VII(4), 649–673.Google Scholar
  91. 91.
    Nikoghossian, A.G., 2011: Group-theoretical description of radiative transfer in onedimensional media, Astrophysics, 54, 126–138.CrossRefGoogle Scholar
  92. 92.
    Wigner, E., 1959: Group Theory, New York: Academic Press.Google Scholar
  93. 93.
    Nikoghossian, A.G., 2012: Solution of linear radiation transfer problems in planeparallel atmosphere, II, Astrophysics, 55, 261–274.CrossRefGoogle Scholar
  94. 94.
    Bellman, R., and G.M. Wing, 1973: An Introduction to Invariant Imbedding, New York: Wiley & Sons.Google Scholar
  95. 95.
    Nikoghossian, A.G., 2007: Spectral lines formation in a mesoturbulent atmosphere, Astrophysics, 50, 175–186.CrossRefGoogle Scholar
  96. 96.
    Gray, D.F., 1978: Turbulence in stellar atmospheres, Sol. Phys., 59, 193–236.CrossRefGoogle Scholar
  97. 97.
    Traving, G., 1964: Über die Bildung von Fraunhoferlinen in turbulenten Sternatmosphären, Z. Astrophys., 60, 167–175.Google Scholar
  98. 98.
    Hundt, E., 1973: Microturbulence in stellar spectroscopy: The turbulent element approach, Astron. Astrophys., 29, 17–21.Google Scholar
  99. 99.
    Frish, H., 1975: Finite eddy-size effects on centre-to-limb variations: An alternative to anisotropic microturbulence, Astron. Astrophys., 40, 267–276.Google Scholar
  100. 100.
    Frish, H., and U. Frish, 1976: Non-LTE transfer – II, Mon. Not. Roy. Astron. Soc., 175, 157–175.Google Scholar
  101. 101.
    Bharucha-Reid, A.T., 1960: Elements of the theory of markov processes and their applications, New York: McGraw-Hill.Google Scholar
  102. 102.
    Gail, H.P., and Sedlmayr, E., 1974: Effects of correlated turbulent velocities on photospheric line formation, Astron. Astrophys., 36, 17–25.Google Scholar
  103. 103.
    Schmid-Burgk, J., 1975: Line formation in turbulent media: Mathematics of profile computation, Astron. Astrophys., 32, 73–78.Google Scholar
  104. 104.
    Gail, H.P., Sedlmayr, E., and G. Traving, 1975: Non-LTE line formation in turbulent media, Astron. Astrophys., 44, 421–429.Google Scholar
  105. 105.
    Batchelor, G., 1970: The Theory of Homogeneous Turbulence, Cambridge: Cambridge University Press.Google Scholar
  106. 106.
    Nikoghossian, A.G., 2002: Intensity fluctuations of radiation escaping from a multicomponent stochastic atmosphere, I, Astrophysics, 45, 223–231.CrossRefGoogle Scholar
  107. 107.
    Nikoghossian, A.G., 2005: Intensity fluctuations of radiation escaping from a multicomponent stochastic atmosphere, II, Astrophysics, 48, 253–261.CrossRefGoogle Scholar
  108. 108.
    Nikoghossian, A.G., 2007: Spectral line formation in a dynamically active multicomponent and stochastic atmosphere, Astrophysics, 50, 94–104.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.V. A. Ambartsumian Byurakan Astrophysical ObservatoryAragatsotn region, ByurakanArmenia

Personalised recommendations