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Formation of Emission Lines

  • Tomokazu Kogure
  • Kam-Ching Leung
Part of the Astrophysics and Space Science Library book series (ASSL, volume 342)

Abstract

When we consider the radiation fields of stellar envelopes exposed to the photospheric UV radiation, the basic feature is their anisotropic nature. The degree of anisotropy is expressed by the geometrical dilution factor, W, defined as the ratio of the solid angle, ω, of the photosphere seen from a point of interest, P, relative to the total solid angle 4π. Thus we have
$$ W = \frac{\varpi } {{4\pi }}. $$
(4.1.1)
If point P is located at a distance r from the star’s center, and θ be the angle subtended by the stellar radius at point P, as seen in Figure 4.1, the solid angle ω is expressed as
$$ \omega = 2\pi \int_0^\theta {\sin \theta d\theta = 2\pi \left( {1 - \cos \theta } \right)} . $$
(4.1.2)
Then the dilution factor is given by
$$ W = \frac{1} {2}\left( {1 - \cos \theta } \right). $$
(4.1.3)
Converting cosθ to the ratio of stellar radius R and distance r, we have
$$ W = \frac{1} {2}\left\{ {1 - \sqrt {1 - \left( {\frac{R} {r}} \right)^2 } } \right\}. $$
(4.1.4)
In case of rR, we have
$$ W \sim \frac{1} {4}\frac{{R^2 }} {{r^2 }}. $$
(4.1.5)
The value of W ranges from 0.5 at the stellar surface (r = R) to 10−15 in extended planetary nebulae. In stellar envelopes the typical value of W is in between 10−1 and 10−5. The relation between W and x = r/R is partly given in Table 4.1.
Figure 4.1

Dilution factor at point P is defined as the ratio of solid angle subtended to the photospheric disk, relative to the whole solid angel 4π.

Table 4.1

The relation between the dilution factor W and x = r/R

Keywords

Emission Line Optical Depth Line Profile Planetary Nebula Stellar Disk 
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.

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Further reading

  1. Kitchin, C.R. (1982). Early Emission Line Stars. Adam Hilger Ltd., Bristol.Google Scholar
  2. Williams, R. and Livoi, M. (eds.) (1995). The Analysis of Emission Lines. Cambridge University Press, Cambridge.Google Scholar

References

  1. Aller, L. H. (1956). Chapter IV, Section 2. The Balmer decrement. Gaseous Nebulae. Chapman & Hall, London.Google Scholar
  2. Anderson, L. S. and Athay, R.G. (1989). Model solar chromosphere with prescibed heating. Ap. J., 346, 1010–1018.CrossRefADSGoogle Scholar
  3. Baker, J. G. and Menzel, D. (1938). Physical processes in gaseous nebulae. III. The Balmer decrements. Ap. J., 88, 52–64.MATHCrossRefADSGoogle Scholar
  4. Baker, J. G. Menzel, D., and Aller, L.H. (1938). Physical processes in gaseous nebulae. V. Electron temperature. Ap. J., 88, 422–428.MATHCrossRefADSGoogle Scholar
  5. Böhm, T. and Catala, C. (1995). Rotation, winds and active phenomena in Herbig Ae/Be stars. A. A., 301, 155–169.Google Scholar
  6. Bowen, I. S. (1935). The spectrum and composition of the gaseous nebulae. Ap. J., 81, 1–16.MATHCrossRefADSGoogle Scholar
  7. Brocklehurst, M. (1971). Calculations of the level populations for the low levels of hydrogenic ions in gaseous nebulae. M. N. R. A. S., 153, 471–490.ADSGoogle Scholar
  8. Bruevich, E. A., Katsova, M. M., and Livshits, M. A. (1990) Kinetics of hydrogen in the chromospheres of red dwarfs. Sov. Ast., 34, 60–65.ADSGoogle Scholar
  9. Castor, J.I. 1970. Spectral line formation in WR envelopes. M. N. R. A. S., 149, 111–127.Google Scholar
  10. Castor, J. I. & van Blerkom, D. (1970). Excitation of HeII in WR envelopes. Ap. J., 161, 485–502.CrossRefADSGoogle Scholar
  11. Castor, J. I. and Lamers, H. J. G. L. M. (1979). An atlas of theoretical P Cyg profiles. Ap. J. Suppl., 39, 481–511.CrossRefADSGoogle Scholar
  12. Cram, L. E. and Giampapa, M.S. (1987). Formation of chromospheric lines in cool dwarf stars. Ap. J., 323, 316–324.CrossRefADSGoogle Scholar
  13. Cuntz, M., Rammacher, W., and Ulmschneider, P. (1994). Chromospheric heating and metal deficiency in cool giants: Theoretical results versus observations. Ap. J., 432, 690–700.CrossRefADSGoogle Scholar
  14. Drake, S. A. and Ulrich, R.K. (1980). The emission-line spectrum from a slab of hydrogen at moderate to high densities. Ap. J. Suppl., 42, 351–383.CrossRefADSGoogle Scholar
  15. Elitzur, M., Ferland, G. J., Mathews, S. G., and Shields, G.A. (1983). Stimulated emission and flat Balmer decrements in cataclysmic variables. Ap. J., 272, L55–L59.CrossRefADSGoogle Scholar
  16. Emerson, D. (1996). Interpreting Astronomical Spectra. John Wiley & Sons, West Sussex, UK.Google Scholar
  17. Gutierrez-Moreno, A. and Moreno, H. (1996). Spectroscopic observations of some D-type symbiotic stars. P. A. S. Pacific, 108, 972–979.CrossRefADSGoogle Scholar
  18. Hamann, W.R. (1985). Line formation in expanding atmospheres: Accurate solution using approximate lambda operators. A. A., 148, 364–368.Google Scholar
  19. Hamann, W. R. and Schmutz, W. (1987). Computed HeII spectra for WR stars: a grid of models. A. A., 174, 173–182.Google Scholar
  20. Hamann, W. R., Wessolowski, U., and Koesterke, L. (1994). Non-LTE spectral analysis of WR stars.: the nitrogen spectrum of the WN6 prototype HD 192163 (WR136). A. A., 281, 184–198.Google Scholar
  21. Hummer, D.G. (1964). The mean number of scatterings by a resonance-line photon. Ap. J., 140, 276–281.CrossRefADSGoogle Scholar
  22. Hummer, D. G. and Rybicki, G.B. (1982). A unified treatment of escape probabilities in static and moving media. I. Plane geometry. Ap. J., 254, 767–779.CrossRefADSGoogle Scholar
  23. Jeffery, D. (1990). The Sobolev-P method.III. The Sobolev-P method generalized for three-dimensional systems. Ap. J., 352, 267–278.CrossRefADSGoogle Scholar
  24. Kogure, T. (1959a). The radiation field and theoretical Balmer decrements of Be stars. I. P. A. S Japan, 11, 127–137.ADSGoogle Scholar
  25. Kogure, T. (1959b). The radiation field and theoretical Balmer decrements of Be stars. II. P. A. S Japan, 11, 278–291.ADSGoogle Scholar
  26. Kogure, T. (1961). The radiation field and theoretical Balmer decrements of Be stars. III. P. A. S Japan, 13, 335–360.ADSGoogle Scholar
  27. Kogure, T. (1969). Contribution à l’étude des profils d’émission d’étoiles Be dites “Pole-on.” A. A.,1, 253–269.Google Scholar
  28. Kogure, T., Hirata, R., and Asada, Y. (1978). On the formation of hydrogen shell spectrum and the envelopes of some shell stars. P. A. S Japan, 30, 385–407.ADSGoogle Scholar
  29. Lamers, H. J. G. L. M., Cerruti-Sola, M., and Perinotto, M. (1987). The “SEI” method for accurate and efficient calculations of line profiles in spherically symmetric stellar winds. Ap. J., 314, 726–738.CrossRefADSGoogle Scholar
  30. Marlborough, J. M. (1969). Models for the envelopes of Be stars. Ap. J., 156, 135–155.CrossRefADSGoogle Scholar
  31. Marsh, T. R. (2001). Doppler tomography. Astrotomography, Indirect Imaging Methods in Observational Astronomy, H. M. J. Boffin, D. Steeghs, and J. Cruypers (eds.), Lecture Notes in Physics, 573, 1–27.Google Scholar
  32. Marsh, T. R. and Horne, K. (1988). Images of accretion discs — II. Doppler tomography. M. N. R. A. S., 235, 269–286.ADSGoogle Scholar
  33. Mauas, P. J. D., Falchi, A., Pasquini, L., and Pallavicini, R. (1997). Chromospheric models of dwarf M stars. A. A., 326, 249–256.Google Scholar
  34. Mendoza, C. (1983). Recent advances in atomic calculation and experiments of interest in the study of planetary nebulae. Planetary Nebulae, IAU Symp., No. 103, D. R. Flower (ed.), D. Reidel Publ. Co., Dordrecht, 143–172.Google Scholar
  35. Menzel, D. H. and Baker, J. G. (1937). Physical processes in gaseous nebulae. II. Thoery of the Balmer decrement. Ap. J., 86, 70–77.MATHCrossRefADSGoogle Scholar
  36. Mihalas, D. (1978). Stellar Atmospherres, 2nd edition. Freeman & Comp. San Francisco.Google Scholar
  37. Mihalas, D., Kunasz, P. B., and Hummer, D. G. (1975). Solution of the co-moving frame equation of tranfer in spherically symmetric flows. I. Computational method for equivalent-two-level-atom source functions. Ap. J., 202, 465–489.CrossRefADSGoogle Scholar
  38. Mihalas, D. and Kunasz, P. B. (1978). Solution of the comoving-frame equation of transfer in spherically symmetric flows. V. Multilevel atoms. Ap. J., 219, 635–653.CrossRefADSGoogle Scholar
  39. Miyamoto, S. (1949). On the radiation field of Be stars. I. Jap. J. Ast., 1, 17–25.Google Scholar
  40. Miyamoto, S. (1952a). On the radiation field of Be stars. II. P. A. S. Japan, 4, 1–10.MathSciNetADSGoogle Scholar
  41. Miyamoto, S. (1952b). On the radiation filed of Be stars. III. Theoretical Balmer decrements. P. A. S. Japan, 4, 28–36.ADSGoogle Scholar
  42. Mullan, D. J. and Cheng, Q. Q. (1993). MgII and Lyα fluxes in M dwarfs: Evaluation of an acoustic model. Ap. J., 412, 312–323.CrossRefADSGoogle Scholar
  43. Papkalla, R. (1995). Line formation in accretion disks. 3D comoving frame calculations. A.A. 295, 551–564.Google Scholar
  44. Pottasch, S. R. (1960). Balmer decrements: The diffuse nebulae. Ap. J., 131, 202–214.CrossRefADSGoogle Scholar
  45. Pottasch, S. R. (1961). Balmer decrements: II. The Be stars. Annales d’Astrophys., 24, 159–167.ADSGoogle Scholar
  46. Pottasch, S. R. (1984). Planetary Nebulae. D. Reidel Dordrecht.Google Scholar
  47. Rons, N., Runacres, M., and Blomme, R. (1992). Comoving frame calculations for λ-Cephei. Nonisotropic and variable outflows from stars, ASP Conf. Ser. 22 L. Drissen, C. Leitherer, and A. Nota (eds.), 199–202.Google Scholar
  48. Rosseland, S. (1936). Theory of radiative transformations in nebulae. Chapter 22 Theoretical Astrophysics. Clarendon Press. Oxford.Google Scholar
  49. Rybicki, G. B. (1972). A novel approach to the solution of multilevel transfer problems. Line Formation in the Presence of Magnetic Fields, R. G. Athay, L. L. House, and G. Newkirk, Jr. (eds.). High altitude observatory, Boulder, CO., p. 145.Google Scholar
  50. Schmitz, F. and Ulmschneider, P. (1980). Theoretical stellar chromospheres of late type stars. A.A., 84, 191–199.Google Scholar
  51. Schrijver, C. J. (1983). Coronal activity in F, G, K type stars. A. A., 127, 289–296.Google Scholar
  52. Schrijver, C. J. (1987). Magnetic structure in cool stars. XI. Relation between radiative fluxes measuring stellar activity, and the evidence for two components in stellar chromospheres. A.A., 172, 111–123.Google Scholar
  53. Simon, T., Drake, S. A., and Kim, P. (1995). The X ray emission of A type stars. P.A. S.P., 107, 1034–1041.CrossRefADSGoogle Scholar
  54. Simon, T. and Landsman, W. B. (1991). The onset of chromospheric activity among A and F stars. Ap. J., 380, 200–207.CrossRefADSGoogle Scholar
  55. Simon, T. and Landsman, W. B. (1997). High chromospheres of late A stars. Ap. J., 483, 435–438.CrossRefADSGoogle Scholar
  56. Sobolev, V. V. (1947). Moving Envelopes of Stars (in Russian). English translation, 1960. Harvard University Press, MA.Google Scholar
  57. Stirpe, G. M. (1991). Broad emission lines in active galactic nuclei. A. A., 247, 3–10.Google Scholar
  58. Ulmschneider, P. (1991). Acoustic heating. Mechanisms of Chromospheric and Coronal Heating. P. Ulmschneider, E. R. Priest, and R. Rosner (eds.), Springer-Verlag, Berlin, pp. 328–343.Google Scholar
  59. Werner, K. and Husfeld, D. (1985). Multi-level non-LTE line formation calculation using approximate Λ-operators. A. A., 148, 417–422.Google Scholar
  60. Woolley, R.v.d.R. and Stibbs, D. W. N. (1953). Chapter III, The integral equations of radiative equilibrium: Exact solutions. The Outer Layers of a Star. Clarendon Press, Oxford, pp. 30–51.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Tomokazu Kogure
    • 1
  • Kam-Ching Leung
    • 2
    • 3
    • 4
  1. 1.Kyoto UniversityYawata, KyotoJapan
  2. 2.Institute of Astronomy and AstrophysicsAcademia SinicaTaiwan, China
  3. 3.Department of Physics & AstronomyUniversity of Nebraska-LincolnLincolnUSA
  4. 4.Brace LaboratoryUSA

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