Advertisement

Astrophysics and Space Science

, Volume 49, Issue 2, pp 399–425 | Cite as

The collapse of iron-oxygen stars: Physical and mathematical formulation of the problem and computational method

  • D. K. Nadyozhin
Article

Abstract

A statement of the problem of gravitational collapse and a computational method are described. The main feature of the collapse — its extremely high heterogeneity — is taken into account. The structure of a collapsing star is characterized by a dense and hot nucleon core which is opaque with respect to neutrino radiation and is embedded in to and extended envelope, almost transparent to neutrinos. The envelope is gradually being accreted onto the core. The enormous amount of energy, radiated in the form of neutrinos and antineutrinos, make us pay particular attention to relatively small absorption of neutrino radiation by extended envelope (so-called energy of deposition). The inclusion of the energy deposition in the calculations is of importance for the problem of transformation of an implosion into an explosion. The deposition is taken into consideration in the approximation of diluted neutrino radiation which escapes from neutrino photosphere and is partially absorbed in the envelope. Both the generation of energy due to deposition and the change of neutronto-proton ratio are taken into account. The increase of the mass of the core, which is opaque with respect to neutrino radiation, is fully taken into account in the calculations of the gravitational collapse.

Keywords

Radiation Mathematical Formulation Small Absorption Energy Deposition Enormous Amount 
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. Ahlberg, J. H., Nilson, E. N., and Walsh, J. L.: 1967,The Theory of Splines and Their Applications, Academic Press, New York/London.Google Scholar
  2. Arnett, W. D.: 1966,Can. J. Phys. 44, 2553.Google Scholar
  3. Arnett, W. D.: 1967,Can. J. Phys. 45, 1621.Google Scholar
  4. Bahcall, J. N.: 1964,Phys. Rev. 136B, 1164.Google Scholar
  5. Beaudet, G., Petrosian, V., and Salpeter, E. E.: 1967,Astrophys. J. 150, 979.Google Scholar
  6. Colgate, S. A. and White, R. H.: 1966,Astrophys. J. 143, 626.Google Scholar
  7. Domogatsky, G. V.: 1969,Nauchnye Informatsii Astron. Soveta U.S.S.R. Acad. Sci. 13, 94.Google Scholar
  8. Domogatsky, G. V.: 1970, Master's Thesis, P.N. Lebedev Physical Institute, Moscow.Google Scholar
  9. Fowler, W. A. and Hoyle, F.: 1964,Astrophys. J. Suppl. Ser. 91, 9.Google Scholar
  10. Godunov, S. K. and Ryabenzhkii, V. S.: 1964,Theory of Difference Schemes. An Introduction, North-Holland Publishing Company, Amsterdam.Google Scholar
  11. Ikeuchi, S., Nakazawa, K., Murai, T., Hoshi, R. and Hayashi, C.: 1971,Prog. Theor. Phys. 46, 1713.Google Scholar
  12. Ikeuchi, S., Nakazawa, K., Murai, T., Hoshi, R., and Hayashi, C.: 1972,Prog. Theor. Phys. 48, 1870.Google Scholar
  13. Imshennik, V. S. and Nadyozhin, D. K.: 1965,Astron. Zh. 42, 1154. Translation in English:Sov. Astron.-AJ 9, 896.Google Scholar
  14. Imshennik, V. S. and Nadyozhin, D. K.: 1972,Zh. Eksp. Teor. Fiz. 63, 1548. Translation in English:Soviet Physics JETP 36, 821.Google Scholar
  15. Imshennik, V. S. and Nadyozhin, D. K.: 1974, in R. J. Tayler (ed.),Late Stages of Stellar Evolution, D. Reidel Publ. Co., Dordrecht, Holland, p. 130.Google Scholar
  16. Imshennik, V. S., Nadyozhin, D. K., and Pinaev, V. S.: 1966,Astron. Zh. 43, 1215. Translation in English:Sov. Astron.-AJ 10, 970.Google Scholar
  17. Imshennik, V. S., Nadyozhin, D. K., and Pinaev, V. S.: 1967,Astron. Zh. 44, 768. Translation in English:Sov. Astron.-AJ 11, 617.Google Scholar
  18. Ivanova, L. N., Imshennik, V. S., and Nadyozhin, D. K.: 1969,Nauchnye Informatsii Astron. Sovieta U.S.S.R. Acad. Sci. 13, 3.Google Scholar
  19. Korn, G. A. and Korn, T. M.: 1961,Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Co., New York-Toronto-London.Google Scholar
  20. Nadyozhin, D. K.: 1974,Nauchnye Informatsii Astron. Sovieta U.S.S.R. Acad. Sci. 32, 3.Google Scholar
  21. Rabinowitz, P. and Weiss, G.: 1959,Mathematical Tables and Other Aids to Computations 13, No. 68, 285.Google Scholar
  22. Rhodes, P.: 1950,Proc. Roy. Soc. A204, No. 1078, 396.Google Scholar
  23. Richtmyer, R. D.: 1957,Difference Methods for Initial Value Problems, Wiley (Interscience), New York.Google Scholar
  24. Wilson, J. R.: 1971,Astrophys. J. 163, 209.Google Scholar
  25. Zel'dovich, Ya. B. and Novikov, I. D.: 1971,Relativistic Astrophysics, Vol. 1,Stars and Relativity, The University of Chicago Press, Chicago and London.Google Scholar
  26. Zentsova, A. S. and Nadyozhin, D. K.: 1975,Astron. Zh. 52, 234. Translation in English:Sov. Astron.-AJ 19, 146.Google Scholar

Copyright information

© D. Reidel Publishing Company 1977

Authors and Affiliations

  • D. K. Nadyozhin
    • 1
  1. 1.Institute of Applied MathematicsUSSR Academy of SciencesMoscowUSSR

Personalised recommendations