Numerical Sensitivity of Nonlinear Stellar Pulsation Computations

  • G. Kovacs
Part of the NATO ASI Series book series (ASIC, volume 302)


The limit cycle properties of pulsating stellar models are studied in the context of spatial zoning and artificial viscosity. Two standard models representing the RR Lyrae and 8 Cephei stars are thoroughly tested. At moderate amplitudes the strong shocks are shown to be confined to the hydrogen ionization zone, but most of the ‘shock’ dissipation originates from the nonviolent layers beneath this zone, where shocks should not exist. The limit cycle behavior (amplitude, velocity and light curves, stability) depends on the artificial viscosity and on the zone number and distribution. Comparison of our Lagrangean code with other non-Lagrangean codes for the same models leads to the conclusion that they all give very similar results if the mass shells are distributed properly in the Lagrangean code. It is very important to implement a more accurate numerical treatment of shocks in order to clarify the cause of the amplitude limitation.


Velocity Curve Mass Shell Stellar Model Artificial Viscosity Spatial Zoning 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adams, T. F., and Castor, J. I. 1979, Ap. J., 230, 826.ADSCrossRefGoogle Scholar
  2. Adams, T. F., Davis, C. G., and Keller, C. F. 1978, Theoretical Light and Velocity Curves for Cepheid Variables, Los Alamos Scientific Laboratory report LA-7598-MS.CrossRefGoogle Scholar
  3. Aikawa, T., and Simon, N. R. 1983, Ap. J., 273, 346.ADSCrossRefGoogle Scholar
  4. Baker, N. H., and Gough, D. O. 1979, Ap. J., 234, 232.ADSCrossRefGoogle Scholar
  5. Baker, N. H., and von Sengbush, K. 1969, Mitteilungen der Astronomischen Gesellschaft, 27, 162.ADSGoogle Scholar
  6. Bowen, G. 1990, these proceedings.Google Scholar
  7. Buchler, J. R., and Kovacs, G. 1987, Ap. J., 318, 232.ADSCrossRefGoogle Scholar
  8. Buchler, J. R., Moskalik, P., and Kovacs, G. 1989, Ap. J., submitted.Google Scholar
  9. Castor, J. I., Davis, C. G., and Davison, D. K. 1977, Dynamical Zoning within a Lagrangean Mesh by Use of DYN, a Stellar Pulsation Code, Los Alamos Scientific Laboratory report LA-6664.Google Scholar
  10. Christy, R. F. 1964, Rev. Mod. Phys., 36, 555.ADSCrossRefGoogle Scholar
  11. Cox, A. N., Hodson, S. W., and Davey, W. R. 1976, Proc. Solar and Stellar Pulsation Conf., eds. A. N. Cox and R. G. Deupree (Los Alamos: LA-6544-O), p. 188.Google Scholar
  12. Davis, C. G. 1972, Ap. J., 172, 419.ADSCrossRefGoogle Scholar
  13. Deupree, R. G. 1985, Ap. J., 296, 160.ADSCrossRefGoogle Scholar
  14. Fraley, G. S. 1968, Ap. Space Sci., 2, 96.ADSCrossRefGoogle Scholar
  15. Glasner, A. 1990, these proceedings.Google Scholar
  16. Gonczi, G., and Osaki, Y. 1980, Astr. Ap., 84, 304.ADSGoogle Scholar
  17. Hill, S. J. 1972, Ap. J., 178, 793.ADSCrossRefGoogle Scholar
  18. Keller, C. F., and Mutschlecner, J. P. 1971, Ap. J., 167, 127.ADSCrossRefGoogle Scholar
  19. Kovacs, G., and Buchler, J. R. 1988a, Ap. J., 324, 1026.ADSCrossRefGoogle Scholar
  20. Kovacs, G., and Buchler, J. R. 1988b, Ap. J., 334, 971.ADSCrossRefGoogle Scholar
  21. Kuhfuss, R. 1986, Astr.Ap., 160, 116.ADSzbMATHGoogle Scholar
  22. Moffett, J. T., and Barnes III, T. G. 1985, Ap. J. Suppl., 58, 843.ADSCrossRefGoogle Scholar
  23. Moskalik, P., and Buchler, J. R. 1989, Ap. J., submitted.Google Scholar
  24. Ostlie, D. A. 1988, Proc. AU Coll No. 111., in press.Google Scholar
  25. Ostlie, D. A. 1990, these proceedings.Google Scholar
  26. Richtmyer, R. D. 1957, Difference Methods for Initial Value Problems (New York: Interscience).zbMATHGoogle Scholar
  27. Simon, N. R., and Aikawa, T. 1986, Ap. J., 304, 249.ADSCrossRefGoogle Scholar
  28. Simon, N. R., and Lee, A. S. 1981, Ap. J., 248, 291.ADSCrossRefGoogle Scholar
  29. Simon, N. R., and Teays, T. J. 1982, Ap. J., 261, 586.ADSCrossRefGoogle Scholar
  30. Simon, N. R., andTeays, T. J. 1983, Ap. J., 265, 996.ADSCrossRefGoogle Scholar
  31. Stellingwerf, R. F. 1974, Ap. J., 192, 139.ADSCrossRefGoogle Scholar
  32. Stellingwerf, R.F. 1975a, Ap. J., 195, 441.ADSCrossRefGoogle Scholar
  33. Stellingwerf, R. F. 1975b, Ap. J., 199, 705.ADSCrossRefGoogle Scholar
  34. Stellingwerf, R. F. 1984, Ap. J., 284, 712.ADSCrossRefGoogle Scholar
  35. Stellingwerf, R.F. 1990, these proceedings. Google Scholar
  36. Stobie, R.S. 1969, M. N. R. A. S., 144, 461.ADSGoogle Scholar
  37. Takeuti, M. 1990, these proceedings.Google Scholar
  38. Ulrych, T. J., and Clayton, R.W. 1976, Phys. Earth Planet Inter., 12, 188.ADSCrossRefGoogle Scholar
  39. von Sengbush, K. 1973, Mitteilungen der Astronomischen Gesellschaft, 32, 228.ADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • G. Kovacs
    • 1
    • 2
  1. 1.Department of PhysicsUniversity of FloridaGainesvilleUSA
  2. 2.Konkoly ObservatoryBudapest XIIHungary

Personalised recommendations