Abstract
We present a finite difference code intended for computing linear, adiabatic, non radial pulsations of spherical stars. This code is based on a slight modification of the general Newton-Raphson technique in order to handle the relaxation of the eigenvalue(square of the eigenfrequency) of the modes and their corresponding eigenfunctions. This code has been tested computing the pulsation spectra of polytropic spheres finding a good agreement with previous work. Then, we have coupled this code to our evolutionary code and applied it to the computation of the pulsation spectrum of a low mass, pure-helium white dwarf of 0.3 M ⊙ for a wide range of effective temperatures. In making this calculation we have taken an evolutionary time step short enough such that eigenmodes corresponding to a given model are used as initial approximation to those of the next one. Specifically, we have computed periods, period spacing, eigenfunctions, weight functions, kinetic energies and variational periods for a wide range of modes. To our notice this is the first effort in studying the pulsation properties of helium white dwarfs. The solution we have found working with these realistic white dwarf models are in good accord with the predictions of the asymptotic theory of Tassoul (1980) for high order modes. This indicates that the code presented here is able to work adequately also with realistic stellar models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Althaus, L.G. and Benvenuto, O.G.: 1997, Astrophys. J. 477, 313.
Benvenuto, O.G. and Althaus, L.G.: 1998, Mon. Not. R. Astron. Soc. 293, 177.
Bradley, P.A.: 1996, Astrophys. J. 468, 350.
Bradley, P.A. and Winget, D.E.: 1994, Astrophys. J. 430, 850.
Bradley, P.A., Winget, D.E. and Wood: 1993, Astrophys. J. 406.
Brassard, P., Pelletier, C., Fontaine, G. and Wesemael, F.: 1992a, Astrophys. J. Suppl. 80, 725.
Brassard, P., Pelletier, C., Fontaine, G. and Wesemael, F.: 1992b, Astrophys. J. Suppl. 81, 747.
Brown, T.M. and Gilliland, R.L.: 1994, Annu. Rev. Astron. Astrophys. 32, 37.
Christensen-Dalsgaard, J. and Mullan, D.J.: 1994, Mon. Not. R. Astron. Soc. 270, 921.
Cox, J.P.: 1980, Theory of Stellar Pulsation, Princeton University Press.
Dziembowski, W. and Koester, D.: 1981, Astron. Astrophys. 97, 16.
Gaustchy, A. and Saio, H.: 1995, Annu. Rev. Astron. Astrophys. 33, 75.
Gaustchy, A. and Saio, H.: 1996, Annu. Rev. Astron. Astrophys. 34, 551.
Goldreich, P. and Wu, Y.: 1999, Astrophys. J. 511, 904.
Kawaler, S.D.: 1993, Astrophys. J. 404, 294.
Kawaler, S.D., Hansen, C.J. and Winget, D.E.: 1985, Astrophys. J. 295, 547.
Kippenhahn, R., Weigert, A. and Hofmeister, E.: 1967, in: Methods in Computational Physics 6, 129.
Mullan, D.J.: 1989, Astrophys. J. 337, 1017.
Mullan, D.J. and Ulrich, R.K.: 1988, Astrophys. J. 331, 1013.
Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P.: 1992, Numerical Recipes, The Art of Scientific Computing, Cambridge Univ. Press.
Tassoul, M.: 1980, Astrophys. J. Suppl. 43, 469.
Tassoul, M., Fontaine, G. and Winget, D.E.: 1990, Astrophys. J. Suppl. 72, 335 (TFW).
Unno, W., Osaki, Y., Ando, H., Saio, H. and Shibahashi, H.: 1989, Nonradial Oscillations of Stars, University of Tokyo Press.
Winget, D.E., Van Horn, H.M., Tassoul, M., Hansen, C.J., Fontaine, G. and Carroll, B.W.: 1982, Astrophys. J. Lett. 252, L65.
Winget, D.E., Nather, R.E., Clemens, J.C., Provencal, J., Kleinman, S.J., et al.: 1991, Astrophys. J. 378, 326.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Córsico, A., Benvenuto, O. A New Code for Nonradial Stellar Pulsations and its Application to Low-Mass, Helium White Dwarfs. Astrophysics and Space Science 279, 281–300 (2002). https://doi.org/10.1023/A:1015101629358
Issue Date:
DOI: https://doi.org/10.1023/A:1015101629358