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Oscillations of Hamada-Salpeter White Dwarfs including General Relativistic Effects

  • J. Skilling
Chapter

Abstract

Following a recent communication1, I have now computed radial oscillation periods for the fundamental modes of zero temperature white dwarfs obeying the Salpeter equation of state2, using general relativistic, rather than Newtonian, dynamics. As before, a variational approach was used, which maximizes the period given by various trial eigenfunctions. The Tolman-Oppenheimer-Volkoff3,4 equation of hydrostatic equilibrium
$$\frac{{dp}}{{dr}} = - \frac{{G(\rho + p/{c^2})(m + 4\pi {r^3}p/{c^2})}}{{{r^2}\left( {1 - 2Gm/r{c^2}} \right)}} $$
and the equation for the mass enclosed by r
$$ dm/dr = 4\pi {r^2}\rho$$
were integrated numerically in Refsllel with several trial eigenfunctions of the form
$$\xi \propto \,r + \alpha {r^2} + \beta {r^3} + \gamma {r^4} + \delta {r^5} + k{r^{256}}$$
using the Gill modification of the Runge-Kutta procedure. In these formulae, r is the Schwarzschild radial co-ordinate, and m is the gravitationally effective mass enclosed by r. M, the surface value of m, is the Schwarzschild mass of the star, which is the mass “felt” by exterior orbiting bodies.

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Copyright information

© Springer Science+Business Media New York 1968

Authors and Affiliations

  • J. Skilling
    • 1
  1. 1.Mullard Radio Astronomy Observatory, Cavendish LaboratoryUniversity of CambridgeUK

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