A new code for nonradial stellar pulsations and its application to low-mass, helium white dwarfs

We present a finite difference code intended for computing linear, adiabatic, nonradial 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.