Equations Of Radial Oscillations Research Articles

Properties of the ionisation glitch

Aims. In the present paper, we aim to constrain the properties of the ionisation region of a star from the oscillation frequency variation (a so-called glitch) caused by rapid structural variations in this very region. In particular, we seek tof avoid the use of calibration based on stellar models, thus providing a truly independent estimate of these properties. These include both the helium abundance and other physical quantities that can have a significant impact on the oscillation frequencies, such as the electronic degeneracy parameter or the extent of the ionisation region. Methods. Building on previous findings, we applied structural perturbations of the ionisation zone to the wave equation for radial oscillations in an isentropic region. The resulting glitch model is thus able to exploit the information contained in the fast frequency oscillation caused by the helium ionisation but also that in the slow trend accompanying the ionisation of hydrogen. This information can be directly expressed in terms of parameters related to the helium abundance, electronic degeneracy, and the extent of the ionisation region, respectively. Results. Using Bayesian inference, we show that substantial recovery of the properties at the origin of the glitch is possible. We find a degeneracy between the helium abundance and the electronic degeneracy, which particularly affects the helium estimate. Extending the method to cases where the glitch is subject to contamination (e.g., surface effects), we note the importance of the slow glitch trend associated with hydrogen ionisation. We propose the use of a Gaussian process to disentangle the frequency glitch from surface effects.

Radial oscillations of neutral and charged hybrid stars

We construct stellar models of hadron stars and hybrid stars and calculate the frequencies of their lowest radial mode of vibration. Chandrasekhar's equation for radial oscillations is generalized for stars with internal electric fields and earlier versions of that generalization are simplified. For the hybrid stars a Gibbs construction is employed. It is found that the softening of the equation of state associated with the presence of deconfined quarks reduces the oscillation frequency. We show that a slight charge inbalance should lead to increased maximum mass, decreased central density and lower oscillation frequencies.

Computation of the lowest eigenvalue arising from the problem of stellar stability by the method of Schwartz iteration

The Schwartz iteration procedure is used to compute the lowest eigenvalue from the equation for radial oscillations of stars. It was found that the convergence of the iteration had an oscillating convergence. This made it unsuitable for the computation of the higher eigenvalues. A series of associated Laguerre functions is suggested as a method of obtaining better results.