Radial oscillations of extended envelopes of neutron stars

We study the radial oscillations of neutron star envelopes where radiation pressure predominates. We consider adiabatic oscillations and oscillations during which the luminosity is kept constant. We find the eigenvalues of the oscillation period of a fundamental mode for various cases of extended envelope. We show that in the case of the adiabatic oscillations the oscillation periods are given by the dynamical time, while in the case of the oscillations of constant luminosity the oscillation periods are longer than the dynamical time by a factor of β-1/2, where β is the ratio of the gas pressure to the total pressure. We apply the results of our study to the 0.65-s oscillation observed during a Type I X-ray burst from X1608-522. We find that the radial oscillation of constant luminosity can consistently explain observed facts such as the oscillation frequency, the constancy of luminosity, the high luminosity almost equal to the Eddington limit, and the anticorrelation between the counts in the low- and high-energy bands. We also discuss the relevance of the oscillations of extended envelopes to the quasi-periodic oscillations observed from the luminous X-ray stars. (author)