Atmospheric oscillations provide simultaneous measurement of neutron star mass and radius

Abstract: Neutron stars with near-Eddington observable luminosities were shown to harbor levitating atmospheres, suspended above their surface. We report a new method to simultaneously measure the mass and radius of a neutron star based on oscillations of such atmospheres. In this paper, we present an analytic derivation of a family of relativistic, oscillatory, spherically symmetric eigenmodes of the optically and geometrically thin levitating atmospheres, including the damping effects induced by the radiation drag. We discover characteristic maxima in the frequencies of the damped oscillations and show that using the frequency maxima, one can estimate mass and radius of the neutron star, given the observed frequency and the corresponding luminosity of the star during the X-ray burst. Thus, our model provides a new way to probe the stellar parameters. We also show that the ratio of any two undamped eigenfrequencies depends only on the adiabatic index of the atmosphere, while for the damped eigenfrequencies, this ratio varies with the luminosity. The damping coefficient is independent of the mode number of the oscillations. Signatures of these atmospheres' dynamics will be reflected in the source's X-ray light curves.