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Neutron stars with near-Eddington observable luminosities were shown toharbor levitating atmospheres, suspended above their surface. We report a newmethod to simultaneously measure the mass and radius of a neutron star based onoscillations of such atmospheres. In this paper, we present an analyticderivation of a family of relativistic, oscillatory, spherically symmetriceigenmodes of the optically and geometrically thin levitating atmospheres,including the damping effects induced by the radiation drag. We discovercharacteristic maxima in the frequencies of the damped oscillations and showthat using the frequency maxima, one can estimate mass and radius of theneutron star, given the observed frequency and the corresponding luminosity ofthe star during the X-ray burst. Thus, our model provides a new way to probethe stellar parameters. We also show that the ratio of any two undampedeigenfrequencies depends only on the adiabatic index of the atmosphere, whilefor the damped eigenfrequencies, this ratio varies with the luminosity. Thedamping coefficient is independent of the mode number of the oscillations.Signatures of these atmospheres' dynamics will be reflected in the source'sX-ray light curves.

Atmospheric oscillations provide simultaneous measurement of neutron star mass and radius