Bounds on the Compactness of Neutron Stars from Brightness Oscillations during X-Ray Bursts

Abstract

The discovery of high-amplitude brightness oscillations at the spin frequency or its first overtone in six neutron stars in low-mass X-ray binaries during type~1 X-ray bursts provides a powerful new way to constrain the compactness of these stars, and hence to constrain the equation of state of the dense matter in all neutron stars. Here we present the results of general relativistic calculations of the maximum fractional rms amplitudes that can be observed during bursts. In particular, we determine the dependence of the amplitude on the compactness of the star, the angular dependence of the emission from the surface, the rotational velocity at the stellar surface, and whether there are one or two emitting poles. We show that if two poles are emitting, as is strongly indicated by independent evidence in 4U 1636-536 and KS 1731-26, the resulting limits on the compactness of the star can be extremely restrictive. We also discuss the expected amplitudes of X-ray color oscillations and the observational signatures necessary to derive convincing constraints on neutron star compactness from the amplitudes of burst oscillations.