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

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 I 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 report general relativistic calculations of the maximum fractional rms amplitudes that can be observed during bursts, as a function of stellar compactness. We compute the dependence of the oscillation amplitude on the compactness of the star, on the angular dependence of the emission from the surface, on the rotational velocity at the stellar surface, and on whether there are one or two emitting spots. We show that color oscillations caused by the spectral variation with the angle of emission, the rotation of the star, and the limited bandwidth of the detector all tend to increase the observed amplitude of the oscillation. Nevertheless, if two spots are emitting, as appears to be the case in 4U 1636-536 and KS 1731-26, very restrictive bounds on the compactness of the star can be derived.