Bounds on compactness for low-mass X-ray binary neutron stars from X-ray burst oscillations

We have modeled X-ray burst oscillations observed with the Rossi X-Ray Timing Explorer from two low-mass X-ray binaries (LMXB): 4U 1636-53 with a frequency of 580 Hz and 4U 1728-34 at a frequency of 363 Hz. We have computed least-squares fits to the oscillations observed during the rising phase of bursts using a model that includes emission from either a single circular hot spot or a pair of circular antipodal hot spots on the surface of a neutron star. We model the spreading of the thermonuclear hot spots by assuming that the hot spot angular size grows linearly with time. We calculate the flux as a function of rotational phase from the hot spots and take into account photon deflection in the relativistic gravitational field of the neutron star, assuming the exterior spacetime is the Schwarzschild metric. We find acceptable fits with our model in a chi(2) sense and use these to place constraints on the compactness of the neutron stars in these sources. For 4U 1636-53, in which detection of a 290 Hz subharmonic supports the two-spot model, we find that the compactness (i.e., mass/radius ratio) is constrained to be M/R<0.163 at 90% confidence (G=c=1). This requires a relatively stiff equation of state (EOS) for the stellar interior. For example, if the neutron star has a mass of 1.4 M-⊙, then its radius must be greater than 12.8 km. Fits using a single hot spot model are not as highly constraining. We discuss the implications of our findings for recent efforts to calculate the EOS of dense nucleon matter and the structure of neutron stars.