  We have modelled X-ray burst oscillations observed with the Rossi X-ray
Timing Explorer (RXTE) 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 which 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 and we 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 sub-harmonic 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 Msun then
its radius must be > 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.
