  A bound on the compactness of the neutron star in the low mass x-ray binary
4U 1636-53 is used to estimate the equation of state of neutron star matter at
high density. Observations of 580 Hz oscillations during the rising phase of
x-ray bursts from this system appear to be due to two antipodal hot spots on
the surface of an accreting neutron star rotating at 290 Hz, implying the
compactness of the neutron star is less than 0.163 at the 90% confidence level.
The equation of state of high density neutron star matter estimated from this
compactness limit is significantly stiffer than extrapolations to high density
of equations of state determined by fits of experimental nucleon-nucleon
scattering data and properties of light nuclei to two- and three-body
interaction potentials.
