  We discuss millisecond period brightness oscillations and surface atomic
spectral lines observed during type I X-ray bursts from a neutron star in a low
mass X-ray binary system. We show that modeling of these phenomena can
constrain models of the dense cold matter at the cores of neutron stars. We
demonstrate that, even for a broad and asymmetric spectral line, the stellar
radius-to-mass ratio can be inferred to better than 5%. We also fit our
theoretical models to the burst oscillation data of the low mass X-ray binary
XTE J1814-338, and find that the 90% confidence lower limit of the neutron
star's dimensionless radius-to-mass ratio is 4.2.
