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Simultaneous, precise measurements of the mass $M$ and radius $R$ of neutronstars can yield uniquely valuable information about the still uncertainproperties of cold matter at several times the density of nuclear matter. Onemethod that could be used to measure $M$ and $R$ is to analyze theenergy-dependent waveforms of the X-ray flux oscillations seen during somethermonuclear bursts from some neutron stars. These oscillations are thought tobe produced by X-ray emission from hotter regions on the surface of the starthat are rotating at or near the spin frequency of the star. Here we explorehow well $M$ and $R$ could be determined by generating, and analyzing usingBayesian techniques, synthetic energy-resolved X-ray data that we produceassuming a future space mission having 2--30 keV energy coverage and aneffective area of 10 m$^2$, such as the proposed \textit{LOFT} or\textit{AXTAR} missions.  We find that if the hot spot is within 10$^\circ$ of the rotation equator,both $M$ and $R$ can usually be determined with an uncertainty of about 10% ifthere are $10^6$ total counts from the spot, whereas waveforms from spotswithin 20$^\circ$ of the rotation pole provide no useful constraints. Theseconstraints can usually be achieved even if the burst oscillations vary withtime and data from multiple bursts must be used to obtain 10$^6$ counts fromthe hot spot. This is therefore a promising method to constrain $M$ and $R$tightly enough to discriminate strongly between competing models of cold,high-density matter.

Determining neutron star masses and radii using energy-resolved waveforms of X-ray burst oscillations