The Equation of State from Observed Masses and Radii of Neutron Stars

We determine an empirical dense matter equation of state from a heterogeneous dataset of six neutron stars: three type I X-ray bursters with photospheric radius expansion, studied by Ozel et al., and three transient low-mass X-ray binaries. We critically assess the mass and radius determinations from the X-ray burst sources and show explicitly how systematic uncertainties, such as the photospheric radius at touchdown, affect the most probable masses and radii. We introduce a parameterized equation of state and use a Markov Chain Monte Carlo algorithm within a Bayesian framework to determine nuclear parameters such as the incompressibility and the density dependence of the bulk symmetry energy. Using this framework we show, for the first time, that these parameters, predicted solely on the basis of astrophysical observations, all lie in ranges expected from nuclear systematics and laboratory experiments. We find significant constraints on the mass-radius relation for neutron stars, and hence on the pressure-density relation of dense matter. The predicted symmetry energy and the equation of state near the saturation density are soft, resulting in relatively small neutron star radii around 11-12 km for M=1.4 Msun. The predicted equation of state stiffens at higher densities, however, and our preferred model for X-ray bursts suggests that the neutron star maximum mass is relatively large, 1.9-2.2 Msun. Our results imply that several commonly used equations of state are inconsistent with observations.