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We present a comprehensive study of spectroscopic radius measurements oftwelve neutron stars obtained during thermonuclear bursts or in quiescence. Weincorporate, for the first time, a large number of systematic uncertainties inthe measurement of the apparent angular sizes, Eddington fluxes, and distances,in the composition of the interstellar medium, and in the flux calibration ofX-ray detectors. We also take into account the results of recent theoreticalcalculations of rotational effects on neutron star radii, of atmosphericeffects on surface spectra, and of relativistic corrections to the Eddingtoncritical flux. We employ Bayesian statistical frameworks to obtain neutron starradii from the spectroscopic measurements as well as to infer the equation ofstate from the radius measurements. Combining these with the results ofexperiments in the vicinity of nuclear saturation density and the observationsof ~2 Msun neutron stars, we place strong and quantitative constraints on theproperties of the equation of state between approximately 2-8 times the nuclearsaturation density. We find that around M=1.5 Msun, the preferred equation ofstate predicts radii between 10.1 - 11.1 km. When interpreting the pressureconstraints in the context of high density equations of state based oninteracting nucleons, our results suggest a relatively weak contribution of thethree-body interaction potential.

The Dense Matter Equation of State from Neutron Star Radius and Mass Measurements