Abstract

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