Neutron Star Masses and Radii and the Equation of State of Dense Matter

The idea that neutron observations can be used to determine the equation of state of dense matter precedes the observation of the first neutron star by almost a decade. However, only in the past ten years have neutron star mass and radius measurements led to quantitative constraints on the equation of state over a range of densities. In this talk, we present a quantitative analysis of neutron star mass and radius measurements from quiescent low-mass X-ray binaries and photospheric radius expansion bursts. We combine this information with tidal deformability constraints from GW 170817 and recent constraints from NICER on the mass and radius of J0030+451 to obtain a probability distribution of mass-radius curves. We also obtain a probability distribution for the equation of state. Finally, we examine the impact of statistical and systematic uncertainties in these determinations.