Reconstructing the neutron-star equation of state from astrophysical measurements

The properties of matter at ultrahigh densities, low temperatures, and with a significant asymmetry between protons and neutrons can be studied exclusively through astrophysical observations of neutron stars. We show that measurements of the masses and radii of neutron stars can lead to tight constraints on the pressure of matter at three fiducial densities, from 1.85 to 7.4 times the density of nuclear saturation, in a manner that is largely model independent and that captures the key characteristics of the equation of state. We demonstrate that observations with 10% uncertainties of at least three neutron stars can lead to measurements of the pressure at these fiducial densities with an accuracy of 0.11 dex or similar or equal to 30%. Observations of three neutron stars with 5% uncertainties are sufficient to distinguish at a better than 3 sigma confidence level between currently proposed equations of state. In the electromagnetic spectrum, such accurate measurements will become possible for weakly magnetic neutron stars during thermonuclear flashes and in quiescence with future missions such as the International X-ray Observatory.