Neutron stars and the dense matter equation of state

The past two decades have witnessed tremendous progress in understanding the properties of neutron stars, their maximum mass and radii, and the properties of the dense matter in their cores, made possible by electromagnetic observations of neutron stars and the detection of gravitational waves from their mergers. These observations have provided novel constraints on neutron-star structure that are intimately related to the properties of dense neutron-rich matter described by the nuclear equation of state. Nevertheless, constraining the equation of state over the wide range of densities probed by astrophysical observations is still challenging, as the physics involved is broad and the system spans many orders of magnitude in density. Theoretical approaches to calculate and model the neutron-star equation of state in various regimes of densities are reviewed, and the related consequent properties of neutron stars are discussed. How the equation of state at low densities can be calculated from nuclear interactions that are constrained and benchmarked by nuclear experiments is described. Neutron-star observations, with a particular emphasis on information provided by gravitational-wave signals and electromagnetic observations, are reviewed. Finally, future challenges and opportunities in the field are discussed. Neutron stars, the remnants of supernova explosions, are the densest objects in the Universe. A typical neutron star has a mass between one and two solar masses, and a radius of around 12 km. The density at the center of the star is higher than that in atomic nuclei. As a result, the properties of neutron stars provide important information about the behavior of ordinary matter under extreme compression. In recent years, new information about neutron stars has emerged from two sources. The first is the observation of the gravitational-wave signal from the final inspiral of a coalescing binary neutron star. The second is a careful measurement of the x-ray pulse profile of a spinning neutron star. This review discusses these measurements and summarizes how they constrain masses, radii, and central densities. The results are compared to predictions based on calculations of the nuclear equation of state at densities comparable to that in atomic nuclei, which are then extrapolated to higher density. The review ends with an outlook on future observational opportunities.