Estimating the equation of state from measurements of neutron star radii with 5% accuracy

Abstract

Context. Observations of heavy (⋍2 M⊙) neutron stars, such as PSR J1614−2230 and PSR J0348+0432, in addition to the recent measurement of tidal deformability from the binary neutron-star merger GW170817, place interesting constraints on theories of dense matter. Currently operating and future observatories, such as the Neutron star Interior Composition Explorer (NICER) and the Advanced Telescope for High ENergy Astrophysics (ATHENA), are expected to collect information on the global parameters of neutron stars, namely masses and radii, with an accuracy of a few percent. Such accuracy will allow for precise comparisons of measurements to models of compact objects and significantly improve our understanding of the physics of dense matter. Aims. The dense-matter equation of state is still largely unknown. We investigate how the accuracy of measurements expected from the NICER and ATHENA missions will improve our understanding of the dense-matter interior of neutron stars. Methods. We compared global parameters of stellar configurations obtained using three different equations of state: a reference (SLy4 EOS) and two piecewise polytropes manufactured to produce mass-radius relations indistinguishable from an observational point of view, i.e. within the predicted error of radius measurement. We assumed observational errors on the radius determination corresponding to the accuracies expected for the NICER and ATHENA missions. The effect of rotation was examined using high-precision numerical relativity computations. Because masses and rotational frequencies might be determined very precisely in the most optimistic scenario, only the influence of observational errors on radius measurements was investigated. Results. We show that ±5% errors in radius measurement lead to ~10% and ~40% accuracy in central parameter estimations for low-mass and high-mass neutron stars, respectively. Global parameters, such as oblateness and surface area, can be established with 8–10% accuracy, even if only compactness (instead of mass and radius) is measured. We also report on the range of tidal deformabilities corresponding to the estimated masses of GW170817 for the assumed uncertainty in radius.