Estimating the EOS from the measurement of NS radii with 5% accuracy.

Observations of heavy (${\simeq}2\,M_\odot$) neutron stars in addition to the recent measurement of tidal deformability from the binary neutron-star merger GW170817, place interesting constraints on theories of dense matter. Current and future observatories, such as the NICER and ATHENA are expected to collect information on the global parameters of neutron stars, namely masses and radii, with the accuracy of a few percent. Such accuracy will allow for precise comparisons of measurements to models of compact objects. Here we investigate how the measurement accuracy of the NICER and ATHENA missions will improve our understanding of the dense-matter interior of neutron stars. We compare 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 the observational point of view i.e. within the predicted error of the radius measurement. We assume observational errors on the radius determination corresponding to the expected accuracies. The effect of rotation is examined using high-precision numerical relativity computations. Due to the fact that masses and rotational frequencies might be determined very precisely in the most optimistic scenario, only the influence of observational errors on the radius measurements is investigated. We show that ${\pm}5\%$ errors in radius measurement lead to ${\sim}10\%$ and ${\sim}40\%$ accuracy in central parameter estimation, 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.