The prospect of confining the equation of state of neutron stars with future mass and radius measurements

Abstract Simultaneous measurement of mass and radius with high precision is essential to unravelling the equation of state of matter at the core of neutron stars. Measurement of massive pulsars indicates that they have to be stiff at low densities. In this work, an ensemble of agnostically constructed equations of state was studied for the mass-radius measurement. The radius of neutron stars obtained from the ensemble was confined within a 10.5–14.5 km bound. Among the NICER measurements, PSR J0437–4715 provides the most stringent constraint on the equation of state. It was found that the detection of stars with smaller radii would prefer a softer equation of state, and the detection of stars with larger radii would prefer a stiffer equation of state. However, irrespective of the detection of stars with a smaller or larger radius, the sound speed peak indicates that stars are likely to have a smooth phase transition at a few times saturation densities, and the matter at the core may not be pure conformal quark matter. A better precision of the radius measurement drastically increases the chances of constraining the equation of state. The equation of state would be more effectively constrained if the measurement of large-radius stars with high precision were to happen. Precise radius measurements of neutron stars with smaller radii provide limited constraints on the equation of state over the density range relevant to neutron stars, largely independent of the stellar mass. Also, measurements for different masses are necessary to constrain the equation of state at all density ranges relevant to neutron stars.