The prospect of confining the equation of state of neutron star with future mass and radius measurement

Abstract: Simultaneous measurement of mass and radius with high precision is essential to unravel the equation of state of matter at the centre of neutron stars. Measurement of massive pulsars indicates that the equation of state has to be stiff at low densities. The radius measurement of PSR J0030+0451 has rejected several relatively softer equations of state. In this work, an ensemble of agnostically constructed EoS was studied for the mass and radius measurement. The range of radius of neutron stars obtained from the ensemble was confined within a radius bound from 10.5 - 14.5 km. It is seen that higher masses prefer stiffer EoS. However, the slope of the speed of sound (the stiffness of the EoS) is very sensitive to the radius measurement. Assuming the radius measurement to be precise up to 2 km, then a higher radius indicates sharp stiffening of the equation of state at low density; however, it also indicates a sharp fall after the peak, indicating a relatively softer core for massive neutron stars. On the other hand, for the same precision, a lower radius measurement indicates a relatively softer equation of state.