Constraining neutron star matter from the slope of the mass-radius curves

TL;DR

This paper explores how local derivatives of the neutron star mass-radius relationship can constrain the star's internal properties and the equation of state, especially with upcoming precise measurements.

Contribution

It demonstrates that the slope of the mass-radius curve at specific masses can predict maximum neutron star masses and radii, providing a model-independent way to constrain neutron star matter.

Findings

Negative slope at 1.4 M_sun implies radius below 12 km for 2 M_sun neutron stars.

Negative slope across masses above 1 M_sun suggests a maximum mass below 2.3 M_sun.

Positive slope in some mass range is necessary for maximum masses above 2.4 M_sun.

Abstract

We analyse the implications of information about local derivatives from the mass-radius diagram in neutron star matter. It is expected that the next generation of gravitational wave and electromagnetic detectors will allow the determination of the neutron star radius and mass with a small uncertainty. Observations of neutron stars clustered around a given neutron star mass allow the estimation of local derivatives in the $M(R)$ diagram, which can be used to constrain neutron star properties. From a model-independent description of the neutron star equation of state, it is shown that a $M(R)$ curve with a negative slope at 1.4$M_\odot$ predicts a $2M_\odot$ neutron star radius below 12 km. Furthermore, a maximum mass below 2.3$M_\odot$ is obtained if the $M(R)$ slope is negative in the whole range of masses above $1M_\odot$, and a maximum mass above 2.4$M_\odot$ requires the $M(R)$ slope to be positive in some range of masses. Constraints on the mass-radius curve of neutron stars will place strong constraints on microscopic models.