Neutron Star Equation of State

The neutron star equation of state is the functional relation between pressure and energy density inside a neutron star, determining the star's mass-radius relationship, maximum mass, and internal structure. It is one of the most important unsolved problems in nuclear astrophysics because the extreme densities — several times nuclear saturation density — exceed the range where laboratory experiments can directly constrain the behavior of matter. The equation of state is not a single curve but a family of models, ranging from soft equations that predict relatively large radii and low maximum masses to stiff equations that permit massive, compact stars.

Gravitational wave observations of binary neutron star mergers, particularly by the A+ LIGO network, provide a novel constraint on the equation of state through the measurement of tidal deformability. As two neutron stars spiral together, each deforms under the tidal field of its companion, and this deformability imprints a phase correction on the gravitational waveform that depends sensitively on the star's compactness and thus on the equation of state. The detection of GW170817 in 2017 provided the first such constraint, ruling out the stiffest and softest models in a single observation. Future detections at higher signal-to-noise ratio will narrow the allowed family to a precision comparable to laboratory nuclear physics.