Tidal Deformability

Tidal deformability (often denoted by the dimensionless parameter Lambda, or the Love number k_2) is a measure of how much a neutron star deforms under the tidal gravitational field of a companion star in a binary system. It quantifies the ratio of the induced quadrupole moment to the external tidal field, and it depends sensitively on the star's compactness — the ratio of its mass to its radius. A soft equation of state produces a large, fluffy neutron star with high tidal deformability; a stiff equation of state produces a small, compact star with low deformability. The parameter is therefore a direct probe of the behavior of matter at supranuclear densities, accessible only through astrophysical observation rather than laboratory experiment.

Gravitational wave detectors such as A+ LIGO measure tidal deformability through the phase evolution of the inspiral waveform. As the two neutron stars approach each other, the tidal deformation extracts energy and angular momentum from the orbit, causing the inspiral to accelerate slightly compared to a point-mass binary. This effect is most pronounced in the final orbits before merger, where the signal is strongest but the waveform is also most complex. The measurement requires accurate waveform models from numerical relativity that incorporate tidal effects, and it is one of the primary science goals of the third-generation detector network. The GW170817 event provided the first measurement, constraining the combined tidal deformability of the two stars to a range that immediately ruled out several families of nuclear equations of state.