Upper limit set by causality on the tidal deformability of a neutron star

Understand

A principal goal of gravitational-wave astronomy is to constrain the neutron star equation of state (EOS) by measuring the tidal deformability of neutron stars.

• The tidally induced departure of the waveform from that of point-particle (or spinless binary black hole (BBH)) increases with the stiffness of the EOS.
• We show that causality (the requirement that the speed of sound is less than the speed of light for a perfect fluid satisfying a one-parameter equation of state) places an upper bound on tidal deformability as a function of mass.
• Like the upper mass limit, the limit on deformabity is obtained by using an EOS with $v_{sound} = c$ for high densities and matching to a low density (candidate) EOS at a matching density of order nuclear saturation density.