Measuring Neutron-Star Radii with Gravitational-Wave Detectors

Coalescing binary neutron stars (NS) are expected to be an important source of gravitational waves (GW) detectable by laser interferometers. We present here a simple method for determining the compactness ratio $M/R$ of NS based on the observed deviation of the GW energy spectrum from point-mass behavior at the end of inspiral. Our method is based on the properties of quasiequilibrium binary NS sequences and does not require the computation of the full GW signal $h(t)$. Combined with the measurement of the NS masses during inspiral, the determination of $M/R$ will allow very strong constraints to be placed on the equation of state of dense nuclear matter.

Figure 1

ADM mass (total mass energy) of a binary NS system as a function of GW frequency (twice the orbital frequency), computed along each of our four irrotational equilibrium sequences. From bottom to top, the sequences correspond to NS with compactness $M/R=0.12,0.14,0.16$, and $0.18$. All models assume a polytropic EOS with $\Gamma =2$ and a NS mass of $1.35M_{\odot }$ for both components. The asterisks indicate the individual equilibrium configurations calculated along each sequence, while the lines show our best fit using Eq. (1) and the values of Table .

Figure 2

Energy spectrum $d{E}_{\mathrm{G}\mathrm{W}}/df$ of GW emission emitted along each of the four sequences of Fig. 1 in the quasiequilibrium approximation. Also shown is an irrotational 3PN point mass binary from Ref. 30, which closely tracks our most compact model. Asterisks indicate the terminal point along each sequence, where a cusp develops. The slanted straight lines show, from top to bottom, the point-mass Newtonian energy spectrum ($\propto f^{-1/3}$) multiplied by 1.0, 0.9, 0.75, and 0.5. The last three values are used to define characteristic break frequencies $f_{10}$, $f_{25}$, and $f_{50}$, where the energy spectrum has dropped by the corresponding fraction. The units on the right and top axes show the corresponding dimensionless quantities, with the mass dependence scaled away.