Neutron-Star Radius from a Population of Binary Neutron Star Mergers

We show how gravitational-wave observations with advanced detectors of tens to several tens of neutron-star binaries can measure the neutron-star radius with an accuracy of several to a few percent, for mass and spatial distributions that are realistic, and with none of the sources located within 100 Mpc. We achieve such an accuracy by combining measurements of the total mass from the inspiral phase with those of the compactness from the postmerger oscillation frequencies. For estimating the measurement errors of these frequencies, we utilize analytical fits to postmerger numerical relativity waveforms in the time domain, obtained here for the first time, for four nuclear-physics equations of state and a couple of values for the mass. We further exploit quasiuniversal relations to derive errors in compactness from those frequencies. Measuring the average radius to well within 10% is possible for a sample of 100 binaries distributed uniformly in volume between 100 and 300 Mpc, so long as the equation of state is not too soft or the binaries are not too heavy. We also give error estimates for the Einstein Telescope.

Figure 1

Top panels: Postmerger strain from NR waveforms for four EOSs and a representative mass of $\overline{M}=1.325M_{\odot }$; our analytical ansatz is shown as a transparent line of the same color. Only the initial 12 ms of the complete 25 ms waveforms are reported to aid the comparison. Bottom panels: Corresponding spectral amplitudes shown with the same color convention, superposed on the strain sensitivity curves of aLIGO and the Einstein Telescope (ET) [28]. Similarly good matches are produced also for $\overline{M}=1.250M_{\odot }$ (cf. Table I and Fig. 3 in the Supplemental Material [27]).

Figure 2

Estimated relative error in the radius measured, at 90% confidence level, versus the average population radius for different EOSs and $N=20$, 50, 100 (different shadings) BNSs distributed uniformly in a comoving volume between 100 and 300 Mpc. The two panels refer to binaries whose distribution in mass in the range $[1.2,1.38]M_{\odot }$ is either uniform (top) or Gaussian (bottom). Shown with dashed lines are the errors from the Fisher-matrix analysis for $N=50$.