Demonstrating the Feasibility of Probing the Neutron-Star Equation of State with Second-Generation Gravitational-Wave Detectors

Fisher matrix and related studies have suggested that, with second-generation gravitational-wave detectors, it may be possible to infer the equation of state of neutron stars using tidal effects in a binary inspiral. Here, we present the first fully Bayesian investigation of this problem. We simulate a realistic data analysis setting by performing a series of numerical experiments of binary neutron-star signals hidden in detector noise, assuming the projected final design sensitivity of the Advanced LIGO-Virgo network. With an astrophysical distribution of events (in particular, uniform in comoving volume), we find that only a few tens of detections will be required to arrive at strong constraints, even for some of the softest equations of state in the literature. Thus, direct gravitational-wave detection will provide a unique probe of neutron-star structure.

Figure 1

Median and 95% confidence interval evolution for the ${\lambda }_0$ parameter as an increasing number of sources is taken into consideration, for three different equations of state in the signals: a hard (MS1), a moderate (H4), and a soft (SQM3) EOS. In each case, the dashed line indicates the true value.

Figure 2

Cumulative distributions of log odds ratios for $\mathcal{O}(30)$ simulated catalogs of sources, for various EOS against the true EOS model, with different panels corresponding to different true EOS in the signal model (stated at the top of each panel). For each signal model, the number of sources per catalog was fixed to 20. Using the Jeffreys criterion, we consider the true EOS ${\mathcal{H}}_j$ to be identified correctly if $\ln O_j^i<-5$ (odds less than $1:150$) for all the other EOS ${\mathcal{H}}_i$. In the cases where the true EOS are MS1, H4, and SQM3, this happens for 77%, 62%, and 57% of catalogs, respectively. Note how hypotheses tend to get ranked correctly by “goodness of fit”, i.e., hardness of the EOS.