Ranking Love Numbers for the Neutron Star Equation of State: The Need for Third-Generation Detectors

Gravitational-wave measurements of the tidal deformability in neutron-star binary coalescences can be used to infer the still unknown equation of state (EOS) of dense matter above the nuclear saturation density. By employing a Bayesian-ranking test, we quantify the ability of current and future gravitational-wave observations to discriminate among families of nuclear-physics based EOS which differ in particle content and ab initio microscopic calculations. While the constraining power of GW170817 is limited, we show that even twenty coalescences detected by LIGO-Virgo at design sensitivity are not enough to discriminate between EOS with similar softness but distinct microphysics. However, just a single detection with a third-generation detector such as the Einstein Telescope or Cosmic Explorer will rule out several families of EOS with very strong statistical significance and can discriminate among models which feature similar softness, hence, constraining the properties of nuclear matter to unprecedented levels.

Figure 1

Mass-radius and mass-tidal deformability diagrams for the EOS considered in the Bayesian analysis. The blue band on the left panel corresponds to the most massive pulsar observed in the EM band ($M=2.08_{-0.07}^{+0.07}{M}_{\odot }$ [91]), while dashed lines identify configurations with fixed compactness $\mathcal{C}=M/R$. Solid (dashed) curves correspond to stellar configurations with the speed of sound at the center smaller (larger) than the speed of light.

Figure 2

Bayes factors for different EOS models computed for GW170817 and normalized with respect to the EOS with maximum evidence in the catalog (WFF2). Vertical dashed lines identify the threshold above which the Bayes factor provides a strong and decisive evidence in favor of WFF2.

Figure 3

Evolution of the EOS Bayes factor with the number of events for the LIGO-Virgo network at design sensitivity. Top and bottom panels refer to the ALF2 (stiff EOS) and AP4 (soft EOS) injections, respectively. In each panel, the quantity ${\log }_{10}{\mathcal{B}}_T^i$ is normalized with respect to the injected EOS. Shaded bands mark the boundaries of the evidence criteria according to the Kass-Raftery scale [103]. In particular, ${\log }_{10}{\mathcal{B}}_T^i<-2$ indicates decisive unfavorable evidence.

Figure 4

Bayes factors for simulated observations with ET, relative to the injected EOS APR4, for WFF2 and SLY. The remaining set of ten EOS yield ${\log }_{10}{\mathcal{B}}_{\mathrm{APR}4}^i<-10$ for all events, and they are not shown in the plot.