Will black hole-neutron star binary inspirals tell us about the neutron star equation of state?

The strong tidal forces that arise during the last stages of the life of a black hole-neutron star binary may severely distort, and possibly disrupt, the star. Both phenomena will imprint signatures about the stellar structure in the emitted gravitational radiation. The information from the disruption, however, is confined to very high frequencies, where detectors are not very sensitive. We thus assess whether the lack of tidal distortion corrections in data-analysis pipelines will affect the detection of the inspiral part of the signal and whether these may yield information on the equation of state of matter at nuclear densities. Using recent post-Newtonian expressions and realistic equations of state to model these scenarios, we find that point-particle templates are sufficient for the detection of black hole-neutron star inspiralling binaries, with a loss of signals below 1% for both second- and third-generation detectors. Such detections may be able to constrain particularly stiff equations of state, but will be unable to reveal the presence of a neutron star with a soft equation of state.

Figure 1

Tracks of inspiralling BH-NS binaries at 100 Mpc, for $a=0$ and a PS EOS (red lines), and their position with respect to the sensitivities of AdLIGO (black line) and AdVirgo (light blue line). To avoid cluttering, we show only the strongest and the weakest signals, which refer to a $1.9M_{\odot }$ and a $1.2M_{\odot }$ NS, respectively, in binaries with mass ratio $q=0.1$ and $q=1/3$. Each track is terminated at $(f_{\mathrm{end}},\tilde{h}(f_{\mathrm{end}})\sqrt{f_{\mathrm{end}}})$; the red dashed continuations are shown only for reference. The shaded region is the one spanned by all the termination points obtained by varying $M_{\mathrm{NS}}$ and $q$. A magnification reporting the lines at constant $M_{\mathrm{NS}}$ and $q$ that limit the shaded area is shown in the right panel.

Figure 2

Tidal distortion contribution to the quadrupole GW phase $\Delta \varphi$ for the three representative EOSs. The tracks end at $f_{\mathrm{end}}$ and yield larger dephasings for stiffer EOSs, such as PS.

Figure 3

Overlaps between PN wave forms for BH-NS binary systems modeled as point particles and with the inclusion of tidal distortion effects (“$\lambda$”). The overlap is calculated for the AdLIGO detector and for nonspinning BHs.

Figure 4

Distinguishability $\delta h_{\mathrm{PP},\lambda }$ by AdLIGO for binaries at 100 Mpc and with $a=0$. In the white area $\delta h_{\mathrm{PP},\lambda }<1$ for all EOSs, in the red-shaded one $\delta h_{\mathrm{PP},\mathrm{PS}}>1$, and in the blue-shaded one $\delta h_{\mathrm{PP},\mathrm{GNH}3}>1$. Contours for $h_{\mathrm{PP},\lambda }=1$, 4 are shown for both EOSs. The black star marks a canonical $10M_{\odot }-1.4M_{\odot }$ BH-NS binary.