Identifying a First-Order Phase Transition in Neutron-Star Mergers through Gravitational Waves

We identify an observable imprint of a first-order hadron-quark phase transition at supranuclear densities on the gravitational-wave (GW) emission of neutron-star mergers. Specifically, we show that the dominant postmerger GW frequency $f_{\mathrm{peak}}$ may exhibit a significant deviation from an empirical relation between $f_{\mathrm{peak}}$ and the tidal deformability if a strong first-order phase transition leads to the formation of a gravitationally stable extended quark matter core in the postmerger remnant. A comparison of the GW signatures from a large, representative sample of microphysical, purely hadronic equations of state indicates that this imprint is only observed in those systems which undergo a strong first-order phase transition. Such a shift of the dominant postmerger GW frequency can be revealed by future GW observations, which would provide evidence for the existence of a strong first-order phase transition in the interior of neutron-stars.

Figure 1

Evolution of the maximum rest-mass density comparing DD2F-SF-1 (green line) and DD2F (black line) for $1.35M_{\odot }-1.35M_{\odot }$ mergers (solid curves). Horizontal dotted green lines mark the onset density ${\rho }_{\text{onset}}$ of the phase transition for DD2F-SF-1 at $T=0$ and at 20 MeV.

Figure 2

GW spectrum of the cross polarization at a distance of 20 Mpc along the polar axis comparing the DD2F-SF-1 EOS (green curve) and the DD2F EOS (black curve).

Figure 3

Dominant postmerger GW frequency $f_{\mathrm{peak}}$ as a function of tidal deformability $\mathrm{\Lambda }$ for $1.35M_{\odot }-1.35M_{\odot }$ mergers. The DD2F-SF models with a phase transition to deconfined quark matter (green symbols) appear as clear outliers (big symbol for DD2F-SF-1). Solid curve shows the least-squares fit Eq. (1) for all purely hadronic EOSs (including three models with hyperons marked by asterisks). ALF2 and ALF4 are marked by black plus signs. EOSs incompatible with GW170817 are not shown. Arrows mark DD2F-SF models 3, 6, and 7, which feature differently strong density jumps $\mathrm{\Delta }n$ (in ${\mathrm{fm}}^{-3}$) with roughly the same onset density and stiffness of quark matter.

Figure 4

Maximum rest-mass density ${\rho }_{\max }^{\max }$ during the first milliseconds of the postmerger phase as a function of the dominant postmerger GW frequency $f_{\mathrm{peak}}$ for $1.35M_{\odot }-1.35M_{\odot }$ mergers. Green symbols show results for DD2F-SF (big symbol for DD2F-SF-1). Asterisks indicate models with hyperons. Black plus signs indicate ALF2 and ALF4. Solid curve is a second-order polynomial least-squares fit to the data excluding hybrid EOSs.