Gravitational-wave imprints of nonconvex dynamics in binary neutron star mergers

Explaining gravitational-wave (GW) observations of binary neutron star (BNS) mergers requires an understanding of matter beyond nuclear saturation density. Our current knowledge of the properties of high-density matter relies on electromagnetic and GW observations, nuclear physics experiments, and general relativistic numerical simulations. In this paper we perform numerical-relativity simulations of BNS mergers subject to nonconvex dynamics, allowing for the appearance of expansive shock waves and compressive rarefactions. Using a phenomenological nonconvex equation of state we identify observable imprints on the GW spectra of the remnant. In particular, we find that nonconvexity induces a significant shift in the quasiuniversal relation between the peak frequency of the dominant mode and the tidal deformability (of order $\mathrm{\Delta }{f}_{\mathrm{peak}}\gtrsim 380\mathrm{Hz}$) with respect to that of binaries with convex (regular) dynamics. Similar shifts have been reported in the literature, attributed however to first-order phase transitions from $\mathrm{nuclear}/\mathrm{hadronic}$ matter to deconfined quark matter. We argue that the ultimate origin of the frequency shifts is to be found in the presence of anomalous, nonconvex dynamics in the binary remnant.

Figure 1

Relativistic fundamental derivative ${\mathcal{G}}_R$ as a function of baryon density $n_b$ for a few selected EOS with (DD2F-SF and DD2-SF) and without (DD2) a first-order hadron-quark phase transition.

Figure 2

Gravitational mass $M_G$ vs circumferential radius $R_{\mathrm{circ}}$ for all the EOSs listed in Table 1 along with the observational NS mass constraints within 95% confidence levels from the measurements of pulsars from $\mathrm{NICER}/\mathrm{XMM}$-Newton [65, 66, 71], and the BNS observations from the $\mathrm{LIGO}/\mathrm{Virgo}/\mathrm{KAGRA}$ Collaboration [70, 72].

Figure 3

Convexity behavior of the GGL EOS for the canonical values of the free parameters used in our simulations. We set ${\mathrm{\Gamma }}_{\mathrm{th}}=1.8$ (as in typical BNS simulations; see e.g., [14, 88, 89]), ${\mathrm{\Gamma }}_1=3.0$, ${\rho }_1=9.1\times {10}^{14}\mathrm{g}{\mathrm{cm}}^{-3}$, and $\mathrm{\Sigma }=0.35{\rho }_1$. The blue area corresponds to the region of the parameter space where the EOS is convex (i.e., $\mathcal{G}>0$ and ${\mathcal{G}}_R>0$). The green region corresponds to the region where $\mathcal{G}<0$ (and thus ${\mathcal{G}}_R<0$), i.e., the EOS is nonconvex. The red area is the relativistic nonconvex region (i.e., $\mathcal{G}>0$ and ${\mathcal{G}}_R<0$). Noncausal regions are displayed in black.

Figure 4

Minimum value of the relativistic fundamental derivative ${\mathcal{G}}_R$ vs coordinate time for some selected EOSs, evolved with the GGL EOS setting ${\mathrm{\Gamma }}_1=3.0$ (see Table 2). The inset displays the evolution of ${\mathcal{G}}_R$ for two configurations evolved with ${\mathrm{\Gamma }}_1=3.5$. Notice that the coordinate time has been shifted to the merger time.

Figure 5

Rotational profiles of the binary remnant along the coordinate radius $r$ at $t\sim 15\mathrm{ms}$ after merger for the EOS indicated in the legend. Binaries with nonconvex (convex) dynamics are displayed with dashed (continuous) lines. Horizontal lines show the pattern speed frequencies of the main modes ($f_{\mathrm{peak}}/2$) for each model. The colors of the horizontal lines are the same as for the EOS labels. Similar profiles are observed for all other EOSs in Table 1.

Figure 6

Rest-mass density ${\rho }_0$, normalized to its initial maximum value ${\rho }_{0,\max }\sim {10}^{14.8}\mathrm{g}{\mathrm{cm}}^{-3}$ (see Table 1 for all cases), in log scale of the BNS remnant at $t\sim 6\mathrm{ms}$ following merger for some of the EOSs listed in Table 2. Negative values of the relativistic fundamental derivative are displayed in greenish (cold) color. Each panel shows a side-by-side comparison between the quasisteady configuration of the remnant evolved using either the phenomenological GGL EOS (left) or the constant $\mathrm{\Gamma }$-law EOSs (right).

Figure 7

GW spectra of both GGL and constant $\mathrm{\Gamma }$-law binaries at 50 Mpc with optimal orientation and with a time window $t-t_{\mathrm{mer}}=[-20,5]\mathrm{ms}$ which emphasizes the contribution of the dominant spectral mode $f_{\mathrm{peak}}$ following merger. The two spectra for the GGL EOS correspond to ${\mathrm{\Gamma }}_1=3.0$ and ${\mathrm{\Gamma }}_1=3.5$. Sensitivity curves of Advanced Virgo (aVirgo) [91], Advanced LIGO (aLIGO) [92], Einstein Telescope (ET-D) [93], and Cosmic Explorer (CE) [94] are also displayed. Vertical lines mark the location of the peak frequency $f_{\mathrm{peak}}$.

Figure 8

GW peak frequency of the postmerger remnant $f_{\mathrm{peak}}$ as a function of the tidal deformability $\mathrm{\Lambda }$ for all simulations in Table 2. Each circle corresponds to one initial-data EOS, the corresponding colors indicating the EOS used in the evolutions (see legend). Solid curves display the quasiuniversal relations given by Eqs. (8) and (9). Colored regions represent the standard deviation of the corresponding fit.