Merger and Postmerger of Binary Neutron Stars with a Quark-Hadron Crossover Equation of State

Fully general-relativistic binary-neutron-star (BNS) merger simulations with quark-hadron crossover (QHC) equations of state (EOS) are studied for the first time. In contrast to EOS with purely hadronic matter or with a first-order quark-hadron phase transition (1PT), in the transition region QHC EOS show a peak in sound speed and thus a stiffening. We study the effects of such stiffening in the merger and postmerger gravitational (GW) signals. Through simulations in the binary-mass range $2.5<M/M_{\odot }<2.75$, characteristic differences due to different EOS appear in the frequency of the main peak of the postmerger GW spectrum ($f_2$), extracted through Bayesian inference. In particular, we found that (i) for lower-mass binaries, since the maximum baryon number density ($n_{\max }$) after the merger stays below 3–4 times the nuclear-matter density ($n_0$), the characteristic stiffening of the QHC models in that density range results in a lower $f_2$ than that computed for the underlying hadronic EOS and thus also than that for EOS with a 1PT; (ii) for higher-mass binaries, where $n_{\max }$ may exceed $4–5n_0$ depending on the EOS model, whether $f_2$ in QHC models is higher or lower than that in the underlying hadronic model depends on the height of the sound-speed peak. Comparing the values of $f_2$ for different EOS and BNS masses gives important clues on how to discriminate different types of quark dynamics in the high-density end of EOS and is relevant to future kilohertz GW observations with third-generation GW detectors.

Figure 1

Schematic plots for the (main figure) mass-radius relations and (inset) pressure $P$ vs energy density $e$ for some EOS satisfying constraints from terrestrial experiments and the observational fact that a NS of mass $\approx 2M_{\odot }$ exists; $H$ refers to a purely hadronic model, 1PT to a hybrid model with a first-order quark-hadron phase transition, and QHC to models with a quark-hadron crossover. QHC models show stiffening at densities lower than in the other two cases, typically leading to larger radii and smaller central densities for NSs with masses $1.4–2M_{\odot }$. The gray, green, and yellow shaded areas in both the main figure and inset correspond to the number density ranges of $n\sim 1–2n_0$, $\sim 2–4n_0$, and $\gtrsim 4n_0$, respectively.

Figure 2

Square of sound speed normalized to the speed of light, $c_s^2/c^2=dP/de$, for our QHC EOS with soft and stiff sets of quark model parameters and for representative hadronic EOS: Togashi EOS [22], SFHo [23], and DD2 [24]. The yellow band is the allowed region in the model-agnostic approach of Legred et al. [25] (see also [26]). The conformal limit, $c_s^2=c^2/3$, which should be reached in the high-density limit, is also shown as a guide.

Figure 3

Evolution of the maximum number density for simulations employing the QHC19 and Togashi EOS with different initial masses. $t_{\text{merger}}$ is the merger time defined as the time of the maximum amplitude of $|h|\equiv (h_{+}^2+h_{\times }^2{)}^{1/2}$.

Figure 4

Top: fundamental and dominant harmonic mode ($\ell =m=2$) of the plus polarization of the GW strain with amplitude envelope for the M1.35 models. Bottom: spectrogram (brighter colors indicate higher power in the spectrum) and instantaneous frequency of the same models.

Figure 5

Relation between $f_2$ and the total mass of the binary.