Signatures of deconfined quark phases in binary neutron star mergers

We investigate the quark deconfinement phase transition in the context of binary neutron star (BNS) mergers. We treat hadronic matter using a Brueckner-Hartree-Fock quantum many-body approach and modern two-body and three-body nuclear interactions derived within chiral effective field theory. Quark matter is modeled using an extended version of the bag model. We combine these approaches to construct a new finite-temperature composition-dependent equation of state (EOS) with a first-order phase transition between hadrons and deconfined quarks. We perform numerical relativity simulations of BNS mergers with this new EOS and compare results obtained with or without the deconfinment phase transition. We find that deconfined quark production in a neutron star merger results from matter crossing the phase boundary over a wide range of temperatures and densities. The softening of the EOS due to the phase transition causes the merger remnants to be more compact and to collapse to a black hole at earlier times. The phase transition is imprinted on the postmerger gravitational wave (GW) signal duration, amplitude, and peak frequency. However, this imprint is only detectable for binaries with sufficiently long-lived remnants. Moreover, the phase transition does not result in significant deviations from quasiuniversal relations for the postmerger GW peak frequency. Consequently, the postmerger GW peak frequency alone is not sufficient to conclusively exclude or confirm the presence of a phase transition in a BNS merger. We also study the impact of the phase transition on dynamical ejecta, remnant accretion disk masses, $r$-process nucleosynthetic yields and associated electromagnetic counterparts. While there are differences in the electromagnetic counterparts and nucleosynthesis yields between the purely hadronic models and the models with phase transitions, these can be primarily ascribed to the difference in remnant collapse time between the two, so they are degenerate with other effects. An exception is the nonthermal afterglow caused by the interaction of the fastest component of the dynamical ejecta and the interstellar medium, which is systematically boosted in the binaries with phase transition as a consequence of the more violent merger they experience.

Figure 1

The pressure-density variation at $T=0$ and the mass-radius relationship for isolated, cold ($T=0$), $\beta$-equilibrated, and spherically symmetric neutron stars constructed with the two equations of state used in this work. The circle and square markers represent the individual masses of the neutron stars simulated for BL and BLQ EOS, respectively. The BLQ mass-radius sequence departs from the BL sequence for neutron stars having a mass $\mathrm{M}\gtrsim 1.7{\mathrm{M}}_{\odot }$. These stars possess in fact a core made of hadron-quark mixed matter.

Figure 2

Evolution of the remnant’s density, temperature, electron fraction and quark fraction across the xy plane for a merger of the $1.3325–1.3325{\mathrm{M}}_{\odot }$ binary. Deconfined quarks appear as matter is compressed and heated up during the merger. The quark distribution strongly correlates with the temperature distribution in the middle panel, indicating that quarks are formed due to heating during the merger. At later times, the quark distribution is centrally condensed and most strongly correlated with the density.

Figure 3

Evolution of a BNS merger of masses 1.4 and $1.2{\mathrm{M}}_{\odot }$ evolved with the BLQ EOS. The mass configuration corresponds to the pulsar PSR $\mathrm{J}1829+2456$ [65]. The blue and gray color scales represent isodensity surfaces corresponding to densities ${10}^{14}$ and ${10}^{13}\mathrm{g}{\mathrm{cm}}^{-3}$, respectively. The deconfined quark phase that appears near the core of the remnant after merger is represented in red.

Figure 4

Thermodynamic trajectory of a representative tracer particle from the binary system $1.3325–1.3325{\mathrm{M}}_{\odot }$. The trajectory is superposed on a ${\mathrm{Y}}_{\mathrm{e}}$ weighted equilibrium slice of the BLQ EOS. The trajectories themselves are color coded according to the relative time from merger and the radial distance of a tracer from the center of the remnant. Matter in the NS cores crosses the phase boundary several times starting from the moment of merger and until the time of collapse and BH formation.

Figure 5

Time evolution of quark fraction and density of fluid elements traced by Lagrangian tracers for two binary neutron star systems $1.482–1.259{\mathrm{M}}_{\odot }$ and $1.3325–1.3325{\mathrm{M}}_{\odot }$. Noticeable is the fact that the period of oscillations of density matches the period of oscillations of quark fraction.

Figure 6

A two-dimensional histogram of the thermodynamic variables $\rho$ and $\mathrm{T}$ and weighted by bins of tracer mass. Also shown are contours of quark fraction. Both the bulk of the remnant’s core and the periphery of the core can exhibit deconfined quark matter depending upon $\rho$ and $\mathrm{T}$.

Figure 7

Evolution of the instantaneous GW frequency $f_{\mathrm{GW}}$, the“$+$” polarization strain amplitude for the ($l=2$, $m=2$) mode of the GW signal, the central density $\rho$, and the binding energy $E_b$ of the $1.3325–1.3325{\mathrm{M}}_{\odot }$ binary. The inspiral ($t\le t_{\mathrm{merg}}$) evolution predicted by both the BLh and BLQ EOSs is identical. The appearance of quarks is imprinted on the postmerger dynamics and GW signal.

Figure 8

Amplitude of the ($l=2$, $m=2$) mode of the GW strain $h_{+}$ and binding energies for the $1.4–1.2{\mathrm{M}}_{\odot }$, $1.482–1.259{\mathrm{M}}_{\odot }$, and $1.856–1.020{\mathrm{M}}_{\odot }$ binaries. As the binaries become more massive or more asymmetric, the length of the postmerger signal decreases. The postmerger is further shortened by an onset of deconfinement phase transition.

Figure 9

Power spectrum of the $(l=2,m=2)$ mode of the GW strain for the $1.4–1.2{\mathrm{M}}_{\odot }$, $1.3325–1.3325{\mathrm{M}}_{\odot }$, $1.482–1.259{\mathrm{M}}_{\odot }$, and $1.856–1.020{\mathrm{M}}_{\odot }$ binaries. An exponential filter was applied to the data to remove the inspiral signal. The difference in the peak frequency between the BLQ and the BLh binaries in the top panels is sufficiently large to be measured. On the other hand, because of the short length of the BLQ postmerger signals, the differences in the peak frequency for the binaries in the bottom panels is smaller than the nominal uncertainty of the Fourier transform, so they cannot be measured.

Figure 10

Correlations between the total mass-scaled postmerger peak frequency $M{f}_2$ and the tidal parameter $\xi$. Also shown is the fit from the quasiuniversal relation presented in [26] along with its 90% confidence interval. The gray points correspond to simulations cataloged in the core database [88]. It can be seen that deviations in $f_2$ (red circles) by virtue of phase transitions are not large enough to violate the quasiuniversal relation.

Figure 11

Histograms of the asymptotic velocity $v_{\infty }$, specific entropy $s$, angle with the orbital plane $\theta$, and electron fraction $Y_e$ of the ejecta for three representative binary configurations evolved with the BLh and BLQ EOSs. The most significant differences are seen in the $1.4–1.4{\mathrm{M}}_{\odot }$ binary, for which the BLQ EOS predicts rapid BH formation, while the BLh EOS predicts a long-lived remnant. We note that $M$ here represents the mass of the ejecta in the corresponding bins normalized to $M_{\mathrm{ej}}$ i.e. the total ejecta mass as reported in Table 3.

Figure 12

Nucleosynthesis yields of the dynamical ejecta from selected binaries. The final relative abundances in the ejecta are insensitive to the appearance of quarks, but are instead sensitive to the binary mass ratio. Comparable-mass binaries produce $r$-process elements with relative abundances close to solar $r$-process residual, while high-mass ratio binaries show ratios of heavy to light $r$-process abundances that are significantly larger than the solar $r$-process residual. We normalize the yields at a given $\mathrm{A}$ with respect to the yields in the third $r$-process peak i.e. $\mathrm{A}\in [180,200]$ to report the relative abundance Y.

Figure 13

Evolution of disk mass for a subset of our simulations. Binaries with the BLh EOS (solid lines) form stable, long-lived remnants with disks evolving on long timescales. The binaries with deconfined quarks (dotted lines) result in the formation of BHs. The gravitational collapse is accompanied by the accretion of a significant fraction of the disk over a timescale of few milliseconds. Binaries where remnants from both EOSs undergo prompt collapse do not show significant differences in their disk mass evolution.

Figure 14

Kilonova light curves for a subset of our simulations with $q=1$. The color code represents the total mass of the binary with the dashed (solid) curves indicating models with (without) a QCD phase transition. In general, BLh binaries are more luminous and the brightness decreases with increasing mass.

Figure 15

Kilonova afterglow light curves at 1 keV for a set of equal mass models. The models’ total mass is color coded. Dashed (solid) curves indicate models with (without) phase transition. The plot shows that the afterglow of models with phase transition in general is brighter and more extended in time.

Figure 16

The ejecta kinetic energy (left two panels) and kilonova afterglow properties (right two panels) for the simulations with and without phase transition (BLQ and BLh, respectively). The kinetic energy is shown separately for the entire ejecta (lower subpanel) and for the fast component only (upper panel). The kilonova afterglow properties are the light curves’ peak time (upper panel) and flux (lower panel). Circle (square) markers indicate models with (without) phase transition, i.e. models with BLQ (BLh) EOS. The plot shows a correlation between the peak flux and the total kinetic energy. The effect of the phase transition is very prominent at high mass binaries, where the softening of EOS leads to prompt collapse, reducing the ejecta kinetic energy and peak flux.