Equation of State of Decompressed Quark Matter, and Observational Signatures of Quark-Star Mergers

Abstract

Quark stars are challenging to confirm or exclude observationally because they can have similar masses and radii as neutron stars. By performing the first calculation of the non-equilibrium equation of state of decompressed quark matter at finite temperature, we determine the properties of the ejecta from binary quark-star or quark star-black hole mergers. We account for all relevant physical processes during the ejecta evolution, including quark nugget evaporation and cooling, and weak interactions. We find that these merger ejecta can differ significantly from those in neutron star mergers, depending on the binding energy of quark matter. For relatively high binding energies, quark star mergers are unlikely to produce r-process elements and kilonova signals. We propose that future observations of binary mergers and kilonovae could impose stringent constraints on the binding energy of quark matter and the existence of quark stars.

Figures (8)

• Figure 1: Final nugget fraction (when the gas temperature reaches $T=1\,{\rm MeV}$) for different binding energies $\Delta E$ and initial temperatures $T_0$. Dashed line represents the critical boundary calculated using the equilibrium condition [Eq.(\ref{['eq:critical line']})]. The grey shaded region represents the regime $\Delta E < 8.8\,{\rm MeV}$, where quark matter is less stable than the $^{56}{\rm Fe}$ nucleus.
• Figure 2: Same as Fig. \ref{['fig:nugget fraction']}, but for the proton fraction in the gas phase.
• Figure 3: Final nugget fraction ($f_A$) and proton fraction ($Y_p$) as functions of binding energy $\Delta E$, for different initial temperatures. The dashed lines represent the results obtained from the parameter set used in Fig. \ref{['fig:nugget fraction']} and Fig. \ref{['fig:proton fraction']}. The solid bands represent the results when the parameters are varied over wide ranges (see text).
• Figure 4: Thermal adiabatic index of the decompressed quark matter as a function of density. The upper panel shows $\Gamma_{\rm th} =P_{\rm th}/u_{\rm th}+1$, where $u_{\rm th}$ includes the internal thermal energy of the nuggets [see Eqs.(\ref{['eq: pressure']}--\ref{['eq: e density']})]. The lower panel shows $\Gamma_{\rm th}^{\rm gas} =P_{\rm th}/u_{\rm th}^{\rm gas}+1$, where $u_{\rm th}^{\rm gas}=u_{\rm th}-u_A$ does not include the internal thermal energy of the nuggets.
• Figure S5: Density and pressure evolution tracks for three representative tracers. The black points represents the starting points chosen in our calculations.