Confining density functional approach to the QCD phase diagram at low temperatures and thermal twin stars

Abstract

We present a density functional-based equation of state for warm, dense nuclear matter with a transition to deconfined quark matter for applications to simulations of supernova explosions and neutron star mergers, but also for the cosmological evolution of Q-balls. For the quark matter equation of state, we employ a recently developed confining density functional approach while nuclear matter is described within a relativistic density functional model of the DD2 class. The phase transition is obtained by a Maxwell construction at constant entropy per baryon. We discuss the solutions of TOV equations for isentropic hybrid stars for the hybrid equation of state model DDf-SFM (DD2-$χ$CDF) without (with) color superconductivity and find that at finite temperatures above a critical value of entropy per baryon sequences of disconnected third family branches ("thermal twin stars") may appear for the DDf-SFM model, while they are absent for the color superconducting model and at $T=0$. We discuss the relation of this critical entropy per baryon to the Seidov criterion of gravitational instability for $T=0$ and find that it is a good guide. We suggest that the presence of thermal twin stars may be regarded as an indicator for the core-collapse supernova explodability of massive blue supergiant stars and thus serve as a new criterion for the reliability of hybrid equation of state models. By this argument, strong color superconductivity shall be excluded and it remains to be shown whether models with moderate diquark pairing could fulfill the thermal twin constraint. For the case of symmetric matter, we compare the resulting hybrid EOS with the flow constraint by Danielewicz et al. and find a a sensitivity of the onset density for deconfinement on the presence or absence of color superconductivity.