Phenomenological QCD equations of state for neutron star dynamics: Nuclear-2SC continuity and evolving effective couplings

Abstract

We delineate the quark-hadron continuity by constructing QCD equations of state for neutron star dynamics, covering the wide range of charge chemical potential ($\mu_Q$) and temperatures ($T$). Based on the nuclear-2SC continuity scenario, we match equations of state for nuclear and two-flavor color-superconducting (2SC) quark matter, where the matching baryon density is $n_B\simeq 1.5n_0$ ($n_0\simeq 0.16\, {\rm fm^{-3}}$: nuclear saturation density). The effective vector and diquark couplings in a quark matter model evolve as functions of $n_B, \mu_Q, T$, whose low density values are constrained by the nuclear matter properties and neutron star radii, with the high density behavior by the two-solar mass ($2M_\odot$) constraint. With couplings dependent on $n_B$, we examined how smooth the nuclear-2SC continuity can be, and found problems in matching nuclear and 2SC entropies at low temperatures. To proceed with the continuity scenario, we enforce smooth matching by making the couplings ($n_B, \mu_Q, T$)-dependent. In effect, this adds phenomenological contributions which we call "X". After the phenomenological matching, we take the rest as our predictions. The 2SC and color-flavor-locked (CFL) phases computed with these evolving couplings are called 2SCX and CFLX. The CFLX appears around $n_B\simeq 2$-$4n_0$ and, in contrast to the conventional CFL, has non-negligible dependence on $(\mu_Q,T)$. To examine the astrophysical consequences of our modeling, we add charged leptons and neutrinos, and study the composition of matter for lepton fractions relevant for protoneutron stars and neutron star mergers. The abundance of neutrinos and thermal effects reduce the strangeness fraction and stiffen equations of state. For a neutrino trapped neutron star at $T\simeq 30 $ MeV with a lepton fraction $Y_L\simeq 0.05$, the mass is larger than its cold static counterpart by $\sim 0.1M_\odot$.