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

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