On the Possibility of a Strong First-Order Phase Transition in Neutron Stars

Whether cold dense QCD matter undergoes a strong first-order phase transition remains an open question. In nature, neutron stars provide the most direct probe of cold dense QCD matter. Theoretically, chiral effective field theory constrains the equation of state of dense matter near nuclear saturation density, while perturbative QCD calculations constrain it at densities well beyond stable neutron-star interiors. We perform Bayesian inference with non-parametric Gaussian-process equation of state for $\beta$-equilibrated neutron-star matter under the assumption with and without a strong first-order phase transition, using the tidal deformability from GW170817, the NICER mass--radius measurements of PSR~J0740$+$6620, PSR~J0030$+$0451, PSR~J0437$-$4715, PSR~J0614$-$3329, chiral effective field theory, and perturbative QCD. Our results favor a strong first-order phase transition, with its onset most likely lying \emph{above} the central density of the most massive neutron star. Such an onset reconciles the stiffness required to support massive neutron stars with the softening favored by perturbative QCD from asymptotically high density.