Maximum mass of neutron stars and strange neutron-star cores

Context. The recent measurement of mass of PSR J1614-2230 rules out most existing models of the equation of state (EOS) of dense matter with high-density softening due to hyperonization that were based on the recent hyperon-nucleon and hyperon-hyperon interactions, which leads to a “hyperon puzzle”. Aims. We study a specific solution of this hyperon puzzle that consists of replacing a too soft hyperon core by a sufficiently stiff quark core. In terms of the quark structure of the matter, one replaces a strangeness-carrying baryon phase of confined quark triplets, some of them involving s quarks, by a quark plasma of deconfined u, d, and s quarks. Methods. We constructed an analytic approximation that fits modern EOSs of the two flavor (2SC) and the color-flavor-locked (CFL) color-superconducting phases of quark matter very well. Then, we used it to generate a continuum of EOSs of quark matter. This allowed us to simulate continua of sequences of first-order phase transitions at prescribed pressures, from hadronic matter to the 2SC and then to the CFL state of color-superconducting quark matter. Results. We obtain constraints in the parameter space of the EOS of superconducting quark cores, EOS.Q, resulting from Mmax > 2 M� . These constraints depend on the assumed EOS of baryon phase, EOS.B. We also derive constraints that would