The uncertainties in neutron star radii and crust properties due to our limited knowledge of the equation of state are quantitatively analyzed. We first demonstrate the importance of a unified microscopic description for the different baryonic densities of the star. If the pressure functional is obtained matching a crust and a core equation of state based on models with different properties at nuclear matter saturation, the uncertainties can be as large as ∼30 % for the crust thickness and 4% for the radius. Necessary conditions for causal and thermodynamically consistent matchings between the core and the crust are formulated and their consequences examined. A large set of unified equations of state for purely nucleonic matter is obtained based on twenty-four Skyrme interactions and nine relativistic mean-field nuclear parametrizations. In addition, for relativistic models fifteen equations of state including a transition to hyperonic matter at high density are presented. All these equations of state have in common the property of describing a 2M star and of being causal within stable neutron stars. Spans of ∼3 and ∼4 km are obtained for the radius of, respectively, 1.0M and 2.0M stars. Applying a set of nine further constraints from experiment and ab initio calculations the uncertainty is reduced to ∼1 and 2 km, respectively. These residual uncertainties reflect lack of constraints at large densities and insufficient information on the density dependence of the equation of state near the nuclear matter saturation point. The most important parameter to be constrained is shown to be the symmetry energy slope L. Indeed, this parameter exhibits a linear correlation with the stellar radius, which is particularly clear for small mass stars around 1.0M . The other equation-of-state parameters do not show clear correlations with the radius, within the present uncertainties. Potential constraints on L, the neutron star radius, and the equation of state from observations of thermal states of neutron stars are also discussed. The unified equations of state are made available in the Supplemental Materials and via the CompOSE database.

Aims. Heating associated with non-equilibrium nuclear reactions in accreting neutron-star crusts is reconsidered, taking into account suppression of neutrino losses demonstrated recently by Gupta et al. Two initial compositions of the nuclear burning ashes, Ai = 56 and Ai = 106, are considered. Dependence of the integrated crustal heating on uncertainties plaguing pycnonuclear reaction models is studied. Methods. One-component plasma approximation is used, with compressible liquid-drop model of Mackie and Baym to describe nuclei. Evolution of a crust shell is followed from 10 8 g cm −3 to 10 13.6 g cm −3 . Results. The integrated heating in the outer crust agrees nicely with results of self-considtent multicomponent plasma simulations of Gupta et al.; their results fall between our curves obtained for Ai = 56 and Ai = 106. Total crustal heat per one accreted nucleon ranges between 1.5 MeV/nucleon to 1.9 MeV/nucleon for Ai = 106 and Ai = 56, respectively. The value of Qtot depends weakly on the presence of pycnonuclear reactions at 10 12 − 10 13 g cm −3 . Remarkable insensitivity of Qtot on the details of the distribution of nuclear processes in accreted crust is explained.

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 M max > 2 M . These constraints depend on the assumed EOS of baryon phase, EOS.B. We also derive constraints that would result from significantly higher measured masses. For 2.4 M the required stiffness of the CFL quark core is close to the causality limit while the density jump at the phase transition is very small. Conclusions. The condition M max > 2 M puts strong constraints on the EOSs of the 2SC and CFL phases of quark matter. Density jumps at the phase transitions have to be sufficiently small and sound speeds in quark matter sufficiently large. The condition of thermodynamic stability of the quark phase results in a maximum mass of hybrid stars similar to that of purely baryon stars. This is due to the phase transition of quark matter back to the baryon phase (reconfinement) that we find for both EOS.B. Therefore, to obtain M max > 2 M for hybrid stars, both sufficiently strong additional hyperon repulsion at high-density baryon matter and a sufficiently stiff EOS of quark matter would be needed. However, we think that the high-density instability, which results in the reconfinement of quark matter, indicates actually the inadequacy of the point-particle model of baryons in dense matter at ρ 5 ÷ 8ρ 0 . We expect that reconfinement can be removed by a sufficient stiffening of the baryon phase, resulting from the repulsive finite size contribution for baryons to the EOS.