Cooling Evolution of Hybrid Stars

The cooling of compact isolated objects for different values of the gravitational mass has been simulated for two alternative assumptions. One is that the interior of the star is purely hadronic and second that the star can have a rather large quark core. It has been shown that within a nonlocal chiral quark model the critical density for a phase transition to color superconducting quark matter under neutron star conditions can be low enough for these phases to occur in compact star configurations with masses below 1.3 M_sun. For a realistic choice of parameters the equation of state (EoS) allows for 2SC quark matter with a large quark gap ~ 100 MeV for u and d quarks of two colors that coexists with normal quark matter within a mixed phase in the hybrid star interior. We argue that, if in the hadronic phase the neutron pairing gap in 3P_2 channel is larger than few keV and the phases with unpaired quarks are allowed, the corresponding hybrid stars would cool too fast. Even in the case of the essentially suppressed 3P_2 neutron gap if free quarks occur for M < 1.3 M_sun, as it follows from our EoS, one could not appropriately describe the neutron star cooling data existing by today. It is suggested to discuss a "2SC+X" phase, as a possibility to have all quarks paired in two-flavor quark matter under neutron star constraints, where the X-gap is of the order of 10 keV - 1 MeV. Density independent gaps do not allow to fit the cooling data. Only the presence of an X-gap that decreases with increase of the density could allow to appropriately fit the data in a similar compact star mass interval to that following from a purely hadronic model.Comment: 10 pages, 5 figures, Talk given at Joint Meeting Heidelberg-Liege-Paris-Rostock (HLPR 2004), Spa, Belgium, 16-18 Dec 200

Strangeness in the cores of neutron stars

The measurement of the mass 1.97 +/- 0.04 M_sun for PSR J1614-2230 provides a new constraint on the equation of state and composition of matter at high densities. In this contribution we investigate the possibility that the dense cores of neutron stars could contain strange quarks either in a confined state (hyperonic matter) or in a deconfined one (strange quark matter) while fulfilling a set of constraints including the new maximum mass constraint. We account for the possible appearance of hyperons within an extended version of the density-dependent relativistic mean-field model, including the phi-meson interaction channel. Deconfined quark matter is described by the color superconducting three-flavor NJL model.Comment: 6 pages, 2 figures, contribution to "Strangeness in Quark Matter 2011", Cracow, September 18-24, 201

Effects of quark matter and color superconductivity in compact stars

The equation of state for quark matter is derived for a nonlocal, chiral quark model within the mean field approximation. We investigate the effects of a variation of the form factors of the interaction on the phase diagram of quark matter under the condition of beta-equilibrium and charge neutrality. Special emphasis is on the occurrence of a diquark condensate which signals a phase transition to color superconductivity and its effects on the equation of state. We calculate the quark star configurations by solving the Tolman- Oppenheimer- Volkoff equations and obtain for the transition from a hot, normal quark matter core of a protoneutron star to a cool diquark condensed one a release of binding energy of the order of Delta M c^2 ~ 10^{53} erg. We study the consequences of antineutrino trapping in hot quark matter for quark star configurations with possible diquark condensation and discuss the claim that this energy could serve as an engine for explosive phenomena. A "phase diagram" for rotating compact stars (angular velocity-baryon mass plane) is suggested as a heuristic tool for obtaining constraints on the equation of state of QCD at high densities. It has a critical line dividing hadronic from quark core stars which is correlated with a local maximum of the moment of inertia and can thus be subject to experimental verification by observation of the rotational behavior of accreting compact stars.Comment: 14 pages, 12 figures, Talk given at 2nd International Workshop on Hadron Physics: Effective Theories of Low-Energy QCD, Coimbra, Portugal, 25-29 Sep 200

Bayesian Analysis for Extracting Properties of the Nuclear Equation of State from Observational Data including Tidal Deformability from GW170817

We develop a Bayesian analysis method for selecting the most probable equation of state under a set of constraints from compact star physics, which now include the tidal deformability from GW170817. We apply this method for the first time to a two-parameter family of hybrid equations of state that is based on realistic models for the hadronic phase (KVORcut02) and the quark matter phase (SFM$\alpha$) which produce a third family of hybrid stars in the mass-radius diagram. One parameter ($\alpha$) characterizes the screening of the string tension in the string-flip model of quark matter while the other ($\Delta_P$) belongs to the mixed phase construction that mimics the thermodynamics of pasta phases and includes the Maxwell construction as a limiting case for $\Delta_P=0$. We present the corresponding results for compact star properties like mass, radius and tidal deformabilities and use empirical data for them in the newly developed Bayesian analysis method to obtain the probabilities for the model parameters within their considered range.Comment: 8 pages, 4 figures, version accepted for publication in univers