Neutral color-spin locking phase in neutron stars

We present results for the spin-1 color-spin locking phase (CSL) using a NJL-type model in two flavor quark matter for compact stars applications. The CSL condensate is flavor symmetric and therefore charge and color neutrality can easily be satisfied. We find small energy gaps ~1 MeV, which make the CSL matter composition and the EoS not very different from the normal quark matter phase. We keep finite quark masses in our calculations and obtain no gapless modes that could have strong consequences in the late cooling of neutron stars. Finally, we show that the region of the phase diagram relevant for neutron star cores, when asymmetric flavor pairing is suppressed, could be covered by the CSL phase.Comment: 3 pages, 4 figures, contribution talk to the IVth International Conference on Quarks and Nuclear Physics(QNP06), Madrid, Spain, 5-10 Jun 200

Algorithms For Extracting Timeliness Graphs

We consider asynchronous message-passing systems in which some links are timely and processes may crash. Each run defines a timeliness graph among correct processes: (p; q) is an edge of the timeliness graph if the link from p to q is timely (that is, there is bound on communication delays from p to q). The main goal of this paper is to approximate this timeliness graph by graphs having some properties (such as being trees, rings, ...). Given a family S of graphs, for runs such that the timeliness graph contains at least one graph in S then using an extraction algorithm, each correct process has to converge to the same graph in S that is, in a precise sense, an approximation of the timeliness graph of the run. For example, if the timeliness graph contains a ring, then using an extraction algorithm, all correct processes eventually converge to the same ring and in this ring all nodes will be correct processes and all links will be timely. We first present a general extraction algorithm and then a more specific extraction algorithm that is communication efficient (i.e., eventually all the messages of the extraction algorithm use only links of the extracted graph)

Nonlocality effects on spin-one pairing patterns in two-flavor color superconducting quark matter and compact stars applications

We study the influence of nonlocality in the interaction on two spin one pairing patterns of two-flavor quark matter: the anisotropic blue color paring besides the usual two color superconducting matter (2SCb), in which red and green colors are paired, and the color spin locking phase (CSL). The effect of nonlocality on the gaps is rather large and the pairings exhibit a strong dependence on the form factor of the interaction, especially in the low density region. The application of these small spin-one condensates for compact stars is analyzed: the early onset of quark matter in the nonlocal models may help to stabilize hybrid star configurations. While the anisotropic blue quark pairing does not survive a big asymmetry in flavor space as imposed by the charge neutrality condition, the CSL phase as a flavor independent pairing can be realized as neutral matter in compact star cores. However, smooth form factors and the missmatch between the flavor chemical potential in neutral matter make the effective gaps of the order of magnitude $\simeq 10$ keV, and a more systematic analysis is needed to decide whether such small gaps could be consistent with the cooling phenomenology.Comment: 18 pages, 7 figures, corrected version with revised parameterizatio

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

Vertex adjacencies in the set covering polyhedron

We describe the adjacency of vertices of the (unbounded version of the) set covering polyhedron, in a similar way to the description given by Chvatal for the stable set polytope. We find a sufficient condition for adjacency, and characterize it with similar conditions in the case where the underlying matrix is row circular. We apply our findings to show a new infinite family of minimally nonideal matrices.Comment: Minor revision, 22 pages, 3 figure

How robust is a 2SC quark matter phase under compact star constraints?

We study the phase structure and equation of state for two-flavor quark matter at low temperature under compact star constraints within a nonlocal chiral quark model. We find that the occurence of a two-flavor color superconducting (2SC) phase is sensitive to variations of both the formfactor of the interaction and the ratio \eta between the coupling constants in the diquark and the scalar meson channels. Our study suggests that for standard values of the coupling ratio 0.5<\eta<0.75 either the 2SC phase does not occur (Gaussian formfactor) or it exists only in a mixed phase with normal quark matter (NQ-2SC) with a volume fraction less than 20 - 40 %, occuring at high baryon chemical potentials \mu_B >1200 MeV and most likely not relevant for compact stars. We also present the relevant region of the phase diagram for compact star applications and obtain that no gapless 2SC occurs at low temperatures.Comment: 19 pages, 9 figures, Subsec.2.5: "Phase diagram" adde

Spin-one color superconductivity in compact stars?- an analysis within NJL-type models

We present results of a microscopic calculation using NJL-type model of possible spin-one pairings in two flavor quark matter for applications in compact star phenomenology. We focus on the color-spin locking phase (CSL) in which all quarks pair in a symmetric way, in which color and spin states are locked. The CSL condensate is particularly interesting for compact star applications since it is flavor symmetric and could easily satisfy charge neutrality. Moreover, the fact that in this phase all quarks are gapped might help to suppress the direct Urca process, consistent with cooling models. The order of magnitude of these small gaps (~1 MeV) will not influence the EoS, but their also small critical temperatures (T_c ~800 keV) could be relevant in the late stages neutron star evolution, when the temperature falls below this value and a CSL quark core could form.Comment: 7 pages, 7 figures, revised version, accepted for the Conference Proceedings of "Isolated Neutron Stars: from the Interior to the Surface", London, 24-28. April 200

Nonlocality effects on Color Spin Locking condensates

We consider the color spin locking (CSL) phase of two-flavor quark matter at zero temperature for nonlocal instantaneous, separable interactions. We employ a Lorentzian-type form factor allowing a parametric interpolation between the sharp (Nambu-Jona-Lasinio (NJL) model) and very smooth (e.g. Gaussian) cut-off models for systematic studies of the influence on the CSL condensate the deviation from the NJL model entails. This smoothing of the NJL model form factor shows advantageous features for the phenomenology of compact stars: (i) a lowering of the critical chemical potential for the onset of the chiral phase transition as a prerequisite for stability of hybrid stars with extended quark matter cores and (ii) a reduction of the smallest pairing gap to the order of 100 keV, being in the range of values interesting for phenomenological studies of hybrid star cooling evolution.Comment: 8 pages, 8 figures, 1 table, accepted for publication in Phys.Rev.