Color-magnetic flux tubes in quark matter cores of neutron stars

We argue that if color-superconducting quark matter exists in the core of a neutron star, it may contain a high density of flux tubes, carrying flux that is mostly color-magnetic, with a small admixture of ordinary magnetic flux. We focus on the two-flavor color-superconducting ("2SC") phase, and assume that the flux tubes are energetically stable, although this has not yet been demonstrated. The density of flux tubes depends on the nature of the transition to the color-superconducting phase, and could be within an order of magnitude of the density of magnetic flux tubes that would be found if the core were superconducting nuclear matter. We calculate the cross-section for Aharonov-Bohm scattering of gapless fermions off the flux tubes, and the associated collision time and frictional force on a moving flux tube. We discuss the other forces on the flux tube, and find that if we take in to account only the forces that arise within the 2SC core region then the timescale for expulsion of the color flux tubes from the 2SC core is of order 10^10 years.Comment: 28 pages, LaTeX, 1 figure, 2 appendices; added discussion of energetic stability of flux tube

Damping of differential rotation in neutron stars

We derive the transport relaxation times for quasiparticle-vortex scattering processes via nuclear force, relevant for the damping of differential rotation of superfluids in the quantum liquid core of a neutron star. The proton scattering off the neutron vortices provides the dominant resistive force on the vortex lattice at all relevant temperatures in the phase where neutrons only are in the paired state. If protons are superconducting, a small fraction of hyperons and resonances in the normal state would be the dominant source of friction on neutron and proton vortex lattices at the core temperatures $T\ge 10^{7}$ K.Comment: 5 pages, Revtex, Phys. Rev. D 58, Rapid Communication, in pres

BCS approximation to the effective vector vertex of superfluid fermions

We examine the effective interaction of nonrelativistic fermions with an external vector field in superfluid systems. In contrast to the complicated vertex equation, usually used in this case, we apply the approach which does not employ an explicit form of the pairing interaction. This allows to obtain a simple analytic expression for the vertex function only in terms of the order parameter and other macroscopic parameters of the system. We use this effective vertex to analyze the linear response function of the superfluid medium at finite temperatures. At the time-like momentum transfer, the imaginary part of the response function is found to be proportional to the fourth power of small Fermi velocity, i.e. the energy losses through vector currents are strongly suppressed. As an application, we calculate the neutrino energy losses through neutral weak currents caused by the pair recombination in the superfluid neutron matter at temperatures lower than the critical one for S-wave pairing. This approach confirms a strong suppression of the neutrino energy losses as predicted in Ref.[4].Comment: 19 pages, no figure

Fluctuations of the Color-superconducting Order Parameter in Heated and Dense Quark Matter

Fluctuations of the color superconducting order parameter in dense quark matter at finite temperatures are investigated in terms of the phenomenological Ginzburg - Landau approach. Our estimates show that fluctuations of the di-quark gap may strongly affect some of thermodynamic quantities even far below and above the critical temperature. If the critical temperature of the di-quark phase transition were rather high one could expect a manifestation of fluctuations of the di-quark gap in the course of heavy ion collisions.Comment: 12

Constraining hypernuclear density functional with Λ\Lambda-hypernuclei and compact stars

We present a simultaneous calculation of heavy single-$\Lambda$ hypernuclei and compact stars containing hypernuclear core within a relativistic density functional theory based on a Lagrangian which includes the hyperon octet and lightest isoscalar-isovector mesons which couple to baryons with density-dependent couplings. The corresponding density functional allows for SU(6) symmetry breaking and mixing in the isoscalar sector, whereby the departures in the $\sigma$-$\Lambda$ and $\sigma$-$\Sigma$ couplings away from their values implied by the SU(3) symmetric model are used to adjust the theory to the laboratory and astronomical data. We fix $\sigma$-$\Lambda$ coupling using the data on the single-$\Lambda$ hypernuclei and derive an upper bound on the $\sigma$-$\Sigma$ from the requirement that the lower bound on the maximum mass of a compact star is $2 M_{\odot}$.Comment: 10 pages, 4 figures, to appear in Phys. Lett. B, v2: minor editorial correction

Spatially inhomogeneous condensate in asymmetric nuclear matter

We study the isospin singlet pairing in asymmetric nuclear matter with nonzero total momentum of the condensate Cooper pairs. The quasiparticle excitation spectrum is fourfold split compared to the usual BCS spectrum of the symmetric, homogeneous matter. A twofold splitting of the spectrum into separate branches is due to the finite momentum of the condensate, the isospin asymmetry, or the finite quasiparticle lifetime. The coupling of the isospin singlet and triplet paired states leads to further twofold splitting of each of these branches. We solve the gap equation numerically in the isospin singlet channel in the case where the pairing in the isospin triplet channel is neglected and find nontrivial solutions with finite total momentum of the pairs. The corresponding phase assumes a periodic spatial structure which carries a isospin density wave at constant total number of particles. The phase transition from the BCS to the inhomogeneous superconducting phase is found to be first order and occurs when the density asymmetry is increased above 0.25. The transition from the inhomogeneous superconducting to the unpaired normal state is second order. The maximal values of the critical total momentum (in units of the Fermi momentum) and the critical density asymmetry at which condensate disappears are $P_c/p_F = 0.3$ and $\alpha_c = 0.41$. The possible spatial forms of the ground state of the inhomogeneous superconducting phase are briefly discussed.Comment: 13 pages, including 3 figues, uses RevTeX; minor corrections, PRC in pres

Neutrino radiation from dense matter

This article provides a concise review of the problem of neutrino radiation from dense matter. The subjects addressed include quantum kinetic equations for neutrino transport, collision integrals describing neutrino radiation through charged and neutral current interactions, radiation rates from pair-correlated baryonic and color superconducting quark matter.Comment: 11 pages, 5 figures. Based in part on lectures delivered at the Summer school "Dense Matter In Heavy Ion Collisions and Astrophysics", BLTP, Joint Institute for Nuclear Research, Dubna, Russia. The complete lectures are available online at http://theor.jinr.ru/~dm2006/talks.html v2: matches published versio

Direct Urca neutrino rate in colour superconducting quark matter

If deconfined quark matter exists inside compact stars, the primary cooling mechanism is neutrino radiation via the direct Urca processes d->u+e+antinu_e and u+e->d+nu_e. Below a critical temperature, T_c, quark matter forms a colour superconductor, one possible manifestation of which is a condensate of quark Cooper pairs in an electric-charge neutralising background of electrons. We compute the neutrino emission rate from such a phase, including charged pair-breaking and recombination effects, and find that on a material temperature domain below T_c the pairing-induced suppression of the neutrino emission rate is not uniformly exponential. If gapless modes are present in the condensed phase, the emissivity at low temperatures is moderately enhanced above that of completely unpaired matter. The importance of charged current pair-breaking processes for neutrino emission both in the fully gapped and partially gapped regimes is emphasised.Comment: 5 pages, 2 figures; to appear in Phys. Rev. C (Rapid Comm.