We examine how the properties of inhomogeneous nuclear matter at subnuclear densities depend on the density dependence of the symmetry energy. Using a macroscopic nuclear model we calculate the size and shape of nuclei in neutron star matter at zero temperature in a way dependent on the density dependence of the symmetry energy. We find that for smaller symmetry energy at subnuclear densities, corresponding to the larger density symmetry coefficient L, the charge number of nuclei is smaller and the critical density at which matter with nuclei or bubbles becomes uniform is lower. The decrease in the charge number is associated with the dependence of the surface tension on the nuclear density and the density of a sea of neutrons, whereas the decrease in the critical density can be generally understood in terms of proton clustering instability in uniform matter.

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We study, within Ginzburg-Landau theory, the responses of three-flavor superfluid quark-gluon plasmas to external magnetic fields and rotation, in both the color-flavor locked and isoscalar colorantitriplet diquark phases near the critical temperature. Fields are incorporated in the gradient energy arising from long wavelength distortions of the condensate, via covariant derivatives to satisfy local gauge symmetries associated with color and electric charge. Magnetic vortex formation, in response to external magnetic fields, is possible only in the isoscalar phase; in the color-flavor locked phase, external magnetic fields are incompletely screened by the Meissner effect. On the other hand, rotation of the superfluid produces vortices in the color-flavor locked phase; in the isoscalar phase, it produces a London gluon-photon mixed field. We estimate the coherence and Meissner lengths and critical magnetic fields for the two phases.

We systematically examine relations among the parameters characterizing the phenomenological equation of state (EOS) of nearly symmetric, uniform nuclear matter near the saturation density by comparing macroscopic calculations of radii and masses of stable nuclei with experimental data. The EOS parameters of interest here are the symmetry energy coefficient S 0 , the symmetry energy density derivative coefficient L and the incompressibility K 0 at normal nuclear density. We estimate a range of (K 0 , L) from empirically reasonable values of the slope of the saturation line (the line joining the saturation points of nuclear matter at finite neutron excess) and find a strong correlation between S 0 and L. In light of the uncertainties on the values of K 0 and L, we perform macroscopic calculations of the radii of unstable nuclei expected to be produced in future facilities. We find that the matter radii depend appreciably on L, while being almost independent of K 0 . This dependence implies that if the matter radii are measured with an accuracy of ±0.01 fm for a sufficiently large number of neutron-rich nuclides to allow one to smooth out the expected staggering of the radii due to shell and pairing effects, it might be possible to derive the value of L within ±20 MeV.

The influence of the presence of hyperons in dense hadronic matter on the quantum nucleation of quark matter is examined at low temperatures relevant to neutron star cores. We calculate the equation of state and the composition of matter before and after deconfinement by using a relativistic mean-field theory and an MIT bag model, respectively; the case in which hyperons are present in the hadronic system is considered, together with the case of the system without hyperons. We find that strangeness contained in hyperons acts to reduce a density jump at deconfinement as well as a lepton fraction in the hadronic phase. As a result of these reductions, a quark matter droplet being in a virtual or real state has its effective mass lightened and its electric charge diminished into nearly zero. The Coulomb screening of leptons on the droplet charge, which has significance to the droplet growth after nucleation in the absence of hyperons, is thus shown to be of little consequence. If the effective droplet mass is small enough to become comparable to the height of the potential barrier, the effect of relativity brings about an exponential increase in the rate of droplet formation via quantum tunneling, whereas the role played by energy dissipation in decelerating the droplet formation, dominant for matter without hyperons, becomes of less importance. Independently of the presence of hyperons, the dynamical compressibility of the hadronic phase is unlikely to affect the quantum nucleation of quark matter at temperatures found in neutron star interiors. For matter with and without hyperons, we estimate the overpressure needed to form the first droplet in the star during the compression due to stellar spin-down or mass accretion from a companion star. The temperature at which a crossover from the quantum nucleation to the Arrhenius-type thermal nucleation takes place is shown to be large compared with the temperature of matter in the core. We also determine the range of the bag-model parameters such as the bag constant, the QCD fine structure constant, and the strange quark mass where quark matter is expected to occur in the star.PACS number(s): 26.60.+c, 12.38.Mh, 64.60.Qb, 97.60.Jd

We general-relativistically calculate the frequency of fundamental torsional oscillations of neutron star crusts, where we focus on the crystalline properties obtained from macroscopic nuclear models in a way that is dependent on the equation of state of nuclear matter. We find that the calculated frequency is sensitive to the density dependence of the symmetry energy, but almost independent of the incompressibility of symmetric nuclear matter. By identifying the lowest-frequency quasiperiodic oscillation in giant flares observed from soft gamma-ray repeaters as the fundamental torsional mode and allowing for the dependence of the calculated frequency on stellar models, we provide a lower limit of the density derivative of the symmetry energy as L≃50  MeV.

Thermal color superconducting phase transitions in high density three-flavor quark matter are investigated in the Ginzburg-Landau approach. Effects of nonzero strange quark mass, electric and color charge neutrality, and direct instantons are considered. Weak coupling calculations show that an interplay between the mass and electric neutrality effects near the critical temperature gives rise to three successive second-order phase transitions as the temperature increases: a modified colorflavor locked (mCFL) phase (ud, ds, and us pairings) → a "dSC" phase (ud and ds pairings) → an isoscalar pairing phase (ud pairing) → a normal phase (no pairing). The dSC phase is novel in the sense that while all eight gluons are Meissner screened as in the mCFL phase, three out of nine quark quasiparticles are gapless. 12.38.Mh,26.60.+c Unraveling the phase structure at high baryon density is one of the most challenging problems in quantum chromodynamics (QCD). Among others, color superconductivity in cold dense quark matter has been discussed from various viewpoints [1,2]. In relation to real systems such as newly born compact stars in stellar collapse, it is important to study the color superconductivity not only as a function of the quark chemical potential µ but also as a function of the temperature T . This is because the possible presence of color superconducting quark matter in a star affects the star's thermal evolution [3].The purpose of this Letter is to investigate phase transitions in color superconducting quark matter with three flavors (uds) and three colors (RGB) near the transition temperatures. We consider a realistic situation in which nonzero strange quark mass m s , electric and color charge neutrality, and direct instantons take effect. As we shall see in weak coupling (m s , Λ QCD ≪ µ), the effects of nonzero m s and electric neutrality are important in that they induce multiple phase transitions that change the pattern of diquark pairing as T increases. In particular, we find a new phase, which we call "dSC," as an interface between a modified type of color-flavor locked (mCFL) phase and an isoscalar two-flavor (2SC) phase.Throughout this Letter, we adopt the GinzburgLandau (GL) approach near the transition temperatures, which was previously used to study the massless threeflavor case [4,5,6] and is a more advantageous framework to weak coupling calculations than other mean-field approaches [7,8]. In a realistic situation, the GL potential acquires the following corrections. First of all, nonzero m s affects the potential through the s quark propagator [8] in such a way as to lower the temperature at which a diquark condensate with s quarks dissolves. This is because the pairing interaction due to one-gluon exchange is effectively diminished by m s if the pair contains the s quark. Secondly, when quark matter with nonzero m s is beta equilibrated and neutralized by electrons near the transition temperatures, the chemical potentials between d, s quarks and u quarks differ. Through this chemical potentia...

We consider how superfluidity of dripped neutrons in the crust of a neutron star affects the frequencies of the crust's fundamental torsional oscillations. A nonnegligible superfluid part of dripped neutrons, which do not comove with nuclei, act to reduce the enthalpy density and thus enhance the oscillation frequencies. By assuming that the quasi-periodic oscillations observed in giant flares of soft gamma repeaters arise from the fundamental torsional oscillations and that the mass and radius of the neutron star is in the range of 1.4 M/M ⊙ 1.8 and 10 km R 14 km, we constrain the density derivative of the symmetry energy as 100 MeV < ∼ L < ∼ 130 MeV, which is far severer than the previous one, L > ∼ 50 MeV, derived by ignoring the superfluidity.