The Ginzburg-Landau equations for magnetic and gluomagnetic gauge fields of the semi-superfluid strings in the color superconducting core of the neutron star with diquark condensate in the color-flavor-locking (CFL) phase are derived. The simultaneous coupling of the CFL diquark condensate to the magnetic and gluomagnetic gauge fields is taken into account. The asymptotic values of these string energies are defined from quantization conditions. It is shown that a lattice of semi-superfluid strings with minimal quantum of circulation emerges in the superconducting quark core during rotation of the star. The magnetic field in the core of this string is of order of 10^18 G. The cluster of proton vortices appeared in the hadronic phase around each superfluid neutron vortex due to entrainment effect, creates in the superconducting quark core new semi-superfluid strings with minimal quantum of circulation.
The r-mode instability in rotating compact stars is used to constrain the phase of matter at high density. The color-flavor-locked phase with kaon condensation (CFL-K0) and without (CFL) is considered in the temperature range 10^8K < T <10^{11} K. While the bulk viscosity in either phase is only effective at damping the r-mode at temperatures T > 10^{11} K, the shear viscosity in the CFL-K0 phase is the only effective damping agent all the way down to temperatures T > 10^8 K characteristic of cooling neutron stars. However, it cannot keep the star from becoming unstable to gravitational wave e…
Color superconductivity in high density QCD exhibits the color-flavor locked (CFL) phase. To explore zero modes in the CFL phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem to the Bogoliubov-de Gennes (BdG) Hamiltonian. From the calculation of the topological index, we find that triplet, doublet and singlet sectors of SU(2) have certain number of chiral Majorana zero modes in the limit of vanishing chemical potential. We also solve the BdG equation by the use of the series expansion to show that the number of zero modes and thei…
Quark-hadron continuity was proposed as crossover between hadronic matter and quark matter without a phase transition, based on the matching of the symmetry and excitations in both phases. In the limit of a light strange-quark mass, it connects hyperon matter and the color-flavor-locked (CFL) phase exhibiting color superconductivity. Recently, it was proposed that this conjecture could be generalized in the presence of superfluid vortices penetrating both phases (arXiv:1803.05115 [hep-ph]), and it was suggested that one hadronic superfluid vortex in hyperon matter could be connected to one non…
We calculate neutrino emissivities from the decay and scattering of Goldstone bosons in the color-flavor-locked (CFL) phase of quarks at high baryon density. Interactions in the CFL phase are described by an effective low-energy theory. For temperatures in the tens of keV range, relevant to the long-term cooling of neutron stars, the emissivities involving Goldstone bosons dominate over those involving quarks, because gaps in the CFL phase are $\sim 100$ MeV while the masses of Goldstone modes are on the order of 10 MeV. For the same reason, the specific heat of the CFL phase is also dominated…
The cooling mechanism of compact stars with quark cores in the color-flavor locked phase is discussed. It is argued that the high thermal conductivity of the quark core plays a key role in the stellar cooling. It implies that the cooling time of compact stars with color-flavor locked quark cores is similar to that of ordinary neutron stars, unless the star is almost completely made of color-flavor locked quark matter.
We delineate the quark-hadron continuity by constructing QCD equations of state for neutron star dynamics, covering the wide range of charge chemical potential ($μ_Q$) and temperatures ($T$). Based on the nuclear-2SC continuity scenario, we match equations of state for nuclear and two-flavor color-superconducting (2SC) quark matter, where the matching baryon density is $n_B\simeq 1.5n_0$ ($n_0\simeq 0.16\, {\rm fm^{-3}}$: nuclear saturation density). The effective vector and diquark couplings in a quark matter model evolve as functions of $n_B, μ_Q, T$, whose low density values are constrained…
Quantum vortices in the color-flavor locked (CFL) phase of QCD have bosonic degrees of freedom, called the orientational zero modes, localized on them. We show that the orientational zero modes are electromagnetically charged. As a result, a vortex in the CFL phase nontrivially interacts with photons. We show that a lattice of vortices acts as a polarizer of photons with wavelengths larger than some critical length.
Color-flavor locked quark matter can be described as a three-component superconductor and thus shows unconventional behavior in the transition regime from type-I to type-II superconductivity. We discuss this behavior by studying magnetic line defects in a Ginzburg-Landau approach, taking into account all possible values of the three winding numbers. After a brief discussion of the defects that include baryon circulation we focus on pure magnetic flux tubes. We show that at strong coupling, relevant for neutron stars, type-II behavior is conceivable and the most preferred configuration has mini…
Neutron Star Observations Challenge a Large Colour-Superconducting Gap in Dense Quark Matter
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台暗物质与空间天文重点实验室）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）
The identification of black holes is one of the most important tasks of modern astrophysics. Candidates have been selected among binary stars based on a high mass function, and seriously considered when the lower mass limit exceeds ~ 3 solar masses. More recently the absence of (Type I) thermonuclear bursts has been advanced as an additional criterion in favor of the black hole interpretation, since the absence of a solid surface naturally precludes the accumulation and ignition of accreting material. We discuss in this Letter the possibility that self-bound stars made of CFL-paired quarks mim…
We investigate the effect of the density-dependent proton and neutron gaps on vortex dynamics in neutron stars. We argue that the persistence of neutron star magnetic fields on timescales of $10^9$ y suggests a superconducting gap curve with local maximum at intermediate density. We discuss the implications for exotic core phenomena such as pion/kaon condensation or a transition to quark matter.
We consider the effect of a six-fermion interaction of the {'}t Hooft form in the quark-quark channel on the ground state of matter at finite density. The coupling constant for this new term is varied within the limits suggested by naturalness. The flavor-mixing effects of the additional term destabilize the color-flavor-locked (CFL) and, to a lesser extent, the two-color superconducting (2SC) phases of quark matter, especially for positive values of the coupling. For some values of the coupling, the critical density for the CFL phase is nearly larger than the maximum density in the neutron st…
We calculate the correlation functions needed to describe the linear response of superfluid matter, and go on to calculate the differential cross section for neutral-current neutrino scattering in superfluid neutron matter and in color-flavor locked quark matter (CFL). We report the first calculation of scattering rates that includes neutrino interactions with both pair-breaking excitations and low-lying collective excitations (Goldstone modes). Our results apply both above and below the critical temperature, allowing use in simulations of neutrino transport in supernovae and neutron stars.
We study how vortices in dense superfluid hadronic matter can connect to vortices in superfluid quark matter, as in rotating neutron stars, focusing on the extent to which quark-hadron continuity can be maintained. As we show, a singly quantized vortex in three-flavor symmetric hadronic matter can connect smoothly to a singly quantized non-Abelian vortex in three-flavor symmetric quark matter in the color-flavor locked (CFL) phase, without the necessity for boojums appearing at the transition.
In this review, we discuss various properties of topological solitons in dense QCD matter, with a particular emphasis on the CFL phase exhibiting superfluidity and superconductivity, and their phenomenological implications in terms of the effective field theories such as the Ginzburg-Landau theory, the chiral Lagrangian, or the Bogoliubov--de Gennes equation. The most fundamental topological excitations are non-Abelian vortices, which are 1/3 quantized superfluid vortices and color magnetic flux tubes. They are created at a phase transition or a rotation such compact stars. The intervortex-int…
We consider the the effect of the electron cloud about a vorton in the CFL-$K^0$ high-density phase by numerically solving the ultrarelativistic Thomas-Fermi equation about a toroidal charge. Including electrons removes the electric monopole contribution to the energy, and noticeably decreases the equilibrium radius of these stable vortex loops.
At large baryon number density, it is likely that the ground state of QCD is a color-flavor-locked phase with a K0 condensate. The CFL+K0 phase is known to support superconducting vortex strings, and it has been previously suggested that it may also support vortons, which are superconducting vortex rings. We reexamine the question of the stability of vortons, taking into account electromagnetic effects, which make leading-order contributions to vorton dynamics but were not investigated in previous work. We find that current-carrying and electrically charged vortons can be stabilized either by …
We consider strong interactions at finite density in mean field theory, through an effective lagrangian that can describe both nuclear matter and quark matter. This lagrangian has three couplings that are all fixed by experiment and no other parameters. With increasing baryon density we then find the following hierarchy. At nuclear density and above we have nuclear matter with chiral spontaneous symmetry breaking (SSB), followed by the pion condensed quark matter, again with chiral SSB, albeit with a different realization and finally a transition to the diquark CFL state which also has chiral …
We discuss quantized vortices in neutron $^3P_2$ superfluids, which are believed to realize in high density neutron matter such as neutron stars. By using the Ginzburg-Landau free energy for $^3P_2$ superfluids, we determine the ground state in the absence and presence of the external magnetic field, and numerically construct $^3P_2$ quantized vortices in the absence and presence of the external magnetic field along the vortex axis (poloidal) or angular direction (toroidal). We find in certain situations the spontaneous magnetization of the vortex core, whose typical magnitude is about $10^{7-…
Matter at high density and low temperature is expected to be a color superconductor, which is a degenerate Fermi gas of quarks with a condensate of Cooper pairs near the Fermi surface that induces color Meissner effects. At the highest densities, where the QCD coupling is weak, rigorous calculations are possible, and the ground state is a particularly symmetric state, the color-flavor locked (CFL) phase. The CFL phase is a superfluid, an electromagnetic insulator, and breaks chiral symmetry. The effective theory of the low-energy excitations in the CFL phase is known and can be used, even at m…
Neutron stars or pulsars are very rapidly rotating compact stars with extremely high density. One of the unsolved long-standing problems of these enigmatic celestial bodies is the origin of pulsars' glitches, i.e., the sudden rapid deceleration in the rotation speed of neutron stars. Although many glitch events have been reported, there is no consensus on the microscopic mechanism responsible for them. One of the important characterizations of the glitches is the scaling law $P(E) \sim E^{-α}$ of the probability distribution for a glitch with energy $E$. Here, we reanalyse the accumulated up-t…
At very high densities, as for example in the core of a neutron star, matter may appear in the color-flavor locked (CFL) phase, which is a superfluid. This phase features topologically stable vortex solutions, which arise in a spinning superfluid as localized configurations carrying quanta of angular momentum. Despite the topological stability of these vortices they are not the lowest energy state of the system at neutron star densities and decay into triplets of semi-superfluid fluxtubes. In these proceedings we report on the progress of our numerical study in the Ginzburg-Landau approach, wh…
The possibility of observationally discriminating between various types of neutron stars, described by different equations of state of the nuclear matter, as well as differentiating neutron stars from other types of exotic objects, like, for example, quark stars, is one of the fundamental problems in contemporary astrophysics. We consider and investigate carefully the possibility that different types of rapidly rotating neutron stars, as well as other type of compact general relativistic objects, can be differentiated from the study of the emission properties of the accretion disks around them…
We analyze the phases of dense quark matter at nonzero quark masses. We map out the phase diagrams for charged quark matter as well as charge neutral matter containing leptons. We find that in Color Flavor Locked (CFL) quark matter, the symmetric phase with equal numbers of $u$, $d$ and $s$ quarks is unlikely to occur in nature. Various less symmetric phases with additional meson condensates may play a role in neutron star cores, however, in agreement with the analysis of Bedaque and Schäfer. We discuss the implications of these novel color superconducting quark matter phases and their transit…
We determine characteristic timescales for the viscous damping of r-mode oscillations in rapidly rotating compact stars that contain quark matter. We present results for the color-flavor-locked (CFL) phase of dense quark matter, in which the up, down and strange quarks are gapped, as well as the normal (ungapped) quark phase. While the ungapped quark phase supports a temperature window between 10^8 K and 5x10^9 K where the r-mode is damped even for rapid rotation, the r-mode in a rapidly rotating pure CFL star is not damped in the temperature range 10^10 K - 10^11 K. Rotating hybrid stars with…
Superfluid vortices in the color-flavor-locked (CFL) phase of dense quark matter are known to be energetically disfavored relative to well-separated triplets of "semi-superfluid" color flux tubes. However, the short-range interaction (metastable versus unstable) has not been established. In this paper we perform numerical calculations using the effective theory of the condensate field, mapping the regions in the parameter space of coupling constants where the vortices are metastable versus unstable. For the case of zero gauge coupling we analytically identify a candidate for the unstable mode,…
Color-flavor locked (CFL) quark matter expels color-magnetic fields due to the Meissner effect. One of these fields carries an admixture of the ordinary abelian magnetic field and therefore flux tubes may form if CFL matter is exposed to a magnetic field, possibly in the interior of neutron stars or in quark stars. We employ a Ginzburg-Landau approach for three massless quark flavors, which takes into account the multi-component nature of color superconductivity. Based on the weak-coupling expressions for the Ginzburg-Landau parameters, we identify the regime where CFL is a type-II color super…
The possibility is considered that, after nuclear recoil caused by elastic scattering with Light Dark Matter, atoms in superfluid He4 may create quantized vortex rings, which can thereafter be detected. The concept for sort of telescope for LDM is presented, which would be sensitive to its motion through the Galactic LDM wind. A demonstrator is proposed, which makes use of thermal neutrons.
The neutrino-antineutrino annihilation into electron-positron pairs near the surface of compact general relativistic stars could play an important role in supernova explosions, neutron star collapse, or for close neutron star binaries near their last stable orbit. General relativistic effects increase the energy deposition rates due to the annihilation process. We investigate the deposition of energy and momentum due to the annihilations of neutrinos and antineutrinos in the equatorial plane of the rapidly rotating neutron and quark stars, respectively. We analyze the influence of general rela…
