Topological defects at the boundary of neutron ${}^3{P}_2$ superfluids in neutron stars

Abstract

We study surface effects of neutron ${}^3{P}_2$ superfluids in neutron stars. ${}^3{P}_2$ superfluids are in uniaxial nematic (UN), D${}_2$ biaxial nematic (BN), or D${}_4$ BN phase, depending on the strength of magnetic fields from small to large. We suppose a neutron ${}^3{P}_2$ superfluid in a ball with a spherical boundary. Adopting a suitable boundary condition for ${}^3{P}_2$ condensates, we solve the Ginzburg-Landau equation to find several surface properties for the neutron ${}^3{P}_2$ superfluid. First, the phase on the surface can be different from that of the bulk, and symmetry restoration or breaking occurs in general on the surface. Second, the distribution of the surface energy density has an anisotropy depending on the polar angle in the sphere, which may lead to the deformation of the geometrical shape of the surface. Third, the order parameter manifold induced on the surface, which is described by two-dimensional vector fields induced on the surface from the condensates, allows topological defects (vortices) on the surface, and there must exist such defects even in the ground state thanks to the Poincaré-Hopf theorem: although the numbers of the vortices and antivortices depend on the bulk phases, the difference between them is topologically invariant (the Euler number $\chi =2$) irrespective of the bulk phases. These vortices, which are not extended to the bulk, are called boojums in the context of liquid crystals and helium-3 superfluids. The surface properties of the neutron ${}^3{P}_2$ superfluid found in this paper may provide us useful information to study neutron stars.

arXiv comment30 pages, 11 figures

References in corpus (63)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Shapiro delay measurement of a two solar mass neutron star
• A Massive Pulsar in a Compact Relativistic Binary
• Spinor Bose-Einstein condensates
• From hadrons to quarks in neutron stars: a review
• From low-momentum interactions to nuclear structure
• Pairing in nuclear systems: from neutron stars to finite nuclei
• Rapid Cooling of the Neutron Star in Cassiopeia A Triggered by Neutron Superfluidity in Dense Matter
• Cooling neutron star in the Cassiopeia~A supernova remnant: Evidence for superfluidity in the core
• Cooling neutron stars and superfluidity in their interiors
• Direct Observation of the Cooling of the Cassiopeia A Neutron Star
• Superfluidity in nuclear systems and neutron stars
• 3P_2-3F_2 pairing in neutron matter with modern nucleon-nucleon potentials
• Semi-superfluid strings in High Density QCD
• Ferromagnetism of quark liquid
• Vortices and Other Topological Solitons in Dense Quark Matter
• Non-Abelian Strings in High Density QCD: Zero Modes and Interactions
• Discrete symmetries and 1/3-quantum vortices in condensates of F=2 cold atoms
• Collision Dynamics and Rung Formation of Non-Abelian Vortices
• Superfluidity and Superconductivity in Neutron Stars
• Neutron Stars in the Laboratory
• Superfluidity and Superconductivity in Neutron Stars
• Color Magnetic Flux Tubes in Dense QCD
• Triplet pairing in beta-stable neutron star matter
• Neutrino emission from triplet pairing of neutrons in neutron stars
• Spin Polarized Asymmetric Nuclear Matter and Neutron Star Matter Within the Lowest Order Constrained Variational Method
• Quasi-Nambu-Goldstone Modes in Bose-Einstein Condensates
• Goldstone Bosons in the 3P2 Superfluid Phase of Neutron Matter and Neutrino Emission
• Universalities of Triplet Pairing in Neutron Matter
• Ferromagnetic neutron stars: axial anomaly, dense neutron matter, and pionic wall
• ${}^3{P}_2$-${}^3{F}_2$ Pairing in Dense Neutron Matter: The Spectrum of Solutions
• Anyonic particle-vortex statistics and the nature of dense quark matter
• Triplet Pairing in Neutron Matter
• Spin Polarization and Color Superconductivity in Quark Matter
• Nuclear pairing from microscopic forces: singlet channels and higher-partial waves
• Superfluid phases of triplet pairing and rapid cooling of the neutron star in Cassiopeia A
• Continuity of vortices from the hadronic to the color-flavor locked phase in dense matter
• Colorful boojums at the interface of a color superconductor
• Quark-hadron continuity under rotation: Vortex continuity or boojum?
• Goldstone modes in the neutron star core
• Magnetic Properties of Quantized Vortices in Neutron ${}^3{P}_2$ Superfluids in Neutron Stars
• Collective modes of the order parameter in a triplet superfluid neutron liquid
• Triplet Pairing in pure neutron matter
• ${}^3{P}_2$ Superfluids Are Topological
• Topology and symmetry of surface Majorana arcs in cyclic superconductors
• Reexamining Ginzburg-Landau theory for neutron ${}^3{P}_2$ superfluidity in neutron stars
• The low lying modes of triplet-condensed neutron matter and their effective theory
• Zero sound in triplet-correlated superfluid neutron matter
• Neutrino emission from spin waves in neutron spin-triplet superfluid
• Neutrino emissivity of anisotropic neutron superfluids
• Neutrino emissivity of ${}^3{P}_2$-${}^3{F}_2$ superfluid cores in neutron stars
• Superfluid phases of triplet pairing and neutrino emission from neutron stars
• Phase structure of neutron ${}^3{P}_2$ superfluids in strong magnetic fields in neutron stars
• Collective excitations of a quantized vortex in ${}^3{P}_2$ superfluids in neutron stars
• Possible Ferromagnetism in the Large N(c) and N(f) limit of quark matter
• Half-quantized Non-Abelian Vortices in Neutron ${}^3{P}_2$ Superfluids inside Magnetars
• Massive and massless modes of the triplet phase of neutron matter
• Microscopic description of axisymmetric vortices in ${}^3{P}_2$ superfluids
• Neutrino emissivity from Goldstone boson decay in magnetized neutron matter
• Critical endpoint and universality class of neutron ${}^3{P}_2$ superfluids in neutron stars
• New eigen-mode of spin oscillations in the triplet superfluid condensate in neutron stars
• Possibility of ferromagnetic neutron matter
• Ferromagnetism of dense matter and magnetic properties of neutron stars

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• Coexistence phase of ${}^1{S}_0$ and ${}^3{P}_2$ superfluids in neutron stars
• Spin-polarized phases of ${}^3{P}_2$ superfluids in neutron stars
• Core structures of vortices in Ginzburg-Landau theory for neutron ${}^3{P}_2$ superfluids
• Proximity effects of vortices in neutron ${}^3{P}_2$ superfluids in neutron stars: Vortex core transitions and covalent bonding of vortex molecules
• Strong-coupling effects of pairing fluctuations, and Anderson-Bogoliubov mode in neutron ${}^1$S${}_0$ superfluids in neutron stars
• Strongly interacting matter in extreme magnetic fields
• Symmetry classification of uniform states in spin-2 Bose-Einstein condensates and neutron ${}^3{P}_2$ superfluids
• Emergent chirality and superfluidity of parity-doubled baryons in neutron stars
• Topological Shell Structures in Neutron Stars: Effects on Equilibrium, Oscillations, and Gravitational-Wave Signatures