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パルサーグリッチと超流体渦糸のピンニング 大阪市立大 ２００９／１０／２３ ・中性子星の質量と半径 ・中性子星の内部構造 ・中性子の超流動 ・パルサーグリッチ ・超流体渦糸の Pinning とグリッチのモデル

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重力と縮退圧の模式図 チャンドラセカール質量

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Einstein Equations for a Star Tolman- Oppenheimer- Volkoff (1939) Equation of state (nuclear force)

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中性子星の質量と半径

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Structure of Neutron Stars Yakovlev 2005

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OUTER CRUST Composition: electrons + (ions) nuclei Electrons (e): constitute a strongly degenerate, almost ideal gas, give the main contribution into the pressure Ions (A,Z): fully ionized by electron pressure, give the main contribution into the density Electron background

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INNER CRUST Composition: electrons + nuclei + free (dripped) neutrons e+n background Electrons (e): constitute a strongly degenerate, ultra-relativistic gas Ions (A,Z): neutron-rich, occupy substantial fraction of volume Free neutrons (n): constitute a strongly degenerate Fermi-liquid, which can be superfuid

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Oyamatsu 1993

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OUTER CORE Composition : uniform liquid of neutrons (n), protons (p), and electrons (e), and possibly muons

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INNER CORE Composition: largely unknown Hypotheses: 1.Nucleon/hyperon matter 2.Pion condensation 3.Kaon condensation 4.Quark matter 1. Nucleon-hyperon matter

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超流動・超伝導

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Crab Vela P(ms) n v (cm -2 ) 2E5 7E4 a(cm) 2E-3 4E-3

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Glitch in Vela Pulsar 10h, 3d, 30d~

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TWO GLITCHES Crab glitch Vela glitch Lyne et al McCulloch et al. 1990

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~1 MeV Pinning energy

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The Standard glitch model (Anderson & Itoh 75) Glampedakis 2008

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Alpar et al Unpinning model for a glitch

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I 1 /I~0.01 I 2 /I~0.01 τ τ 1 2 ~ 3 d ~ 60 d Pinning force F p ~ dyn/cm Alpar et al. 1984

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Vela pulsar > required

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Pinning force ・ condensation energy (Alpar et al. 1984) pinning energy E p ~ 1MeV coherence length ξ~ cm lattice constant a ~5 × cm ・ cancellation of the elementary pinning force (Jones 1991) rigid vortex --> equal number of pinning sites on either side of the line --> f p ~ 0 ・ bending of vortex lines (Link & Epstein 1993) finite tension --> kink --> much more efficient pinning

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Vortex pinning

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Kinks propagation along the vortex lines y-component of velocity vortices move together with superfluids almost no pinning Jones et al. 1998

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Vortex configurations ・ equation of motion of vortex lines ・ configurations kinks minimize

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Dispersion relation for the vortex oscillations kink supply rate required in Vela ~2× １ 0 15 s -1 ~1× １ 0 16 rad s -1

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Discussion on vortex pinning (1)We find no unstable mode that grows with time. The vortex equilibrium configurations with static kink structures are stable. Hence, the kink motion as required by Jones is less likely. (2) The kink solution can be expressed as a sum of fourier components of different wave numbers. The dispersion relation shows that the phase velocity of vortex waves depends on the wave number. Hence, even if a kink is formed and start to move, the kink feature will be smeared out during propagation. (3) The vortex equilibrium configuration is composed of the static kink and straight segments. A vortex line in equilibrium lies deep in the pinning potential well and is strongly pinned to the lattice nuclei in its most part, especially when the vortex line is close to the main axis of a crystal lattice. Pinning may be strong enough to explain the large glitches observed in Vela pulsar.

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Glampedakis & Andersson 2008

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