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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 パルサーグリッチと超流体渦糸のピンニング ・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**

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 e+n background

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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 1. Nucleon-hyperon matter Composition: largely unknown**

Hypotheses: Nucleon/hyperon matter Pion condensation Kaon condensation Quark matter 1. Nucleon-hyperon matter

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超流動・超伝導

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Crab Vela P(ms) nv (cm-2) 2E E4 a(cm) E E-3

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

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

Lyne et al. 1992

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Pinning energy ~1 MeV

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**The Standard glitch model (Anderson & Itoh 75)**

Glampedakis 2008

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**Unpinning model for a glitch**

Alpar et al. 1984

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**I1/I~0.01 I2/I~0.01 τ ~ 3 d 1 τ ~ 60 d 2 Pinning force**

Fp ~ 1015 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 Ep ~ 1MeV coherence length ξ~10-12 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 --> fp ~ 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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**vortices move together with superfluids**

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

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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 ~2×１015 s-1 ~1×１016 rad s-1

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**Discussion on vortex pinning**

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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