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

重力と縮退圧の模式図 チャンドラセカール質量

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

中性子星の質量と半径

Structure of Neutron Stars Yakovlev 2005

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

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

Oyamatsu 1993

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

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

超流動・超伝導

Crab Vela P(ms) 33 89 nv (cm-2) 2E5 7E4 a(cm) 2E-3 4E-3

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

TWO GLITCHES Vela glitch Crab glitch McCulloch et al. 1990 Lyne et al. 1992

Pinning energy ~1 MeV

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

Unpinning model for a glitch Alpar et al. 1984

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

Vela pulsar --------> required

Pinning force ・condensation energy (Alpar et al. 1984) pinning energy Ep ~ 1MeV coherence length ξ~10-12 cm lattice constant a ~5×10-12 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

Vortex pinning

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

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

Dispersion relation for the vortex oscillations kink supply rate required in Vela ~2×１015 s-1 ~1×１016 rad s-1

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.

Glampedakis & Andersson 2008