1. 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

2. 重力と縮退圧の模式図
チャンドラセカール質量

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

4. 中性子星の質量と半径

5. Structure of Neutron Stars
Yakovlev 2005

7. 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

8. 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

9. Oyamatsu 1993

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

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

12. 超流動・超伝導

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

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

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

17. Pinning energy
~1 MeV

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

19. Unpinning model for a glitch
Alpar et al. 1984

20. 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

21. Vela pulsar
> required

22. 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

23. Vortex pinning

24. 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

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

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

27. 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.

28. Glampedakis & Andersson 2008