Pulsar Glitch: Superfluid Vortex Unpinning

Crust Spin-Down

Magnetic braking rate 1.0

Pinning strength (critical lag) 1.0

Avalanche fraction 35%

Simulation speed 1.0×

Live State

Lag Δ = Ω_sf − Ω_c0%

Crust freq. ν_c

11.200 Hz

Crust period

89.29 ms

Pinned vortices

600

Glitches so far

Last glitch size Δν/ν

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How it works

A neutron star's crust is threaded by a superfluid neutron sea. That superfluid can only rotate by forming quantized vortex lines, one per unit of circulation, obeying the Feynman–Onsager relation:

n_v = 2Ω / κ     (κ = h / 2m_n, the vortex quantum)

Vortices tend to pin to nuclei in the crustal lattice. While pinned they corotate with the crust, so as electromagnetic braking spins the crust down, the pinned superfluid cannot follow — a rotational lag Δ = Ω_sf − Ω_c builds up, storing angular momentum. Each vortex feels a Magnus force proportional to Δ; once enough vortices exceed the local pinning force at a critical lag Δ_c, they unpin in a catastrophic avalanche and slip outward, dumping their angular momentum into the crust. Because total angular momentum is conserved during the (very fast) avalanche:

I_c · ΔΩ_c  =  −I_sf · ΔΩ_sf  =  ΔL
Δν/ν  ≈  (I_sf / I_c) · f · (Δ / Ω_c)

where I_sf/I_c ≈ 1–2% is the moment-of-inertia fraction carried by the pinned crustal superfluid and f is the fraction of the stored lag released. The crust's rotation suddenly speeds up — a glitch — exactly as observed in real pulsars such as Vela and Crab.

Magnetic braking rate — how fast the crust spins down between glitches (electromagnetic + particle wind torque).
Pinning strength — the critical lag Δ_c the lattice can sustain before an avalanche triggers.
Avalanche fraction — how much of the stored lag a single avalanche releases (real glitches typically relieve a few percent to tens of percent).
Cyan lines are pinned vortices — they corotate with the crust (dashed grid). The faint inner point-cloud is the superfluid core, rotating at its own Ω_sf — watch it visibly drift ahead of the crust as the lag grows, then snap back into step at each glitch.

Time here is heavily accelerated for visibility — a real Vela glitch takes years to build up and seconds to release.

Pinned vortices Superfluid core (Ω_sf) Crust lattice (Ω_c)

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