Pulsar Glitches and Neutron Star Superfluidity

A rotating neutron star is the most precise clock in the sky: its spin frequency $\nu=\Omega/2\pi$ declines with metronomic smoothness as magnetic-dipole braking bleeds off rotational energy. Then, once every few years in a handful of stars, the clock jumps forward — an abrupt spin-up completed faster than the observing cadence, followed by slow relaxation toward the old track. These glitches are a paradox: the only external torque on an isolated pulsar is braking, which can only slow the star. A sudden speed-up cannot come from outside; it must be angular momentum already inside, in a component decoupled from the crust we watch. The reservoir is a neutron superfluid. Above the neutron-drip density $\rho_\mathrm{drip}\approx4\times10^{11}\,\mathrm{g\,cm^{-3}}$ , dripped neutrons form a $^1S_0$ Cooper-paired condensate with critical temperature $T_c\sim10^{9}$ – $10^{10}\,\mathrm{K}$ , well above a mature star's interior temperature. A superfluid cannot rotate rigidly; it threads itself with quantized vortex lines, each carrying $\kappa=h/2m_n$ of circulation, whose areal density sets its mean spin. To slow down it must let vortices drift outward — but in the inner crust they are pinned to nuclei. So the superfluid stays stuck at a higher rate than the braking crust, the lag builds, the Magnus force climbs, and when it overwhelms pinning a vast number of vortices unpin at once, dumping their excess angular momentum into the crust. The crust jumps. This article develops that two-component picture into a laboratory for dense-matter physics no experiment on Earth can reach.

Key takeaways

A pulsar glitch is a sudden increase in a neutron star's rotation frequency, fractional size $\Delta\Omega/\Omega\sim10^{-9}$ to $10^{-6}$ , on otherwise steady electromagnetic spin-down.
Because the external torque can only brake the star, the spin-up must be internal: a decoupled neutron superfluid hands stored angular momentum to the crust, conserving total $L$ .
The superfluid stores it in quantized vortices carrying $\kappa=h/2m_n\approx1.98\times10^{-3}\,\mathrm{cm^2\,s^{-1}}$ ; pinning them to crustal nuclei lets it lag until the Magnus force forces a catastrophic unpinning.
The fractional spin-up measures $I_s/(I_c+I_s)$ times the accumulated lag, so every glitch weighs the reservoir against the rest of the star — a direct probe of the equation of state.
Vela (PSR B0833−45) is the archetype: $\Delta\Omega/\Omega\approx2\times10^{-6}$ every 2–3 years; the younger Crab glitches smaller and less regularly.
Post-glitch recovery over days to months measures the vortex-creep coupling, and cumulative glitch activity sets a lower bound $I_s/I\gtrsim0.017$ now in tension with entrainment.
Key idea: A neutron star has at least two coupled rotating components — a braked crust of moment of inertia $I_c$ and a superfluid interior $I_s$ storing angular momentum in pinned quantized vortices. A glitch is the sudden partial release of the superfluid's excess to the crust, and the fractional spin-up measures $I_s/(I_s+I_c)$ times the accumulated lag.

The core insight

A neutron star has at least two coupled rotating components: a rigid, electromagnetically braked crust of moment of inertia $I_c$ and a superfluid interior $I_s$ that stores angular momentum by pinning quantized vortices. A glitch is the sudden partial release of the superfluid's angular-momentum excess to the crust; the fractional spin-up measures $I_s/(I_s+I_c)$ times the accumulated lag.

Where this lives today

Glitches are now a precision observable. Long-baseline timing programmes — Jodrell Bank, Parkes/Murriyang, MeerKAT, and FAST — maintain catalogues of hundreds of events, and statistical studies (Espinoza and collaborators) map how glitch size and rate depend on spin-down age. The 2016 Vela glitch was the breakthrough: caught in single-pulse data, it resolved the rise to better than a rotation period and revealed a brief overshoot, constraining the mutual-friction coupling as no averaged timing could. At the theory frontier the entrainment problem (Worked Example 3) is the sharpest lever: if crustal entrainment is as strong as band-structure calculations suggest, the crust cannot supply Vela's activity and the core superfluid must glitch too. Glitches also taxonomize: rotation-powered pulsars glitch upward, while magnetars show both glitches and anti-glitches tied to magnetic activity, so the sign of a spin discontinuity diagnoses the dominant engine, and large glitches are candidate gravitational-wave transients for LIGO/Virgo/KAGRA.

The physical picture

Picture the crust as the visible hand of a clock, braking steadily. Inside sits a superfluid flywheel that refuses to slow with it, because its vortices are jammed against the crystal lattice. Over years the flywheel spins faster than the hand; when the jam breaks it dumps its excess spin into the hand and the clock leaps forward. Everything quantitative below makes that cartoon precise. The quantized vortex makes the flywheel possible: a superfluid changes its rotation only by moving vortex lines, so blocking them — pinning — is what lets it hold angular momentum against the crust's slowdown. The first figure fixes the two-component geometry and puts a number on the population: roughly $2\times10^{17}$ pinned vortices in a Vela-like star.

Figure

The two-component neutron star — a braked crust of moment of inertia I_c and an interior superfluid I_s whose quantized vortices pin to the crustal lattice, lagging the crust by ΔΩ_sf until the Magnus force f_M = ρ_s κ r ΔΩ_sf overcomes pinning. For Vela the Feynman density n_v = 2Ω/κ ≈ 7×10⁴ cm⁻² gives about 2×10¹⁷ vortices

The size of the leap is a ratio of moments of inertia: a large glitch such as Vela's, $\Delta\Omega/\Omega\sim2\times10^{-6}$ , implies the reservoir holds a per-cent-level fraction of the star's angular momentum — which is why glitch amplitudes weigh the crust against the core and constrain the equation of state. Between glitches the lag rebuilds linearly as the crust brakes, so the same threshold recurs and the star glitches quasi-regularly. The slow recovery afterward is friction: vortices creep back into a metastable pinned configuration over days to months. The second figure is what a radio timer measures — the frequency history $\nu(t)$ through a glitch and its recovery, with Vela's real numbers.

Figure

The glitch signature in rotation frequency ν(t) — steady spin-down interrupted by a near-instantaneous spin-up ΔΩ, then a partial exponential recovery over τ_r onto a permanently offset track. For Vela ΔΩ/Ω ≈ 2×10⁻⁶ every 2 to 3 years, the archetypal large glitch

The core equations

The baseline against which glitches are measured is the smooth electromagnetic spin-down. A magnetized rotator radiates, losing rotational energy, so its angular velocity decays as a power law set by the dipole geometry.

\dot\Omega = -\frac{2}{3}\frac{\mu^2\sin^2\alpha}{Ic^3}\,\Omega^3 \qquad (1)

where: $\Omega$ — angular frequency of the crust; $\mu$ — magnetic dipole moment; $\alpha$ — angle between magnetic and rotation axes; $I$ — moment of inertia; $c$ — speed of light. Reading it: the torque scales as $\Omega^3$ , and the pure-dipole braking index $n\equiv\Omega\ddot\Omega/\dot\Omega^2=3$ is the reference that decoupling later perturbs. The reservoir works only because superfluid circulation is quantized. Requiring the single-valued condensate wavefunction to wind its phase by a multiple of $2\pi$ forces the circulation into fixed quanta.

\kappa = \frac{h}{2 m_n} \approx 1.98\times10^{-3}\,\mathrm{cm^2\,s^{-1}} \qquad (2)

where: $\kappa$ — circulation per vortex line; $h$ — Planck constant; $m_n$ — neutron mass, with the Cooper-pair mass $2m_n$ in the denominator. Reading it: the superfluid changes its spin only by adding or removing whole vortices. A rotating superfluid mimics rigid rotation on average by filling with a uniform vortex array. Matching a rigid body's circulation to the sum of vortex quanta gives their density.

n_v = \frac{2\Omega}{\kappa} \qquad (3)

where: $n_v$ — vortex lines per unit area; $\Omega$ — superfluid rotation rate; $\kappa$ — circulation quantum. Reading it: for Vela ( $\Omega\approx70\,\mathrm{s^{-1}}$ ) this is $n_v\approx7\times10^4\,\mathrm{cm^{-2}}$ , so a $10$ -km interior holds $\sim2\times10^{17}$ vortices. The glitch itself is the recoupling of the two components at fixed total angular momentum. This central relation turns an observed spin-up into a measurement of the reservoir.

\frac{\Delta\Omega}{\Omega}=\frac{I_s}{I_c+I_s}\,\frac{\Delta\Omega_{sf}}{\Omega} \qquad (4)

where: $\Delta\Omega$ — observed crust spin-up; $I_c$ — moment of inertia of the crust plus tightly coupled matter; $I_s$ — moment of inertia of the decoupled superfluid; $\Delta\Omega_{sf}=\Omega_{sf}-\Omega_c$ — the released lag. Reading it: the fractional glitch is the moment-of-inertia fraction times the fractional lag. What holds the lag in place is a force balance on each vortex. The superfluid streaming past exerts a Magnus force per unit length, opposed by pinning to the nuclei.

f_M = \rho_s\,\kappa\,(\mathbf{v}_L-\mathbf{v}_s)\times\hat{\boldsymbol{\kappa}} \qquad (5)

where: $f_M$ — Magnus force per unit vortex length; $\rho_s$ — superfluid mass density; $\mathbf{v}_L$ — vortex-line velocity; $\mathbf{v}_s$ — local superfluid velocity; $\hat{\boldsymbol{\kappa}}$ — unit vector along the vortex. Reading it: $f_M$ grows with the lag; when it exceeds pinning the vortex tears free and the avalanche begins. Pinning strength sets the maximum lag, and hence the glitch size. Its energy scale is the condensation-energy difference when a vortex core overlaps a nucleus.

E_p \sim (1\text{–}5)\ \mathrm{MeV\ per\ pinning\ site} \qquad (6)

where: $E_p$ — energy gained when a vortex core sits on a nucleus rather than in the surrounding neutron gas. Reading it: an MeV-per-site energy holds vortices against lags of $\sim10^{-2}\,\mathrm{s^{-1}}$ — the reservoir Vela needs. After the jump the crust relaxes rather than simply resuming spin-down, because the superfluid recouples gradually. The frequency history is a decaying exponential plus a permanent offset.

\Omega_c(t)=\Omega_c(t_g)+\Delta\Omega\Big[Q\,e^{-(t-t_g)/\tau_r}+(1-Q)\Big]-|\dot\Omega|\,(t-t_g) \qquad (7)

where: $t_g$ — glitch epoch; $Q$ — healing fraction, $0\le Q\le1$ ; $\tau_r$ — recovery timescale (days to months); $|\dot\Omega|$ — steady spin-down rate. Reading it: a fraction $Q$ decays as vortices re-pin, while $(1-Q)$ is permanent. Summing many glitches over a long baseline gives a bulk measurement. The cumulative fractional spin-up per unit time — the glitch activity — bounds the reservoir fraction from below.

\mathcal{A}\equiv\frac{1}{t}\sum\frac{\Delta\Omega}{\Omega}\approx \frac{I_s}{I}\,\frac{|\dot\Omega|}{\Omega} \qquad (8)

where: $\mathcal{A}$ — glitch activity parameter; $I_s/I$ — fractional moment of inertia of the glitch-driving superfluid; $|\dot\Omega|/\Omega$ — fractional spin-down rate. Reading it: rearranged, $I_s/I\approx\mathcal{A}\,\Omega/|\dot\Omega|$ — a catalogue weighs the reservoir, $\gtrsim1.7\%$ for Vela.

Derivation AGlitch amplitude from angular momentum conservation

Model the star as two rigidly rotating reservoirs — the crust plus everything locked to it (moment of inertia $I_c$ ) and a decoupled neutron superfluid ( $I_s$ ) leading the crust by an accumulated lag $\Delta\Omega_{sf}$ — that suddenly recouple. Because unpinning recouples them far faster than the braking time, the external torque delivers a negligible impulse and total $L$ is conserved, fixing the fractional spin-up from the moment-of-inertia ratio and the lag alone. Every glitch is thus a weighing of the hidden reservoir.

Step 1. Write the total angular momentum just before the glitch, crust at $\Omega_c$ and superfluid leading at $\Omega_{sf}=\Omega_c+\Delta\Omega_{sf}$ : $L=I_c\Omega_c+I_s\Omega_{sf}$ . Why: pinning has kept the two at different rates, so their momenta add separately.

Step 2. Impose conservation: on the sub-day glitch timescale the braking impulse is negligible, so after recoupling to a common rate $\Omega'$ , $L=(I_c+I_s)\Omega'$ . Why: this makes a glitch a redistribution, not an injection — $L$ is merely shared out.

Step 3. Equate, $I_c\Omega_c+I_s(\Omega_c+\Delta\Omega_{sf})=(I_c+I_s)\Omega'$ , and solve: $\Omega'=\Omega_c+\dfrac{I_s}{I_c+I_s}\Delta\Omega_{sf}$ . Why: the excess is diluted across the combined inertia, so only $I_s/(I_c+I_s)$ of the lag reaches the crust.

Step 4. Read off $\Delta\Omega=\dfrac{I_s}{I_c+I_s}\Delta\Omega_{sf}$ and divide by $\Omega\approx\Omega_c$ for the boxed result $\dfrac{\Delta\Omega}{\Omega}=\dfrac{I_s}{I_c+I_s}\dfrac{\Delta\Omega_{sf}}{\Omega}$ . Why: for Vela, $\Delta\Omega/\Omega\approx2\times10^{-6}$ with $I_s/I\approx0.01$ needs only $\Delta\Omega_{sf}/\Omega\approx2\times10^{-4}$ — a modest few-year lag.

Go deeper · Derivation B · 1 minAccumulated lag and the glitch recurrence time

Derivation BAccumulated lag and the glitch recurrence time

If the crustal superfluid is perfectly pinned between glitches, its rotation stays frozen while the crust brakes, so the lag grows linearly until the Magnus force reaches the pinning maximum; at that critical lag vortices unpin and the star glitches. Equating the linear growth to that threshold turns a microscopic pinning force into an observable recurrence interval, and predicts quasi-periodic, similar-sized glitches — Vela's defining behaviour.

Step 1. With the superfluid frozen ( $\dot\Omega_{sf}\approx0$ ) and the crust braking at $\dot\Omega_c<0$ , the lag obeys $\dfrac{d}{dt}(\Omega_{sf}-\Omega_c)=|\dot\Omega|$ , increasing linearly. Why: pinning removes the superfluid's only way to shed rotation, so all the crust's slowdown becomes lag.

Step 2. Set the critical lag by force balance: $f_M=\rho_s\kappa\,r\,\Delta\Omega_{sf}$ climbs until it equals the maximum pinning force $f_p^{\max}$ , giving $\Delta\Omega_{sf}^{\max}=\dfrac{f_p^{\max}}{\rho_s\kappa r}$ . Why: beyond this the balance in the first figure's zoom panel tips and unpinning cascades.

Step 3. Integrate the growth to threshold for the recurrence time $t_g=\dfrac{\Delta\Omega_{sf}^{\max}}{|\dot\Omega|}$ . Why: Vela's $|\dot\Omega|\approx10^{-10}\,\mathrm{s^{-2}}$ and $\Delta\Omega_{sf}^{\max}\sim10^{-2}\,\mathrm{s^{-1}}$ give $t_g\sim10^{8}\,\mathrm{s}$ — a few years, matching observation with no free parameters.

Step 4. Self-regulation: each glitch drains the lag via $\Delta\Omega\,(I_c+I_s)=I_s\,\Delta\Omega_{sf}^{\max}$ , resetting the reservoir before the same threshold rebuilds. Why: identical thresholds give near-identical size and spacing — hence Vela's quasi-regular glitches, unlike the creep-dominated Crab.

Go deeper · Derivation C · 1 minTwo-component coupling and post-glitch relaxation

Derivation CTwo-component coupling and post-glitch relaxation

Between glitches the superfluid is not perfectly frozen but couples to the crust through a weak frictional drag — thermally activated vortex creep — with relaxation time $\tau_c$ . The coupled equations show that on short timescales only the crust feels the torque, responding with reduced inertia, while on long timescales the two co-rotate. The crossover is exactly the exponential post-glitch recovery, tying the observed timescale and healing fraction to the drag and the reservoir fraction.

Step 1. Write the pair $I_c\dot\Omega_c=N_{EM}+\dfrac{I_s}{\tau_c}(\Omega_{sf}-\Omega_c)$ and $I_s\dot\Omega_{sf}=-\dfrac{I_s}{\tau_c}(\Omega_{sf}-\Omega_c)$ , with $N_{EM}=-K\Omega_c^3$ . Why: the drag term is equal and opposite, conserving $L$ internally — the glitch made continuous.

Step 2. Short-time limit $t\ll\tau_c$ : the superfluid has not responded, so $I_c\dot\Omega_c\approx N_{EM}$ and the crust brakes with reduced inertia $I_c<I$ . Why: just after a glitch the decoupled superfluid is dead weight, giving a steeper spin-down.

Step 3. Long-time limit $t\gg\tau_c$ : the two co-rotate and $(I_c+I_s)\dot\Omega\approx N_{EM}$ . The transition is exponential relaxation with $\tau_r\simeq\tau_c\,I_c/(I_c+I_s)$ . Why: this is equation (7)'s recovery term — the star heals as drag re-locks the superfluid, and $\tau_r$ reads out $\tau_c$ .

Step 4. Observables: because $I_\mathrm{eff}$ depends on the coupling state, the apparent braking index departs from $n=3$ , and $Q\simeq I_s/(I_c+I_s)$ . Why: a glitch plus recovery measures the reservoir fraction two ways — jump size and healing fraction — a consistency check.

Limiting cases

Behaviours of the two-component model as the coupling is dialled from perfectly pinned to perfectly locked:

Case	Result	Meaning
Perfect pinning (no creep)	$\dfrac{d\Omega_{sf}}{dt}=0$	Vortices fully locked; the superfluid keeps its rate while the crust brakes, maximizing the eventual glitch.
Perfect coupling (no lag)	$\Omega_{sf}=\Omega_c\Rightarrow\Delta\Omega/\Omega=0$	Instantaneous friction; no reservoir builds — smooth spin-down, no glitches.
Instantaneous recoupling	$\dfrac{\Delta\Omega}{\Omega}=\dfrac{I_s}{I_c+I_s}\dfrac{\Delta\Omega_{sf}}{\Omega}$	Conservation at fixed $L$ fixes the spin-up from the released lag — the glitch itself.
Small vs large glitchers	$\dfrac{\Delta\Omega}{\Omega}\sim10^{-9}$ (Crab) vs $\sim10^{-6}$ (Vela)	Younger, hotter stars glitch small via creep; middle-aged stars show large vortex-avalanche glitches.
Entrainment included	$I_s^{\rm eff}\to I_s/\langle m_n^*/m_n\rangle$	The mobile reservoir shrinks by the effective-mass factor, so the required $I_s/I$ rises above the crust's budget.

Worked examples

1 · The vortex census of the Vela pulsar (fully worked)

Vela (PSR B0833−45) has spin period $P=89.33$ ms. Compute its angular velocity, the circulation quantum, the areal vortex density, and the total number of vortices threading a $10$ -km superfluid interior.

Step 1. Angular velocity from the period: $\nu=1/P=11.19\,\mathrm{Hz}$ , so $\Omega=2\pi\nu=\mathbf{70.3\ s^{-1}}$ — the rate the pinned superfluid must reproduce.

Step 2. Circulation quantum (CGS): $\kappa=h/2m_n=6.626\times10^{-27}/(2\times1.675\times10^{-24})=\mathbf{1.98\times10^{-3}\ cm^2\,s^{-1}}$ .

Step 3. Feynman areal density (equation 3): $n_v=2\Omega/\kappa=\mathbf{7.1\times10^{4}\ cm^{-2}}$ . The vortices sit $n_v^{-1/2}\approx38\,\mu\mathrm{m}$ apart — a startlingly ordered array.

Step 4. Total count over area $A=\pi R^2$ with $R=10\,\mathrm{km}=10^{6}\,\mathrm{cm}$ : $N=n_v\,\pi R^2\approx\mathbf{2.2\times10^{17}}$ . The outward hop of a large fraction of this population is the "vortex avalanche" that makes a glitch.

2 · Reservoir lag and recurrence time for a Vela glitch (fully worked)

Vela glitches with $\Delta\Omega/\Omega\approx2\times10^{-6}$ and spins down at $|\dot\Omega|\approx9.8\times10^{-11}\,\mathrm{s^{-2}}$ . Assuming the glitch-driving superfluid holds $I_s/I\approx0.01$ , find the accumulated lag released and estimate the interval between glitches.

Step 1. Invert equation (4). With $I_s/(I_c+I_s)\approx0.01$ , the required fractional lag is $\dfrac{\Delta\Omega_{sf}}{\Omega}=\dfrac{2\times10^{-6}}{0.01}=\mathbf{2\times10^{-4}}$ ; a small reservoir is wound up only slightly to power a large glitch. In absolute terms $\Delta\Omega_{sf}=2\times10^{-4}\times70.3=\mathbf{1.4\times10^{-2}\ s^{-1}}$ , the critical lag $\Delta\Omega_{sf}^{\max}$ at which pinning fails.

Step 2. Recurrence from linear lag growth (Derivation 2): $t_g=\dfrac{\Delta\Omega_{sf}^{\max}}{|\dot\Omega|}=\dfrac{1.4\times10^{-2}}{9.8\times10^{-11}}\approx\mathbf{4.5\ yr}$ . Given the crude $I_s/I\approx0.01$ , this sits in the observed 2–3 yr band — the model reproduces Vela's cadence from first principles.

Step 3. Energy check: the heat dumped per glitch is $\Delta E\sim I_s\,\Omega\,\Delta\Omega_{sf}\sim10^{42}\,\mathrm{erg}$ (with $I\sim10^{45}\,\mathrm{g\,cm^2}$ ) — tiny against the rotational store but enough to warm the crust detectably.

3 · Weighing the reservoir from decades of glitches

Over a long baseline, Vela's glitches undo a fraction of the spin-down: the cumulative frequency gained in glitches divided by the frequency lost to braking is $\approx1.8\%$ . What does this say about the superfluid?

Step 1. The activity is $\mathcal{A}\approx\dfrac{\sum\Delta\nu}{\nu\,T}$ . With $\Delta\nu\approx2\times10^{-5}\,\mathrm{Hz}$ every $T\approx2.5\,\mathrm{yr}$ , the frequency-gain rate is $\approx2.8\times10^{-13}\,\mathrm{Hz\,s^{-1}}$ against $|\dot\nu|\approx1.57\times10^{-11}\,\mathrm{Hz\,s^{-1}}$ ; their ratio is $\approx\mathbf{0.018}$ . By equation (8) this is a lower bound, so $\mathbf{I_s/I\gtrsim1.7\%}$ — a few per cent of Vela must be decoupled superfluid.

Step 2. The tension: crust-only models give a few per cent (marginal), but entrainment dresses the neutrons with effective mass $\langle m_n^*/m_n\rangle\sim4$ – $5$ , cutting the mobile reservoir and pushing the required fraction to $\sim5\%$ — beyond the crust's budget. The clean resolution is that the core superfluid must also glitch — a headline open problem linking a timing number to nuclear microphysics.

Physics of the portrait

The glitch model carried a laboratory idea — quantized vortices and their pinning — wholesale into an astrophysical object, making predictions that decades of timing confirmed. Its emblem is the pinned vortex: what lets a frictionless fluid hold angular momentum against a braking solid.

Origins · 1 minvortex pinning and how this was discovered

vortex pinning

the mechanism that lets a superfluid store angular momentum against a braking crust · neutron-star superfluid dynamics

Vortex pinning is the physical heart of the glitch, descending from a chain of twentieth-century ideas. Lars Onsager (1949) and Richard Feynman (1955) showed a rotating superfluid carries quantized circulation in discrete vortex lines, each with $\kappa=h/2m$ and density $n_v=2\Omega/\kappa$ — the rule fixing the vortex census inside a neutron star. Arkady Migdal argued in 1959 that dense nucleon matter should be superfluid, an idea academic until pulsars appeared. The synthesis came fast: in 1969, the year the first Vela glitch was timed, Baym, Pethick, Pines and Ruderman laid out the two-component interior and showed its long relaxation time explained post-glitch recovery. In 1975 Anderson and Itoh supplied the trigger: vortices pin to the crustal lattice, and a catastrophic collective unpinning is the glitch. The 1980s added vortex-creep theory (Alpar, Anderson, Pines and Shaham). Today entrainment — the effective-mass dressing of crustal neutrons (Chamel and others) — has sharpened the model into a genuine equation-of-state test, since the observed activity now appears to demand more superfluid than the crust alone holds.

History

1949

— Onsager proposes quantized circulation in a rotating superfluid

1955

— Feynman derives the vortex-density rule n_v = 2Ω/κ

1959

— Migdal argues that dense nucleon matter is superfluid

1969

— the first Vela glitch is timed; Baym, Pethick, Pines and Ruderman publish the two-component interior

1975

— Anderson and Itoh propose vortex unpinning as the glitch trigger

Going further

Texts. Carroll and Ostlie, An Introduction to Modern Astrophysics, 2nd ed., Ch. 16 · Shapiro and Teukolsky, Black Holes, White Dwarfs, and Neutron Stars, Ch. 10 · Lorimer and Kramer, Handbook of Pulsar Astronomy, Ch. 6 · Glendenning, Compact Stars, for the dense-matter equation of state underpinning $I_s/I$ . The circulation quantum $\kappa=h/2m_n\approx1.98\times10^{-3}\,\mathrm{cm^2\,s^{-1}}$ follows from $6.626\times10^{-27}/(2\times1.675\times10^{-24})$ in CGS; combined with $n_v=2\Omega/\kappa$ this gives Vela's $\sim2\times10^{17}$ vortices. Key anchor numbers used throughout: Vela $P=89.33$ ms, $\Delta\Omega/\Omega\approx2\times10^{-6}$ , recurrence 2–3 yr, $|\dot\Omega|\approx10^{-10}\,\mathrm{s^{-2}}$ , $I_s/I\gtrsim1.7\%$ , $\rho_\mathrm{drip}\approx4\times10^{11}\,\mathrm{g\,cm^{-3}}$ .

Prerequisites. Neutron Stars · Neutron Star Structure and Interior · Pulsars · Pulsar Magnetospheres and Spin-Down · Equation of State of Dense Matter. Leads to. Neutron Star Structure and Interior · Magnetars · Millisecond and Recycled Pulsars.

Ask the tutor: Ask me to walk through the vortex census or the reservoir-lag estimate for any pulsar, or to unpack why entrainment forces the core superfluid into the glitch story.

What exactly is a pulsar glitch?

It is a sudden, step-like increase in a pulsar's rotation frequency, superposed on its normally smooth spin-down. Fractional sizes range from about $10^{-9}$ to a few $\times10^{-6}$ , completed faster than the timing cadence — seconds to days, and in the best-resolved case (Vela 2016) faster than a single rotation. Afterward the frequency usually relaxes partway back toward the old spin-down track over days to months. Glitches are common in young and middle-aged pulsars and rare in the very old and millisecond pulsars, with colder, tightly coupled interiors.

Why is a superfluid needed — why not just a stressed solid crust?

Crust-quake models (a cracking, settling lattice) give occasional small jumps but fail for the big glitchers. Energetics: a solid crust cannot repeatedly store and release the angular momentum Vela needs without being ground to pieces. Regularity: Vela's quasi-periodic large glitches demand a reservoir that recharges at the spin-down rate, exactly what a pinned superfluid provides. Recovery: the slow exponential relaxation needs a component coupling on a days-to-months timescale — a hallmark of vortex friction, not elastic solids.

How do we actually know the interior is superfluid?

No single observation "sees" the superfluid, but independent lines converge. Nuclear pairing calculations predict $^1S_0$ and $^3P_2$ neutron superfluidity across crust and core at the relevant densities. The long post-glitch recovery implies a weakly coupled component with vortex-creep drag, and spin-ups against braking demand a decoupled store. The strongest recent evidence is thermal: the rapid cooling of Cassiopeia A's neutron star reads as the onset of core superfluidity.

Where does the "extra" angular momentum in a glitch come from?

It was already in the star. Between glitches the pinned superfluid cannot slow down, so while the crust brakes it keeps spinning faster, building an excess relative to a fully coupled star. The glitch hands that excess to the crust when the vortices unpin, conserving total angular momentum — the crust gains exactly what the superfluid loses. Nothing is added from outside; the reservoir was charged invisibly over the preceding years, which is why the recurrence time equals the accumulated lag divided by the spin-down rate.

What is the entrainment problem?

Entrainment is a non-dissipative coupling in which the crustal lattice drags along, or "entrains", some of the dripped superfluid neutrons, giving them an enhanced effective mass $m_n^*/m_n\sim4$ – $5$ . A given lag then carries less mobile angular momentum, so reproducing the observed activity needs a larger superfluid moment of inertia — pushing the required $I_s/I$ to around $5\%$ , exceeding what the crust alone supplies. The leading resolutions: the core superfluid also glitches, or entrainment is weaker than band-structure calculations indicate. It is an active frontier tying a timing statistic to nuclear microphysics.

Do all pulsars glitch, and what are anti-glitches?

No. Glitching is concentrated in young and middle-aged rotation-powered pulsars; the oldest and the recycled millisecond pulsars almost never glitch, consistent with colder, more tightly coupled interiors. Magnetars are the exception: they glitch frequently and also show anti-glitches — sudden spin-downs — often with X-ray bursts, pointing to magnetic activity rather than superfluid recoupling. The sign of a spin discontinuity thus diagnoses whether a star's dynamics are dominated by superfluid vortices or by its magnetic field.

What sets how fast a glitch rises?

The rise time is set by the mutual-friction coupling between the vortex-laden superfluid and the charged crust–core plasma — how quickly the unpinned vortices transfer their momentum. Most glitches give only an upper limit (shorter than the cadence), but the 2016 Vela event was resolved to under a rotation period and showed a brief overshoot, the crust racing past its final rate. Such measurements constrain how many vortices move collectively and test whether the coupling is electron scattering off magnetized vortex cores — a probe of interior transport.