1. Lila Warszawski & Andrew Melatos
Glitchology
Lila Warszawski & Andrew Melatos
Penn. State, June 2009.

2. The agenda Neutron star basics Pulsar glitches, glitch statistics
Superfluids and vortices
Glitch models
Gravitational waves from glitches

3. Neutron star composition
crust
electrons & ions
inner crust
0.5 km
SF neutrons, nuclei & electrons
1 km
outer core
SF neutrons, SC protons & electrons
7 km
inner core
Mass = 1.4 M
Radius = 10km
1.5 km

4. What we know Pulsars are extremely reliable clocks (∆TOA≈100ns).
We know the  and d/dt very well.
Glitches are sporadic changes in  (), and d/dt ( or ).
Some pulsars glitch quasi-periodically, others glitch intermittently.
Observed glitches in a single object span up to 4 decs in .
Of the approx known pulsars, 9 have glitched at least 5 times (≈ 30 more than once).
Some evidence for age-dependent glitch activity.

5. Anatomy of a glitch t ~ days n Dn (dn/dt)1 (dn/dt)2≠(dn/dt)1 ~ min
time

6. How do we see a glitch? Timing residual Arrival time (days)
Janssen & Stappers, 2006, A&A, 457, 611

7. Pulsar glitch statistics
Must treat glitch statistics from each pulsar individually.
Fractional glitch size follows a different power law for each pulsar.
Waiting times between glitches obey Poissonian statistics.
Glitch activity parameter: mean fractional change in period per year
Accounts for number and size of glitches [McKenna & Lyne (1990)]
Melatos, Peralta & Wyithe, 672, ApJ (2008)
a = 1.1
= 0.55 yr-1

8. A superfluid interior?
Post-glitch relaxation slower than for normal fluid:
Coupling between interior and crust is weak.
Nuclear density, temperature below Fermi temperature.
Spin-up during glitch is very fast (<100 s).
NOT electomagnetic torque
Interior fluid is an inviscid (frictionless) superfluid.

9. What can we learn? Nuclear physics laboratory not possible on Earth
QCD equation of state (mass vs radius)
Compressibility: soft or hard?
State of superfluidity
Viscosity: quantum lower bound?
Lattice structure:
Type, depth & concentration of defects
Of interest to many diverse scientific communities!

10. Glitch mechanisms Starquakes Catastrophic vortex unpinning
Fluid instabilities

11. Starquakes Deposit large amount of energy into NS crust
Changed SF/crust coupling  sudden vortex unpinning
Link & Epstein (1996)
Equilibrium shape of star departs from sphericity until crust cracks
Cannot explain all glitches
Works well for 23 glitches in PSR J
 predict glitches within few days
Middleditch et al. (2006)

12. Vortex unpinning Spindown  Magnus force on pinned vortices
Stress released in bursts as vortices unpin
Anderson & Itoh (1975)
Post-glitch relaxation due to vortex creep
Alpar, Anderson, Pines, Shaham (1984-)
Vortex avalanches
Analogous to superconducting flux vortices
Warszawski & Melatos (2008)
Vortex motion in the presence of pinning
Link (2009)

13. Fluid instability Two-stream intsability analagous to Kelvin-Helmholtz
Activated when relative flow reaches critical value
Andersson, Comer & Prix (2001)
R-mode instability as trigger for vortex unpinning
Sets in when rotational lag reaches critical levels
Glampedakis & Andersson (2009)

14. The unpinning paradigm
Nuclear lattice + neutron superfluid (SF).
Rotation of crust  vortices form  SF rotates.
Pinned vortices co-rotate with crust.
Differential rotation between crust and SF  Magnus force.
Vortices unpin  transfer of L to crust  crust spins up.
Nuclear lattice + neutron superfluid (SF).
Rotation of crust  vortices form  SF rotates.
Pinned vortices co-rotate with crust.
Differential rotation between crust and SF  Magnus force.
Vortices unpin  transfer of L to crust  crust spins up.

15. Avalanche model
Aim:
Using simple ideas about vortex interactions and Self-organized criticality, reproduce the observed statistics of pulsar glitches.

16. The rules of the avalanche game

17. Some simulated avalanches
avalanhce size
Some simulated avalanches
Warszawski & Melatos, MNRAS (2008)
time
avalanhce size
Power laws in the glitch size and duration support scale invariance.
Poissonian waiting times supports statistical independence of glitches.
Relies on large scale inhomogeneities

18. Coherent noise thermal unpinning only
Melatos & Warszawski, ApJ (2009)
Sneppen & Newman PRE (1996)
Coherent noise
Scale-invariant behaviour without macroscopically inhomogeneous pinning distribution .
Magnus forces chosen from Poissonian distribution.
thermal unpinning only

19. Computational output
thermal unpinning only F0 2
all unpin
power law

20. Model fits - Poissonian
F0   gives best fit in most cases.
Broad pinning distribution agrees with theory:  2MeV  1MeV
GW detection will make more precise

21. Gravitational waves from pulsar glitches

22. Recent work Undamped quasiradial fluctuations
Glitch transfers energy to crust  radiated as GWs.
Depends on glitch size AND change in
Crab pulsar h10-26
Sedrakian et al. (2003)
Glitches excite pulsation modes in multi-component core fluid
Acoustic, gravity and Rosby waves
Rezania & Jahan-Miri (2000), Andersson & Comer (2001)

23. GWs three
Strongest signal from time-varying current quadrupole moment (s)
Burst signal:
Vortex rearrangement  changing velocity field
Post-glitch ringing (relaxation):
Viscous component of interior fluid adjusts to spin-up
Stochastic signal:
Turbulence (eddies) [Melatos & Peralta (2009)]

24. Relaxation signal sphere ≠ cylinder
Van Eysden & Melatos (2008)
Stewartson
Ekman
Differentially rotating “cup of tea”
Coriolis → meridional circulation in time ~-1
Viscous boundary layer fills cup in time ~ Re1/2 -1 (Re > 1011)
Erases cos(m) modes
Sinusoidal GW decays in days- weeks
sphere ≠ cylinder

25. Nuclear equation of state! Polarization mixture → source inclination
DECAY TIME
RATIO
 AND 2
AMPLITUDE
RATIO
 AND 2
INTERSECT
van Eysden & Melatos (2008)
Compressibility K, viscosity N set Ekman layer thickness → wave strain and decay time
Nuclear equation of state!
Polarization mixture → source inclination
Wave strain ~10-25: at edge of Advanced LIGO

26. Turbulent signal HVBK two-fluid Re = 3x102
Re ~1010 → Kolmogorov turbulence
T0i  k-5/3, i.e. KE in large eddies
GW ≈ non-axisymmetric modes
BUT,  small eddies faster
GW ≈ “noise”
Strain set by large eddies, decoherence
Time set by large and small eddies
Too weak for Advanced LIGO (h < 10-31) …
… but GW spin down exceeds radio pulsar observations unless shear  /  < 0.01
Re = 3x104
HVBK two-fluid
Peralta et al. (2005), (2006)

27. Gross-Pitaevskii equation
potential
rotation
dissipative term
interaction term
coupling (g > 0)
chemical potential
 ( 0.1) suggests presence of normal fluid, aids convergence
V imposes pinning grid
g ( 1) tunes repulsive interaction
( 1) energy due to addition of a single particle
superfluid density

28. The potential

29. Tracking the superfluid
Circulation counts number of vortices
Angular momentum Lz accounts for vortex positions
Feedback

30. Gravitational waves
Current quadrupole moment depends on velocity field
Wave strain depends on time-varying current quadrupole

31. Simulations with GWs

32. Close-up of a glitch

33. Glitch signal
time
strain

34. Looking forward Wave strain scales as First source?
Estimate strain from ‘real’ glitch:
First source?
Close neutron star (not necessarily pulsar)
Old, populous neutron stars ( )
Many pulsars aren’t timed - might be glitching
Place limit on shear from turbulence [Melatos & Peralta (2009)]
Depends on vortex velocity