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

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

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

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. 1500 known pulsars, 9 have glitched at least 5 times (≈ 30 more than once). Some evidence for age-dependent glitch activity.

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

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

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

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.

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!

Glitch mechanisms Starquakes Catastrophic vortex unpinning Fluid instabilities

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 J0537-6910  predict glitches within few days Middleditch et al. (2006)

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)

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)

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.

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

The rules of the avalanche game

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

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

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

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

Gravitational waves from pulsar glitches

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)

GWs three ways @ 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)]

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

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

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)

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

The potential

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

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

Simulations with GWs

Close-up of a glitch

Glitch signal time strain

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