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This study explores the basics of neutron stars, glitch statistics, superfluids, glitch models, and gravitational waves from glitches. It investigates the composition of neutron stars and the mechanisms behind glitches, such as starquakes, vortex unpinning, and fluid instabilities. The research aims to provide insights into nuclear physics, superfluidity, viscosity, and lattice structure. The study also discusses the possibility of detecting gravitational waves from pulsar glitches.
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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 verywell. • 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 n Dn (dn/dt)1 (dn/dt)2≠(dn/dt)1 t ~days time ~min
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)] • = 0.55 yr-1 Melatos, Peralta & Wyithe, 672, ApJ (2008) a = 1.1
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.
avalanhce size avalanhce size • Power laws in the glitch size and duration support scale invariance. • Poissonian waiting times supports statistical independence of glitches. time Some simulated avalanches Warszawski & Melatos, MNRAS (2008) Relies on large scale inhomogeneities
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 2 power law F0 all unpin Computational output
Model fits - Poissonian • F0 gives best fit in most cases. • Broad pinning distribution agrees with theory: 2MeV 1MeV • GW detection will make more precise
Recent work • Undamped quasiradial fluctuations • Glitch transfers energy to crust radiated as GWs. • Depends on glitch size AND change in • Crab pulsar h10-26 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)]
Stewartson Ekman Relaxation signal Van Eysden & Melatos (2008) • 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
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 Re = 3x102 • Re ~1010→ Kolmogorov turbulence • T0ik-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)
potential rotation chemical potential interaction term coupling (g > 0) dissipative term Gross-Pitaevskii equation ( 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
Feedback Tracking the superfluid • Circulation counts number of vortices • Angular momentum Lz accounts for vortex positions
Gravitational waves • Current quadrupole moment depends on velocity field • Wave strain depends on time-varying current quadrupole
strain time Glitch signal
Depends on vortex velocity Looking forward • Wave strain scales as • 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)]
