Transcript GPE model of pulsar glitches - Pennsylvania State University

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
SF neutrons,
SC protons &
electrons
1 km
outer core
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


(d/dt)1
(d/dt)2≠(d/dt)1
t ~ days
~ min
time
Timing residual
How do we see a glitch?
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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.
Melatos, Peralta & Wyithe, 672, ApJ (2008)
a = 1.1
 = 0.55 yr-1
• Glitch activity parameter: mean fractional change in period per year
– Accounts for number and size of glitches [McKenna & Lyne (1990)]
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
QuickTime™ and a
decompressor
are needed to see this picture.
• 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)
•
Quic kTime™ and a
Post-glitch relaxation due to vortex creep
decompressor
are needed to see this pic ture.
Alpar, Anderson, Pines, Shaham (1984-)
•
Vortex avalanches
– Analogous to superconducting flux vortices
Warszawski & Melatos (2008)
•
Vortex motion in the presence of pinning
Link (2009)
QuickTime™ and a
decompressor
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Fluid instability
• Two-stream intsability analagous to Kelvin-Helmholtz
– Activated when relative flow reaches critical value
Andersson, Comer & Prix (2001)
QuickTime™ and a
decompressor
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• R-mode instability as trigger for vortex unpinning
– Sets in when rotational lag reaches critical levels
Glampedakis & Andersson (2009)
The unpinning paradigm
1.
Nuclear lattice + neutron superfluid
(SF).
2.
Rotation of crust  vortices form  SF
rotates.
3.
Pinned vortices co-rotate with crust.
4.
Differential rotation between crust and
SF  Magnus force.
5.
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
FM =
+
avalanhce size
Some simulated avalanches
avalanhce size
Warszawski & Melatos, MNRAS (2008)
Relies on large scale inhomogeneities
• Power laws in the glitch size and duration support scale invariance.
• Poissonian waiting times supports statistical independence of glitches.
time
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
2
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
F0
power law
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all unpin
Model fits - Poissonian
•F0   gives best fit in
most cases.
•Broad pinning
distribution agrees
with theory:  2MeV 
1MeV
•GW detection will
make more precise
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Gravitational waves from
Quic kTime™ and a
dec ompr es sor
are needed to s ee this pic ture.
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
Van Eysden & Melatos (2008)
Stewartson
Ekman
sphere ≠ cylinder
• 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
DECAY TIME
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
AMPLITUDE
RATIO
 AND 2
Turbulent signal
Re = 3x102
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decompressor
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Re = 3x104
HVBK two-fluid
•
Re ~1010 → Kolmogorov turbulence
•
•
T0i  k-5/3, i.e. KE in large eddies
GW ≈ non-axisymmetric modes
•
•
BUT,
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
 small eddies faster
Peralta et al. (2005), (2006)
Gross-Pitaevskii equation
potential
chemical potential
dissipative term
rotation
interaction term
coupling (g > 0)
 ( 0.1)
suggests presence of normal fluid, aids convergence
V
g ( 1)
 ( 1)
imposes pinning grid
tunes repulsive interaction
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
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Close-up of a glitch
strain
Glitch signal
time
Looking forward
• Wave strain scales as
– Estimate strain from ‘real’ glitch:
• First source?
Depends on
vortex velocity
– 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)]