Double feature:

1
Double feature
Yuri Levin, Leiden
1. The theory of fast oscillations during
magnetar giant flares 2. Measuring
gravitational waves using Pulsar Timing
Arrays
2
Part 1. NEUTRON STARS
B
crust
core n (superfluid) p (supercond.) e
20 km

• spin0.01-716 Hz

km
3
Physics preliminaries magnetic fields in
non-resistive media
Field lines 1. Are frozen into the medium 2.
Possess tension and pressure B
B
2
Alfven waves!
4
15
Magnetars ultra-magnetic neutron stars. B10
Gauss
Duncan Thompson 92 Usov 94 Thompson et al 94-06
crust

• Slowly rotating, with
• X-ray emission powered by
• magnetic energy
• Some magnetars also release flares

3 Giant flares 1979, 1998, 2004 Mazetz,
Hurley, etc.
5
Discovery of Quasi-Periodic Oscillations (Israel
et al 2005)
6
Strohmayer Watts 06
7
Israel et al 05 Barat et al 83 Watts Strohmayer
06 Strohmayer Watts 06
Oscilations at several frequencies 18, 30, 40,
90, 625, etc., Hz.
Interpretation 0 torsional vibration of the
neutron star crust
(starquake!)
Duncan, et al 98-06

• 18 Hz does not work
• QPOs highly intermittent
• Physics does not work

Three caveats
Key issue high B-field
8
Torsional vibration of the whole star
L. 06, L. 07, MNRAS also Glampedakis et 06

• Magnetically coupling to the core on 0.01-0.1
  second timescale.
• Pure crustal modes dont
  exist.
• Alfven continuum in the core.

Initial crustal modes decay in ltsecond What
happens then?
crust

• Normal-mode analysis
• global torsional mode most likely
• doesnt exist

9
Crust-core dynamics

• Magnetically coupling to the core on 0.01-0.1
  second timescale.
• Pure crustal modes dont
  exist.
• Alfven continuum in the core.

Initial crustal displacements decay in
ltsecond What happens then?
crust

• Normal-mode analysis
• global torsional mode likely dont
• exist
• Resonant absorption, cf. solar
• corona (Ionson 78, Hollweg 87,
• Steinolfson 85, etc..)

Resonant Layer
10
Initial-value problem toy model, zero friction
1 kg
10000 small oscillators, 0.01g
11
Zoom in on the residual
12
Zoom in on the residual
Power spectrum 2 Oscillations !!! But edges of
the continuum
Energies of small oscillators
13
Phases of small oscillators
Special Point!
14
Initial-value problem inflected spectrum
1 kg
10000 small oscillators, 0.01g
15
The real magnetar (simulated)!
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The real magnetar (simulated)!
17
Dynamical spectrum (simulations)
18
Dynamical spectrum (simulations)
19
Dynamical spectrum
theory
20
Asteroseismology?

• Low-frequency QPOs (18Hz) probe Alfven
• speed in the core.
• For B10 G, need to decouple 90 of the
• core material from the wave.
• Neutron superfluidity!

15
21
Conclusions main features of Quasi-Periodic
Oscillations

• Steady QPOs---special points of the Alfven
  continuum,
• Intermittent QPOs everywhere, but enhanced near
• crustal frequencies.
• Qualitative agreement between theory and
  observations
• Powerful probe of the Alfven speed in the
  interior of
• magnetars
• 5. Open issue magnetosphere

22
Part 2

• Measuring gravitational waves using
• Pulsar Timing Arrays.

23
Galaxy formation
White Rees 78
Universe becomes matter-dominated at z10000.
Gravitational instability becomes effective.
Small halos collapse first, small galaxies form
first
Smaler galaxies merge to form large spirals and
ellipticals.
24
Merging Galaxies
Merging SBHs?
Komossa et al 02 (Chandra)
Snijders van der Werf 06
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Evidence for mergers?
But
simulations
Mass deficit at the center
do not agree with observations
Milosavljevic Merritt 01 Graham 04
McDermitt et al. 06 (Sauron)
26
Q What to do? A Measure gravitational
waves!
27
LISA the ESA/NASA space mission to detect
gravitational waves. Binary black hole
mergers Out to z3 is one of the main targets
Launch date 1915..
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Detection Amplitude for SBH mergers at
z1. Unprecedented test of GR as dynamical
theory of spacetime!
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Measuring gravitational-wave background with a
Pulsar Timing Array.
Earth
millisecond pulsar
gravitational wave
frequency shift
arrival on Earth
departure from pulsar
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Millisecond pulsars

• Excellent clocks. Current precision 1
  microsecond,
• projected precision 100-200 ns.
• Intrinsic noise unknown and uncorrelated.
• GW noise uknown but correlated. Thus need to
• look for correlations between different pulsars.
• Many systematic effects with correlations local
• noisy clocks, ephemeris errors, etc. However,
• GW signature is unique!

2 Pulsar Timing Arrays Australia (20 pulsars)
Manchester
Europe (20)
Kramer

Stappers
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John Rowe animation/ATNF, CSIRO
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Contributions to timing residuals

• Gravitational waves!!
• Pulsar timing noises
• Quadratic spindowns
• Variations in the ISM
• Clock noises
• Earth ephemeris errors
• Changes of equipment
• Human errors

Our work so far
Optimistic esimate 5000 timing residuals from
all pulsars.
33
Gravitational waves (theory)
Phinney 01 Jaffe Backer 03 Wyithe Loeb 03
-p
S(f)A f
34
Current algorithm
Jenet et al. 05

• ltdt dt gt const6x log(x)-x2,
• 
  xcos(ab)

a
b
GW
pulsar b
pulsar a
Look for correlation of this form!
But statistical significance? Parameter
extraction?
35
LeidenCITA effort
van Haasteren, L., McDonald (CITA), Lu (CITA),
soon tbs
Gravitational-Wave signal extraction

• Bayesian approach
• Parametrize simultaneously GW background and
  pulsar
• noises (42 parameters)
• Parametrize quadratic spindowns (60 parameters)
• derive P(parametersdata), where data5000 timing
• 
  residuals
• marginalize numerically over pulsar noises and
• analytically over the spindowns

36
Advantages

• No loss of information-optimal detection
• Measures the amplitude AND the slope of GWB
• Natural treatment of known systematic errors
• Allows unevenly sampled data

37
Markov Chain simulation
Pulsar noises 100 ns.
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Conclusions part 2

• SBH binaries predicted but not yet observed
• Gravitational-wave detection by LISA and
• Pulsar-Timing Arrays is likely within 1-1.5
  decade.

40
Type-I x-ray bursts.
Spitkovsky, L., Ushomirsky 02 Spitkovsky L., in
prep
Amsterdam, SRON, NASA, MIT,..
accretion
X-ray flux
HHe
He
THERMONUCLEAR BOMB !
ashes
time
ashes
1 sec
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Analogy to hurricanes
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FLAMES
deflagration
fuel
front
heat
heat propagation
speed of the flame
rise time of the burst
reaction speed
Heat propagation
1. microscopic conduction too slow, 10 m/sec
Niemayer 2000
2. turbulence from buoyant convection (Fryxell,
Woosley)

• highly uncertain only upper limit works
• probably irrelevant!

44
HEAT PROPAGATION

• Kelvin-Helmholtz stable!!
• Baroclinic unstable but weak.
• Heat conduction a la Niemeier,
• but across a huge interface!

30m
hot
cold
3m
3 km
Rossby radius
45
ROSSBY RADIUS
Scale where potential kinetic energy
Rossby radius aR is a typical size of synoptic
motions on Earth 1000 km, on NS 1km
46
TWO-LAYER SHALLOW-WATER MODEL
?2
h2(x)
Q(T)
h1(x)
?1
Heat Q(T)
Temperature -- height
Two sets of coupled shallow-water equations in 1
1/2 D. Include mass and momentum transport across
layers and interlayer friction
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Burst QPOs from ocean Rossby waves?
Heyl 2004, Lee 2005, Piro Bildsten
2005, Narayan Cooper 2007

• QPO coherence,
• QPOs in the tail
• - Typically, waves go too fast.
• - Not clear how to excite them.
• - What happens during the burst rise
• (i.e., spreading hot spot)?

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Conclusions

• Good prospects to understand magnetar QPOs and
• to learn about neutron-star interior
• 2. Good prospects to understand type-I burst
  deflagration,
• but QPO behaviour, etc., very difficult to
  understand

50
Precession of radio pulsars.
Theory radio pulsars cannot precess slowly
Shaham 1977
pinned superfluid vortices
Fast precession 1/100 of NS spin
Observations
Pulsar PSR B1828
Stairs et al 2000
Spin period 0.5
seconds Precession period 500 days
Shahams nightmare!!
No strong pinning in the crust?
Link Cutler 03 Jones 98
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What about the core?
L. DAngelo 04
Earth Chandler wobble
Crust precesses Core doesnt
Neutron star
B enforces co-precession between the crust and
core plasma
n-superfluid does not participate in precession
MUTUAL FRICTION damps precession!

52
Mutual friction in neutron stars
B
Magnetization of n-superfluid vortex
n, p supercurrent entrainment of p in n
Superconductivity
Type I Precession damped in 10-100 yr
Type II Precession excluded!
B
n
Sauls Alpar 88 L. DAngelo 04
p
e
Probe of strong n-p forces!
Link 03-important result
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Spitkovsky
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Formation of a neutron star Burrows, Livne,
et al. 2006