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Double feature:. Yuri Levin, Leiden. 1. The theory of fast oscillations during magnetar giant flares 2 . Measuring gravitational waves using Pulsar Timing Arrays. Part 1. NEUTRON STARS:. B. crust. core : n (superfluid) p (supercond.) e. 20 km. spin=0.01-716 Hz. km. - PowerPoint PPT Presentation
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Double feature:Yuri Levin, Leiden
1. The theory of fast oscillations during magnetar giant flares
2. Measuring gravitational waves using Pulsar Timing Arrays
Part 1. NEUTRON STARS:
core:n (superfluid)p (supercond.)e
crust
20 km
• • • spin=0.01-716 Hz•
1.4M M 10R km
8 1510 10 GB
B
Physics preliminaries: magnetic fields in non-resistive media
B
Field lines:
1. Are frozen into the medium
2. Possess tension and pressure
~B2
Alfven waves!
Magnetars: ultra-magnetic neutron stars. B~1015Gauss
Duncan & Thompson 92Usov 94Thompson 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.
Discovery of Quasi-Periodic Oscillations (Israel et al 2005)
Strohmayer & Watts 06
Oscilations at several frequencies: 18, 30, 40, 90, 625, etc., Hz.
Israel et al 05Barat et al 83Watts & Strohmayer 06Strohmayer & Watts 06
Interpretation 0: torsional vibration of the neutron star crust (starquake!)
Three caveats:
Duncan, et al 98-06
• 18 Hz does not work• QPOs highly intermittent• Physics does not work
Key issue: high B-field
L. 06, L. 07, MNRASalso Glampedakis et 06
1. Magnetically coupling to the core on 0.01-0.1 second timescale. Pure crustal modes don’t exist.
2. Alfven continuum in the core. Initial crustal modes decay in <secondWhat happens then?
Torsional vibration of the whole star
crust
• Normal-mode analysis: global torsional mode most likely doesn’t exist
1. Magnetically coupling to the core on 0.01-0.1 second timescale. Pure crustal modes don’t exist.
2. Alfven continuum in the core. Initial crustal displacements decay in <secondWhat happens then?
Crust-core dynamics:
• Normal-mode analysis: global torsional mode likely don’t exist
• Resonant absorption, cf. solar corona (Ionson 78, Hollweg 87, Steinolfson 85, etc…..)
crust
Resonant Layer
Initial-value problem: toy model, zero friction
10000 smalloscillators, 0.01g
1 kg
Zoom in on the residual:
Zoom in on the residual:
Energies of small oscillators
Power spectrum:2 Oscillations !!!But: edges of the continuum
Phases of small oscillators:
SpecialPoint!
Initial-value problem: inflected spectrum
10000 smalloscillators, 0.01g
1 kg
The real magnetar (simulated)!
The real magnetar (simulated)!
Dynamical spectrum (simulations)
Dynamical spectrum (simulations)
Dynamical spectrum
theory
Asteroseismology?
• Low-frequency QPOs (18Hz) probe Alfven speed in the core.
• For B=10 G, need to decouple 90% of the core material from the wave.
Neutron superfluidity!
15
Conclusions: main features of Quasi-Periodic Oscillations
1. Steady QPOs---special points of the Alfven continuum, 2. Intermittent QPOs everywhere, but enhanced near crustal frequencies.
3. Qualitative agreement between theory and observations
4. Powerful probe of the Alfven speed in the interior of magnetars
5. Open issue: magnetosphere
Part 2
Measuring gravitational waves using
Pulsar Timing Arrays.
Galaxy formation:
Universe becomes matter-dominatedat z=10000. Gravitational instabilitybecomes effective.
Small halos collapse first,small galaxies form first
Smaler galaxies merge to form largespirals and ellipticals.
White & Rees 78
Snijders & van der Werf 06 Komossa et al 02 (Chandra)
Merging Galaxies Merging SBHs?
Evidence for mergers?
Milosavljevic & Merritt 01Graham 04
Mass deficit at the center
But:simulations
do not agree with observations:
McDermitt et al. 06 (Sauron)
Q: What to do?
A: Measure gravitational waves!
LISA: the ESA/NASA space mission to detect gravitational waves. Binary black hole mergersOut to z=3 is one of the main targets
Launch date1915+..
Detection Amplitude for SBH mergers at z=1.Unprecedented test of GR as dynamical theoryof spacetime!
Measuring gravitational-wave backgroundwith a Pulsar Timing Array.
millisecondpulsar
Earth
arrivalon Earth
departurefrom pulsar
gravitationalwave
frequencyshift
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: localnoisy clocks, ephemeris errors, etc. However,GW signature is unique!
2 Pulsar Timing Arrays: Australia (20 pulsars) Manchester Europe (~20) Kramer+ Stappers
John Rowe animation/ATNF, CSIRO
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•
Optimistic esimate: ~5000 timing residuals from all pulsars.
Our work so far
Gravitational waves (theory): Phinney 01Jaffe & Backer 03Wyithe & Loeb 03
S(f)=A f-p
Current algorithm
• <δt δt > = const·[6x log(x)-x+2],
x=cos(ab)
Jenet et al. 05
a b
pulsar a pulsar b
GW
Look for correlation of this form!
But: statistical significance? Parameter extraction?
Leiden+CITA effort:
Gravitational-Wave signal extractionvan Haasteren, L.,McDonald (CITA),Lu (CITA), soon tbs
Bayesian approach:
•Parametrize simultaneously GW background and pulsar noises (42 parameters)
•Parametrize quadratic spindowns (60 parameters)
•derive P(parameters|data), where data=5000 timing residuals•marginalize numerically over pulsar noises and analytically over the spindowns
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
Markov Chain simulation:
Pulsar noises 100 ns.
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.
accretion
ashes
H+He
ashes
X-rayflux
time1 sec
THERMONUCLEARBOMB !
nucl coold d
d dT T
He
Type-I x-ray bursts. Spitkovsky, L., Ushomirsky 02Spitkovsky & L., in prepAmsterdam, SRON, NASA, MIT,..
Analogy to hurricanesAnalogy to hurricanes
deflagrationfront
heat
fuel
FLAMES
heat propagation
reaction speedspeed ofthe flame
rise time ofthe burst
Heat propagation:
1. microscopic conduction: too slow, 10 m/sec
2. turbulence from buoyant convection (Fryxell, Woosley):
•highly uncertain; only upper limit works•probably irrelevant!
Niemayer 2000
HEAT PROPAGATION
hotcold
30m
3m
3 km
Rossby radius
•Kelvin-Helmholtz stable!!•Baroclinic: unstable but weak.•Heat conduction a la Niemeier, but across a huge interface!
ROSSBY RADIUSROSSBY RADIUS
Scale where potential = kinetic energy
Rossby radius
aR is a typical size of synoptic motions on Earth: ~1000 km, on NS ~ 1km
fgHaR /
TWOTWO--LAYERLAYER SHALLOW-WATER MODELSHALLOW-WATER MODEL
2 h2(x)
1h1(x)
Q(T)
11
2 Heat Q(T): 21 Temperature -- height: 2hc
gT
p
Two sets of coupled shallow-water equations in 1 1/2 D. Include mass and momentum transport across layers and interlayer friction
Burst QPOs from ocean Rossby waves?
+ 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)?
Heyl 2004, Lee 2005, Piro & Bildsten 2005,Narayan & Cooper 2007
Conclusions:
1. 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
Precession of radio pulsars.
Theory: radio pulsars cannot precess slowly
pinnedsuperfluidvortices
Fast precession:1/100 of NS spin
Observations:
Shaham 1977
Spin period 0.5 seconds
Precession period 500 days
Pulsar PSR B1828
Shaham’s nightmare!!
Stairs et al 2000
No strong pinning in the crust? Link & Cutler 03Jones 98
What about the core?
Earth: Chandler wobble
Crust precesses
Core doesn’t
L. & D’Angelo 04
Neutron star:
B enforces co-precessionbetween the crust and core plasma
n-superfluid does not participate in precession: MUTUAL FRICTION damps precession!
Mutual friction in neutron stars
n, p supercurrent: entrainment of p in n
Magnetizationof n-superfluidvortex
B
Superconductivity:
Type II:Precession excluded!
Link 03;-important result
Type I:Precession damped in 10-100 yr
pn B
Sauls & Alpar 88L. & D’Angelo 04
Probe of strong n-p forces!
e
Spitkovsky
Formation of a neutron star: Burrows, Livne, et al. 2006