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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
• M  1.4M
• R  10 km
• spin=0.01-716 Hz
• B  108  1015 G
20 km
Physics preliminaries: magnetic fields in non-resistive media
Field lines:
1. Are frozen into the medium
B
2. Possess tension and pressure
~B
2
Alfven waves!
Magnetars: ultra-magnetic neutron stars.
B~10 15
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.
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 05
Barat et al 83
Watts & Strohmayer 06
Strohmayer & Watts 06
Interpretation 0: torsional vibration of the neutron
star crust (starquake!) Duncan, et al 98-06
Three caveats:
• 18 Hz does not work
• QPOs highly intermittent
• Physics does not work
Key issue: high B-field
Torsional vibration of the whole star
L. 06, L. 07, MNRAS
also 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 <second
What happens then?
crust
• Normal-mode analysis:
global torsional mode most likely
doesn’t exist
Crust-core dynamics:
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 <second
What happens then?
crust
• Normal-mode analysis:
global torsional mode likely don’t
exist
• Resonant absorption, cf. solar
corona (Ionson 78, Hollweg 87,
Steinolfson 85, etc…..)
Resonant Layer
Initial-value problem: toy model, zero friction
1 kg
10000 small
oscillators, 0.01g
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:
Special
Point!
Initial-value problem: inflected spectrum
1 kg
10000 small
oscillators, 0.01g
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.
15
• For B=10 G, need to decouple 90% of the
core material from the wave.
Neutron superfluidity!
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:
White & Rees 78
Universe becomes matter-dominated
at z=10000. Gravitational instability
becomes effective.
Small halos collapse first,
small galaxies form first
Smaler galaxies merge to form large
spirals and ellipticals.
Merging Galaxies
Snijders & van der Werf 06
Merging SBHs?
Komossa et al 02 (Chandra)
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)
Q: What to do?
A:
Measure gravitational waves!
LISA: the ESA/NASA space mission to detect
gravitational waves. Binary black hole mergers
Out to z=3 is one of the main targets
Launch date
1915+..
Detection Amplitude for SBH mergers at z=1.
Unprecedented test of GR as dynamical theory
of spacetime!
Measuring gravitational-wave background
with a Pulsar Timing Array.
Earth
millisecond
pulsar
gravitational
wave
frequency
shift
arrival
on Earth
departure
from pulsar
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)
Europe (~20)
Manchester
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
•
Our work so far
Optimistic esimate: ~5000 timing residuals from all pulsars.
Gravitational waves (theory):
Phinney 01
Jaffe & Backer 03
Wyithe & Loeb 03
S(f)=A f
-p
Current algorithm
Jenet et al. 05
• <δt a δt b>GW = const·[6x log(x)-x+2],
pulsar a
pulsar b
x=cos(ab)
Look for correlation of this form!
But: statistical significance? Parameter extraction?
Leiden+CITA effort:
Gravitational-Wave signal extraction
van 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.
Type-I x-ray bursts.
Spitkovsky, L., Ushomirsky 02
Spitkovsky & L., in prep
Amsterdam, SRON, NASA, MIT,..
accretion
H+He
He
ashes
ashes
d nucl d cool

dT
dT
X-ray
flux
THERMONUCLEAR
BOMB !
1 sec
time
Analogy to hurricanes
FLAMES
deflagration
front
fuel
heat
heat propagation
reaction speed
speed of
the flame
rise time of
the burst
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!
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
ROSSBY RADIUS
Scale where potential = kinetic energy
Rossby radius aR 
gH / f
aR is a typical size of synoptic
motions on Earth: ~1000 km,
on NS ~ 1km
TWO-LAYER SHALLOW-WATER MODEL


2
1

2
1
1


Heat Q(T): 1  2
Q(T)
h2(x)
h1(x)
Temperature -- height: T 
g
h2
cp
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
Heyl 2004, Lee 2005,
Piro & Bildsten 2005,
Narayan & Cooper 2007
- Typically, waves go too fast.
- Not clear how to excite them.
- What happens during the burst rise
(i.e., spreading hot spot)?
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
Fast precession:
1/100 of NS spin
Observations:
Shaham 1977
pinned
superfluid
vortices
Pulsar PSR B1828
Stairs et al 2000
Spin period
0.5 seconds
Shaham’s nightmare!!
Precession period
500 days
No strong pinning in the crust?
Link & Cutler 03
Jones 98
What about the core?
Earth: Chandler wobble
Crust precesses
Core doesn’t
Neutron star:
B enforces co-precession
between the crust and
core plasma
n-superfluid does not participate in precession:
MUTUAL FRICTION damps precession!
L. & D’Angelo 04
Mutual friction in neutron stars
B
Magnetization
of n-superfluid
vortex
n, p supercurrent:
entrainment of
p in n
Superconductivity:
Type II:
Precession excluded!
n
Type I:
Precession damped in 10-100 yr
B
Sauls & Alpar 88
L. & D’Angelo 04
p
e
Link 03;-important result
Probe of strong n-p forces!
Spitkovsky
Formation of a neutron star: Burrows, Livne, et al. 2006