double feature:

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