Double feature: Yuri Levin, Leiden 1. The theory of fast - - PowerPoint PPT Presentation

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
• 1.4

M M =

• 10

R =

km

8 15

10 10 G B = −

B

Physics preliminaries: magnetic fields in non-resistive media

B

Field lines:

• 1. Are frozen into the medium
• 2. Possess tension and pressure

~B

2

Alfven waves!

Magnetars: ultra-magnetic neutron stars. B~1015

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!) 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, 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?

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 <second What 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 small

• scillators, 0.01g

1 kg

Zoom in on the residual:

Zoom in on the residual:

Energies of small

• scillators

Power spectrum: 2 Oscillations !!! But: edges of the continuum

Phases of small oscillators: Special Point!

Initial-value problem: inflected spectrum

10000 small

• scillators, 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-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.

White & Rees 78

Snijders & van der Werf 06 Komossa et al 02 (Chandra)

Merging Galaxies Merging SBHs?

Evidence for mergers?

Milosavljevic & Merritt 01 Graham 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 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

• f spacetime!

Measuring gravitational-wave background with a Pulsar Timing Array.

millisecond pulsar Earth arrival

• n Earth

departure from pulsar gravitational wave frequency shift

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

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 01 Jaffe & Backer 03 Wyithe & 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 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.

accretion ashes

H+He

ashes X-ray flux time

1 sec

THERMONUCLEAR BOMB !

nucl cool

d d d d T T ε ε ≥

He Type-I x-ray bursts.

Spitkovsky, L., Ushomirsky 02 Spitkovsky & L., in prep

Amsterdam, SRON, NASA, MIT,..

Analogy to hurricanes Analogy to hurricanes

deflagration front heat fuel

FLAMES

heat propagation reaction speed speed of the flame rise time of the 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

hot

cold 30m 3m 3 km Rossby radius

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

but across a huge interface!

ROSSBY RADIUS ROSSBY RADIUS

Scale where potential = kinetic energy

Rossby radius aR is a typical size of synoptic motions on Earth: ~1000 km,

• n NS ~ 1km

f gH aR / =

TWO TWO-

• LAYER

LAYER SHALLOW SHALLOW-

• WATER MODEL

WATER MODEL

ρ2 h2(x) ρ1 h1(x) Q(T)

Ω

• ⊗

⊗

1

1 2 <

= ρ ρ ε

Heat Q(T):

2 1

ρ ρ →

Temperature -- height:

2

h c g T

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

pinned superfluid vortices 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 03 Jones 98

What about the core?

Earth: Chandler wobble

Crust precesses Core doesn’t

• L. & D’Angelo 04

Neutron star:

B enforces co-precession between 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 Magnetization

• f n-superfluid

vortex

B

Superconductivity:

Type II: Precession excluded!

Link 03;-important result

Type I: Precession damped in 10-100 yr

p n B Sauls & Alpar 88

• L. & D’Angelo 04

Probe of strong n-p forces!

e

Spitkovsky

Formation of a neutron star: Burrows, Livne, et al. 2006