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) 20 km p (supercond.) e = 1.4 • M M � R = 10 • km • spin=0.01-716 Hz B = − • 8 15 10 10 G
Physics preliminaries: magnetic fields in non-resistive media Field lines : 1. Are frozen into the medium B 2. Possess tension and pressure 2 ~B 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
Israel et al 05 Oscilations at several frequencies: Barat et al 83 18, 30, 40, 90, 625, etc., Hz. Watts & Strohmayer 06 Strohmayer & Watts 06 Interpretation 0: torsional vibration of the neutron star crust (starquake!) Duncan, et al 98-06 • 18 Hz does not work Three caveats: • 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: Power spectrum: 2 Oscillations !!! Energies of small But: edges of the continuum oscillators
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 Merging SBHs? Komossa et al 02 (Chandra) Snijders & van der Werf 06
Evidence for mergers? But: simulations Mass deficit at the center do not agree with observations: Milosavljevic & Merritt 01 McDermitt et al. 06 (Sauron) Graham 04
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 departure on Earth 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) Manchester Europe (~20) Kramer+ Stappers
John Rowe animation/ATNF, CSIRO
Contributions to timing residuals: •Gravitational waves!! Our work so far •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.
Gravitational waves (theory): Phinney 01 Jaffe & Backer 03 Wyithe & Loeb 03 -p S(f)=A f
Current algorithm Jenet et al. 05 • < δ t δ t > = const ·[6x log(x)-x+2], a b GW pulsar b pulsar a x=cos(ab) Look for correlation of this form! But: statistical significance? Parameter extraction?
Leiden+CITA effort: van Haasteren, L., Gravitational-Wave signal extraction 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 X-ray flux ε ε d d ≥ nucl cool H+He d d T T He THERMONUCLEAR BOMB ! ashes time ashes 1 sec
Analogy to hurricanes Analogy to hurricanes
FLAMES deflagration fuel front heat heat propagation speed of rise time of reaction speed the flame 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 ROSSBY RADIUS Scale where potential = kinetic energy = / Rossby radius a R gH f a R is a typical size of synoptic motions on Earth: ~1000 km, on NS ~ 1km
TWO - LAYER SHALLOW SHALLOW- -WATER MODEL WATER MODEL TWO - LAYER ⊗ ρ 2 � h 2 (x) Q(T) Ω ρ 1 h 1 (x) ⊗ ρ 2 < g ρ → ρ ε = ρ = 1 Heat Q(T): T h Temperature -- height: 1 2 2 c 1 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? 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)?
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 Shaham 1977 Fast precession: pinned 1/100 of NS spin superfluid vortices Observations: 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? L. & D’Angelo 04 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!
Mutual friction in neutron stars B Magnetization n, p supercurrent: of n-superfluid entrainment of vortex p in n Superconductivity: Type I: Type II: Precession damped in 10-100 yr Precession excluded! n B Sauls & Alpar 88 p L. & D’Angelo 04 e Probe of strong n-p forces! Link 03;-important result
Spitkovsky
Formation of a neutron star: Burrows, Livne, et al. 2006
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