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Quasi-Periodic Oscillations in Soft Gamma Repeater giant flares
Mark Bennett
University of Melbourne
with thanks to Chris Thompson
Orange Pulsar Meeting 27 September 2010


Outline
1
Soft Gamma Repeater bursts and giant flares Quasi-periodic Oscillations observed

2

Current modelling of QPOs - strengths and weaknesses

3

Non-linear model with feedback from faults in crust Preliminary results and future directions


Magnetars
Soft Gamma Repeaters and Anomalous X-ray Pulsars Period 2 - 12 s Magnetic field 1014 - 1015 G SGRs: sporadic bursts AXPs: persistent X-ray emission 7 (+2?) SGRs and 9 (+3?) AXPs
(McGill catalogue)


SGR Bursts
Peak luminosity reaches 1041 erg/s (Eddington ~ 1038 erg/s) Power law burst energies, log normal waiting times (e.g. earthquakes, solar flares, avalanches)

time (seconds)
(Woods & Thompson 2006)

bursts per 10 day interval

103 counts/second

year
(Hurley 2010)


Giant Flares
Initial hard spike ~ 0.1 s Pulsating tail 100-300 s Total Energy 44 - 1046 erg 10
March 1979 SGR 0526-66
counts/second k-counts/second counts/second

August 1998 SGR 1900+14

Dec 2004 SGR 1806-20

time (seconds)
(Woods & Thompson 2006, Strohmayer & Watts 2006)


Quasi-Periodic Oscillations
First detected in Dec 2004 giant flare of SGR 1806-20 QPOs also found in 1998 giant flare, three normal bursts of SGR 1806-20

(Israel et al 2005)


Observed QPOs

(Strohmayer & Watts 2006)


Theoretical Models
QPO frequencies identified with torsional shear modes of crust Coupled crust-core oscillations due to large magnetic fields:
- Cerda-Duran et al 2009 - Colaiuda et al 2009
SGR 1806-20 QPO (Hz) 18 26 30 28 53 92 (84, 103) 150 155 625 (648) 1840 84 n = 0, l = 2 n = 0, l = 4 n = 0, l = 6 n = 0, l = 10 n = 0, l = 11 n=1 n=3
(Watts & Strohmayer 2007) (El-Mezeini & Ibrahim 2010)

SGR 1900+14 Shear Mode QPO (Hz)

Core continuum of MHD modes:
- Levin 2007, van Hoven & Levin 2010


Unresolved Issues
Modelling QPOs as shear modes does not explain transient properties observed
Time Evolution of 92 Hz QPO in SGR 1806-20

Frequency drifting?
frequency (Hz)

Phase dependence? Localisation in time?

consecutive pulse profiles
(Strohmayer & Watts 2006)


Feedback Model
Taking inspiration from earthquake physics: Starquake creates fault in crust


Feedback Model
Taking inspiration from earthquake physics: Starquake creates fault in crust Crust slides along fault, sends out elastic shear waves


Feedback Model
Taking inspiration from earthquake physics: Starquake creates fault in crust Crust slides along fault, sends out elastic shear waves Elastic waves trigger further fault rupture, more shear waves Crust oscillation energy increases due to feedback, damped on longer timescale


Numerical Simulation
2 2 - cs 2 = - + (,t) 2 t t t
wave equation dampening fault BC

Boundary condition (, t) controls crust slipping at fault line Test strain at fault turn crust slipping on/off Above threshold strain, crust slides with speed cslip No crust slipping and away from fault ( f): (, t) = 0

f



QPOs?



log power

log power


log power log power

log power

log power


Summary
Quasi-periodic oscillations observed in SGR giant flare tails Non-linear model: shear waves from fault with feedback Our results replicate some of the transient properties observed in QPOs Future: multiple faults, 2D surface model