1. Fast X-ray Oscillations During Magnetar Flares
Three events to date:
March 5th 1979: SGR
August 27th 1998: SGR
December 27th 2004: SGR
Powered by global magnetic instability (reconfiguration), crust fracturing.
Hurley et al. (1998): Ulysses
Short, hard, luminous initial pulse.
Softer X-ray tail persists for minutes, pulsed at neutron star spin period.
Emission from a magnetically confined plasma.
1015 G magnetic fields implied (Thompson & Duncan 95)

2. NASA’s Rossi X-ray Timing Explorer (RXTE)
Launched in December, 1995, in orbit for 11.5 yr!
12th Observing cycle currently underway
RXTE’s Unique Strengths
Large collecting area
High time resolution
High telemetry capacity
Flexible observing

3. SGR 1806-20, 2004 December Giant Flare
Israel et al. (2005)

4. Oscillations in the 2004 December SGR 1806-20 Flare
RXTE recorded the intense flux through detector shielding.
Israel et al. (2005) reported a 92 Hz quasi-periodic oscillation (QPO) during a portion of the flare.
Oscillation is transient, or at least, the amplitude time dependent, associated with particular rotational phase, and increased un-pulsed emission.
Also evidence presented for lower frequency signals; 18 and  30 Hz.
Suggested torsional vibrations of the neutron star crust.
Israel et al. 2005

5. A Look Back at the SGR 1900+14, 1998 August Flare
SGR flare was observed in a manner very similar to the SGR 1806 flare.
Same time resolution, but non-optimal read-out time resulted in data gaps.
Initially searched each good data interval as a whole.
84 Hz QPO detected in 4th data interval searched. The first after the pulse structure had re-emerged.
Strohmayer & Watts (2005)

6. SGR : 84 Hz signal
84 Hz signal localized in time (rotational phase).
~20 % (rms) amplitude
Not centered on a pulse peak.
No other impulsive signals found, but what about weaker, persistent modulations?

7. SGR 1900+14: Other QPO Signals
Computed average power spectra centered on the rotational phase of the 84 Hz QPO.
A sequence of frequencies was detected: 28, 53.5, and 155 Hz!
Amplitudes in the 7 – 11% range.
Strong phase dependence: no signals detected from phases adjacent phase regions.
4 frequencies in SGR , a sequence of toroidal modes?

8. SGR 1806-20: RHESSI Confirmation of the Oscillations
Ramaty High Energy Solar Spectroscopic Imager (RHESSI) also detected the December, 2004 flare from SGR (Hurley et al. 2005).
Timing study by Watts & Strohmayer (2006) confirms 92 Hz oscillation, and evidence for higher frequency (626 Hz) modulation.

9. SGR 1806-20: RHESSI Confirmation of the Oscillations
Ramaty High Energy Solar Spectroscopic Imager (RHESSI) also detected the December, 2004 flare from SGR (Hurley et al. 2005).
Timing study by Watts & Strohmayer (2006) reveals evidence for much higher frequency oscillation in SGR flare, at 625 Hz.

10. The SGR 1806-20 Flare Re-visited
Data now public.
Phase averaging of power spectra confirms strong 92 Hz QPO.
Used Phase averaging analysis as in SGR hyperflare. Detect several new frequencies.

11. The SGR 1806-20 Flare Re-visited II
Strong detection of 625 Hz signal in latter portions of the flare.
Evidence for higher frequencies too!
Phase averaging reveals a 148 Hz QPO feature with high significance, but lower amplitude.

12. The SGR 1806-20 Flare Re-visited: Additional Oscillation Frequencies
SGR 1806 flare data now public.
Phase averaging of power spectra confirms strong 92 Hz QPO.
Phase averaging also shows 625 Hz oscillation with high significance. Detected 200 – 250 s after initial spike.

13. Neutron Star Crusts: A Brief History
Existence of a crust in a “normal” neutron star is not “controversial.” Ruderman (1968) suggested that radio pulsations from the first pulsars were due to torsional vibrations of crust.
To good approximation crust is a Coulomb solid, that solidifies at G = (Ze)2 / akT > 175.
Implies shear modulus, m, scales as n(Ze)2 / a
Ogata & Ichimaru (1990), Strohmayer et al. (1991) calculated m and explored oscillation mode implications.
Crust properties also linked with other observables, ie. Glitches and spin-down of pulsars, for example.
Piro (2005)

14. Shear Waves
Credit: Larry Braile, Purdue Univ.

15. SGR 1900+14: Toroidal (torsional) Oscillation Modes
A neutron star crust supports shear (toroidal) modes. Purely transverse motions. Modes studied theoretically (McDermott, Van Horn & Hansen (1988), Schumaker & Thorne (1983), Duncan (1998), Strohmayer et al. (1991), Samuelsson & Andersson (2007).
Angular dependence of modes described by spherical harmonic functions (l, m); and a radial eigenfunction (n), l tn
l gives the total number of nodal planes, and m the number of azimuthal planes.
An l=7, m=4 toroidal mode (Anna Watts)
( M1.4/R10)1/2
n(2t0) = 29.8 (R10) Hz
( M1.4/R102)
n(lt0) = n(2t0) [ l(l+1)/6 ]1/2
[1 + (B/Bm)2 ]-1/2

16. The SGR 1806-20 Flare: thickness of the crust
Strohmayer & Watts (2006)
For n = 0 modes, effective wavelength is R, for n > 0 it is DR, if Vs = constant, then fn=0 / fn>0 ~ DR/R.
Frequencies at 625 Hz and higher are likely n > 0 modes. Detection of n = 0 and n = 1 constrains crust thickness!

17. Torsional modes: shear modulus, magnetic fields, and mode periods
30 – 150 Hz frequencies are consistent with current estimates of n = 0 mode frequencies, with n > 0 modes above 600 Hz.
Piro (2005)
Piro (2005)
Speed of shear waves, Vs, set by the shear modulus. Vs ~ const (1,000 km/sec) not too bad an approximation.

18. Mode Excitation, the Earth Analogy
Crust fracture in general will excite global modes.
Many such modes observed in the days after the 2004 December Sumatra – Andaman great earthquake.
Spectrum of modes excited depends on fracture geometry, but non-trivial patterns possible.
Park et al. (2005)

19. Implications for Neutron Star Structure
Recently, Samuelsson & Andersson (2007) computed torsional modes in full GR (Cowling approximation).
Determine “allowed” regions in M - R plane that can match observe mode sequences in SGRs and
Caveat: No magnetic field corrections at all.

20. Implications for Neutron Star Structure
Frequencies (Hz)
29.0 : 2t0
92.7 : 6t0
150.3 : 10t0
625.5 : 1t1
: 2t1
1837 : 1t4
APR (A18+UIX+v)
Sahu, Basu & Datta (1993)
Determine “allowed” regions in M - R (B-field) plane that can match observed frequencies. Calculations in progress for a range of realistic EOS (Schwarz & Strohmayer 2008, in preparation).

21. Constraints on Quark Stars?
Watts & Reddy (2007)
Watts & Reddy (2007) investigated crusts on strange quark stars.
Computed torsional mode periods for thin nuclear crusts, and also quark nugget crusts. In general, such stars have thinner crusts.
Computed modes very difficult to reconcile with observed periods.

22. Time and Frequency Variations
90 Hz QPO shows rather complex temporal, phase, and frequency variations.
Amplitudes not constant in time (episodic).
Several factors could be at work; changes in field and particle distributions. Energy exchange with the core.
Strohmayer & Watts 2006

23. Persistence of QPOs

24. Theoretical Issues
Recognized that magnetic coupling of crust with core will likely be significant. Need “global” mode calculations (Levin 2006; Glampedakis et al. 2006; Sotani et al. 2006).
Levin (2006) initially argued that torsional modes will radiate Alfven waves into the core and damp too quickly to be observed (~ 1 sec).
Feedback, energy exchange between crust and core (Levin 2007).
Excitation of modes in the crust, analogies with earthquake fractures.
We see modulations in the X-ray flux, can these be produced by crust motions.
Signal amplification, perhaps modest amplitudes are visible (beaming?)

25. Crust - Core coupling
Levin argues that energy exchanges between the crust and a continuum of MHD modes in the core.
Solving initial value problem, finds QPOs excited at the so called “turning points” or edges of the MHD continuum. Lowest frequency modes (18, 25 Hz).
Also finds drifting QPOs, and amplification of these features near pure crust mode frequencies.
Levin (2007)

26. X-ray Modulation Mechanism
Timokhin, Eichler & Lyubarsky (astro-ph/ )
Suggest that modulation of the particle number density in the magnetosphere by torsional motion of the crust produces the oscillations.
Estimate that 1% amplitude of crust motion needed to explain the observed QPO amplitudes.
The angular dependence of the optical depth to resonant Compton scattering may account for phase dependence.

27. Conclusions, and many questions!
Detection of multiple frequencies with consistent l-scaling, and frequencies consistent with n>0 modes is highly suggestive of torsional oscillations, but need more data!
Two (three, March 5th?) out of three with similar phenomena, suggests fundamental property of magnetars.
Further understanding and detections could help constrain neutron star properties (EOS, and crust properties, magnetic fields). Unfortunately, giant flares are rare!
More theory needed: new mode calculations (with magnetic fields, etc.)
How are modes excited and damped? How do the mechanical motions modulate the X-ray flux?
Could magnetic mode splitting be observed, constrain field geometry?

28. Inside Neutron Stars
Superfluid neutrons
???
Pions, kaons, hyperons, strange quark matter, quark-gluon plasma?
r ~ 1 x 1015 g cm-3
The physical constituents of neutron star interiors still largely remain a mystery after 35 years.

29. QCD phase diagram: New states of matter
Rho 2000, thanks to David Kaplan
Aspects of QCD still largely unconstrained.
Recent theoretical work has explored QCD phase diagram (Alford, Wilczek, Reddy, Rajagopal, et al.)
Exotic states of Quark matter postulated, CFL, color superconducting states.
Neutron star interiors could contain such states. Can we infer its presence??

30. Implications for Neutron Star Structure
For SGR , 28, 53.5, 84, and 155 Hz sequence is plausibly consistent with l=2, 4, 7, 13 modes (n=0)!
Mode frequencies depend on stellar mass, radius and magnetic field.
If modes correctly identified, then it places constraints on the stellar structure, though, with some caveats (such as magnetic field effects).
SGR 1806
SGR 1900
Strohmayer & Watts (2005)

31. Magnetar hyper-flares: Whole lotta shakin’ goin’ on
Tod Strohmayer, NASA’s Goddard Space Flight Center

32. Fundamental Physics: Existence of New States of Matter?
Theoretical work suggests quark matter could exist in neutron stars, possibly co-existing with a nuclear component.
Mass – Radius measurements alone may not be enough to discriminate the presence of quark matter.
Other observables, such as global oscillations might be crucial.
Alford et al. (2005)

33. Anatomy of a Hyperflare
Three events to date:
March 5th 1979: SGR
August 27th 1998: SGR
December 27th 2004: SGR
Powered by global magnetic instability (reconfiguration), crust fracturing.
Hurley et al. (1998): Ulysses
Short, hard, luminous initial pulse.
Softer X-ray tail persists for minutes, and reveals neutron star spin period.
Emission from a magnetically confined plasma.
1015 G magnetic fields implied (Thompson & Duncan 95)

34. The Neutron Star Equation of State
dP/dr = -r G M(r) / r2
Lattimer & Prakash 2004
Mass measurements, limits softening of EOS from hyperons, quarks, other exotic stuff.
Radius provides direct information on nuclear interactions (nuclear symmetry energy).
Other observables, such as global oscillations might also be crucial.