Quasi-Periodic Oscillations in magnetars: linking variability and emission
aa r X i v : . [ a s t r o - ph . S R ] O c t Neutron Stars and Pulsars: Challenges and Opportunities after 80 yearsProceedings IAU Symposium No. 291, 2012J. van Leeuwen, ed. c (cid:13) Quasi-Periodic Oscillations in magnetars:linking variability and emission
Caroline D’Angelo
Instituut Anton Pannekoek, University of Amsterdam, Amsterdam, Netherlands 1098 XHemail: [email protected]
Abstract.
I present recent results studying flare emission in magnetars. Strong quasi-periodicoscillations observed in the tail of giant magnetar flares are frequently interpreted as evidence forglobal seismic oscillations. I demonstrate that such a global oscillation is not directly observablein the lightcurve. New work suggests the amplitude for the strongest QPO stays nearly constantin the rotation phases where it is observed, which I argue suggests it is produced by an additionalemission process from the star.
Keywords. dense matter, radiation mechanisms: general, magnetic fields (magnetohydrody-namics:) MHD, stars: neutron, stars: oscillations, X-rays: stars
1. Introduction
In the past few years, considerably theoretical interest has been focused on the seis-mology of neutron stars (e.g. Levin 2006; Glampedakis et al. 2006; Gabler et al. 2011),largely been motivated by the observation of a series of quasi-periodic oscillations (QPOs)in the decay tails of the giant flares in magnetars SGR 1900+14 and SGR 1806-20 (Israelet al. 2005; Watts & Strohmayer 2006; Strohmayer & Watts 2006). The large amount ofenergy released during a flare ( ∼ erg) is likely powered by a global reconfigurationof the star’s magnetic field (Thompson & Duncan 1995) and some of that energy willtrigger large-scale quakes in the star (Duncan 1998).Comparatively little work has been done to connect the putative starquakes directlyto the observed QPOs. Timokhin et al. (2008) recently proposed that the oscillationscould be attributed to a variable current density in the stellar magnetosphere, created bytwisted magnetic field lines anchored in the vibrating star. These electrons then Comptonupscatter photons from the surface of the star, modifying the observed spectrum.In this article I revisit the properties of the QPOs observed in SGR 1806-20 and arguethat correlations (or lack thereof) between the variability on different timescales can beused to put strong constraints not only on the QPO origins but also on the emissionmechanisms powering the flares themselves.
2. Quasi-Periodic Oscillations in SGR 1806-20
Six distinct QPOs were detected in the SGR 1806-20 giant flare using X-ray data fromboth the
RHESSI and
RXT E satellites. The QPOs have central frequencies between17 and 1837 Hz, with fractional rms amplitudes between 4 and 20%. They are furthercharacterized by a high degree of coherence: of the six detected QPOs, only the one at 150Hz has a width (full-width at half maximum) of 17 Hz; the others have widths between1 and 5 Hz (Strohmayer & Watts 2006). There is some evidence for energy dependencein the QPO at 625 Hz, which had an rms amplitude of ∼
8% below 100 keV, but of rms ∼
20% between 100-200 keV (Watts & Strohmayer 2006). The energy dependence of the1 C. D’Angeloother QPOs is not clearly detected, but cannot be excluded due to uncertainties in themeasured photon energies.Different QPOs were detected at different time intervals in the decay tail of the flareand at different phases in the rotational pulse profile. The majority of the QPOs werestrongest beginning ∼ ∼
3. Direct detection of a starquake
D’Angelo & Watts (2012) studied whether a starquake could have an observable effectdirectly on the lightcurve itself by shaking the emitting region. If the pulse profile is verysteep (i.e. some component of the pulse is beamed) then the sharp edge of the beam willamplify the underlying motion of the surface, much like a flashlight wiggling in and outof an observer’s line of sight. The change to the rotational phase from the crust motionis given by: ∆Φ = ∆ xR ∗ sin i sin α sin(2 πν t ) , (3.1)where ∆ xR ∗ is the fractional amplitude of the starquake, ν is its frequency, and sin i andsin α are geometrical factors depending on the beam orientation.D’Angelo & Watts (2012) found that although significant amplification of a star quakeis possible, for the observed lightcurves and realistic, the effect can be excluded. Thefractional rms amplitude of a QPO with phase change ∆Φ is given by: A ∼ dPd Φ ∆Φ h P Φ i , (3.2)where P (Φ) is the pulse profile as a function of rotation phase. The amplification providedby a steep gradient is not enough to make a starquake (with ∆ x/R ∗ < .
01) directlydetectable. This result also excludes the possibility that weak, extremely steep ‘pencilbeams’ (unresolved in the lightcurve) can provide the amplification. The amplificationfactor in that case will be given by eq. 3.2 times an additional factor P beam / h P i , thefractional amplitude of the steep beam. The beam gradients required in this case aresteep enough to be plausibly excluded.This result strongly suggests the QPOs are produced by variations in the amplitudeof the emission itself, rather than the starquake directly.
4. Modulation versus Emission
The physical properties of the QPO can be somewhat constrained from the observedvariability of the lightcurve. This is most easily seen from the power spectrum, thesquared amplitude of the Fourier transform of a segment of the lightcurve (e.g. van derKlis 1989). The left and right panels of figure 1 show power spectra from the pulsedtail of the giant flare, centered at two different phases of the pulse profile (shown in thebottom panel). In each power spectrum the QPO at 93 Hz is clearly visible, and a fitto the QPO is overlaid. The QPO is significantly narrower in the interpulse region, andthe broadband noise (below ∼
100 Hz) is lower (a second QPO is seen at 30 Hz in the
AUS291. Magnetar QPOs: variability and emission Figure 1.
Power spectrum and pulse profile of the tail of the SGR 1806-20 giant flare for twodifferent segments of the rotational phase (shown by the vertical lines). The QPO at 93 Hz isfit with a Lorentzian distribution (overlaid in red dash-dotted line). interpulse spectrum). At the same time, the mean flux in the lightcurve is ∼
60% lowerthan in the secondary pulse.There are two obvious ways that the observed intensity can vary at the QPO frequen-cies. Either the surface flux can be modulated by a quasi-periodically varying process (likechanging optical depth to electron scattering, cf. Timohkin et al. 2008), or the amount offlux being emitted by the star can vary, either through variations in the overall surfaceemission or via some MHD instability that produces emission. At present the idea ofvariable emission in the magnetar magnetosphere is purely speculative, but mechanismsfor producing QPOs in solar flares are an active research topic, and some of these couldpotentially be relevant for magnetar flares as well (see e.g. the review by Nakariakov &Melnikov 2009).The difference between an emitting process and a modulating one should be observablein the phase-resolved QPOs. A modulating process should produce a correlation betweenthe absolute amplitude of the QPO and the mean flux. In contrast, an emission processshould stay constant in phase, and be stronger at phases when the mean flux is lower.Figure 2 shows the fractional change in flux as a function of phase (black line solid),overplotted with the fractional change in QPO amplitude (integrated power over 20 Hzcentered at 93 Hz; red dot-dashed line). As is evident from the figure, the QPO amplitudedoes not drop as much in the interpulse region, then disappears altogether at the mainpeak of the burst. The lack of correlation between mean flux and QPO amplitude wouldsuggest that an additional emission process is responsible for its production.
5. Markov Chain Monte Carlo Simulations
Determining the amplitude of the QPOs – particularly those below 100Hz – is compli-cated by the presence of low-frequency broadband noise (visible in the left panel of fig.1). Part of the signal at 93 Hz could originate from red noise and not the QPO process,but disentangling the two components is not straightforward (see e.g. Vaughan 2005).To quantify the uncertainty in QPO amplitde, we use Markov Chain Monte Carlosimulations to generate a series of realizations of a power spectrum with a broadbandcomponent and a QPO given by the best fit to the observed spectrum (Vaughan 2010).The variation in the resulting measured parameters can be used to constrain the uncer-tainty on the QPO fit, and more accurately determine the variation in QPO amplitudeas a function of phase. Preliminary results of this analysis suggest that the amplitude C. D’Angelo
Figure 2.
Mean flux (black solid line) and 93Hz QPO amplitude (red dash-dotted line) asa function of phase, for the tail of the SGR 1806-20 giant flare. For the phases where theQPO is detected, the amplitude is consistent with being constant while the mean flux variessubstantially. observed QPO at 93 Hz is consistent with remaining constant over the rotation phasewhere it is detectable. This would seem to suggest it is independent of the secondarypulse peak, and point to an underlying emission process. The definitive results will bepublished in a forthcoming paper.
6. Conclusions
The variability of magnetar giant flares on different timescales shows correlations thatcan constrain the underlying emission mechanism, both for the QPOs and potentially theemission from the giant flares themselves. We have excluded the possibility of directlydetecting surface oscillation of the magnetar crust, and have presented preliminary ev-idence that suggests an additional emission mechanism might be active to produce thequasi-periodic oscillations.
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