Generation of quasi-periodic pulsations in solar flares by MHD waves

1. Nobeyama, Japan 16/03/2006 Generation of quasi-periodic pulsations in solar flares by MHD waves Valery M. Nakariakov University of Warwick United Kingdom http://www.warwick.ac.uk/go/cfsa/

2. A hypothesis or theory is clear, decisive, and positive but it is believed by none but the man who created it. Experimental findings, on the other hand are messy, inexact things which are believed by everyone except the man who did the work. Harlow Shapley

3. Seismological information Observational evidence of quasi-periodic pulsations in solar flares is abundant. • (Quasi) Periodicity: • Resonance (characteristic spatial scales) • Dispersion • Nonlinearity / self-organisation Characteristic scales: 1 Mm-100 Mm, Alfvén speed 1-2 Mm/s, sound speed 0.3-0.5 Mm/s → periods 1 s – several min - MHD waves

4. Standard theoretical model: Magnetohydrodynamic (MHD) equations  Equilibrium  Linearisation  Boundary conditions Dispersion relations of MHD modes of a magnetic flux tube: Zaitsev & Stepanov, 1975- B. Roberts and colleagues, 1981-

5. Dispersion curves of coronal loop: • Main MHD modes in observed in the corona: • sausage (|B|, r) • kink(weakly compressible) • torsional (incompressible) • acoustic (r, V) • ballooning (|B|, r)

6. Kink oscillations of coronal loops (Aschwanden et al. 1999, Nakariakov et al. 1999) • Propagating longitudinal waves in polar plumes and near loop footpoints (Berghmans & Clette, 1999; Nakariakov et al. 2000, De Moortel et al. 2000-2004) • Standing longitudinal waves in coronal loops (Kliem at al. 2002; Wang & Ofman 2002; Nakariakov et al. 2004) • Global sausage mode (Nakariakov et al. 2003) • Propagating fast wave trains. (Williams et al. 2001, 2002; Cooper et al. 2003; Katsiyannis et al. 2003; Nakariakov et al. 2004, Verwichte et al. 2005) Observed wave phenomena (to 2006):

7. In general, MHD waves should be well seen in microwave: E.g., the optically thin gyrosynchrotron emission intensity If at a frequency f can be estimated as Kink mode:θ(t) modulationIf(t) Sausage mode:B(t) modulationIf(t) Longitudinal mode can also modulate the GS emission

11. But, often QPP are seen in both microwave (GS) and hard X-ray : e.g. Asai et al. (2001)

12. Suppose that QPP are connected with some MHD oscillations. The model has to explain: • the modulation of both microwave and hard X-ray (and possibly WL) emission simultaneously and in phase; • the modulation depth (> 50% in some cases, while the amplitudes of known coronal MHD waves are usually just a few percent); • the mechanism responsible for the periodicity; • the “2D” structure of the pulsations.

13. In general, MHD waves can affect the whole chain responsible for the emission: Electron acceleration Nonthermal electron dynamics MHD waves Emission in WL, microwave, X-rays

14. Kink oscillation Faint cool loop Flaring loop 1. Long period pulsations (> 60 s) What if the modulating wave is magnetically disconnected with the flaring loop? Quadrupolar magnetic configuration At the reconnection site:B ~ cos(Ωt)  Ne ~ cos(Ωt)

15. MHD oscillation in the external loop (very small amplitude) Fast wave perpendicular to B approaches X-point Electric currents build up (time variant) Current driven micro-instabilities Acceleration of non-thermal electrons Anomalous resistivity Triggers fast reconnection (Nakariakov et al. A&A, 2006, in press)

16. Full MHD 2.5D simulations of the interaction of a periodic fast wave with a magnetic X-point. The absolute value of the velocity perturbation. run The electric current density, side view run The electric current density. run • The fast wave energy is accumulated near the separatrix. • The current density near the X-point experiences periodic building up.

17. Thus, the electric current at the x-point varies periodically in time: The amplitude of the source fast wave is just 1%.

18. Current-driven plasma microinstabilities were suggested as a triggering mechanism for fast reconnection: Periodic variation of the current density causes periodic triggering of fast reconnection

19. There is some observational evidence: (Foullon et al. 2005) Unseen kink oscillations of the faint trans-equatorial EUV loop cause modulation of the hard X-ray emission near the magnetically conjugate points.

20. 2. Medium period case (10-60 s) • for trapped modes • here L is the loop length Sausage modes: The commonly used expression is incorrect, (here a is the loop minor radius) (Nakariakov et al., 2003; Aschwanden et al., 2004)

21. What about leaky modes? Full MHD simulations: trapped leaky Thus, the period of leaky sausage modes is also determined by the loop length, not by the loop minor radius. (Pascoe et al., 2006)

22. 3. Short period case (< 10 s) • Higher spatial harmonics (but the problem is the selectivity of the excitation); • Fast wave trains formed by dispersion: (But, they should have period modulation - the “crazy tadpole wavelet spectra …)

23. Conclusions: http://www.warwick.ac.uk/go/cfsa/ • There are simple mechanisms for modulation of microwave and hard x-ray emission by the modes. • The longer periodicities can be connected with small-amplitude oscillations of an external cool loop. In this case the cool loop acts as a resonator and determines the period of oscillations. • Sausage mode periods are prescribed by the flaring loop length, even in the leaky mode regime. • Shorter periodicites can be connected with dispersion. However, there should be period modulation. • In general, shorter periodicities (1-5 s) are still without appropriate interpretation (the “fast mode formula” does not work).