Generation of quasiperiodic pulsations in solar flares by MHD waves

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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/
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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
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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
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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-
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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)

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• 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)
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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 ?(t) ? modulation If(t) Sausage mode
B(t) ? modulation If(t) Longitudinal mode can
also modulate the GS emission
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But, often QPP are seen in both microwave (GS)
and hard X-ray e.g. Asai et al. (2001)
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• 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 (gt 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.

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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
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1. Long period pulsations (gt 60 s)
Quadrupolar magnetic configuration
What if the modulating wave is magnetically
disconnected with the flaring loop?
At the reconnection site B cos(Ot) ? Ne
cos(Ot)
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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. AA, 2006, in press)
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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.

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Thus, the electric current at the x-point varies
periodically in time
The amplitude of the source fast wave is just 1.
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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
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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.
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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)
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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)
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3. Short period case (lt 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 )
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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).