Current trends in coronal seismology EGU, Vienna, Austria 20/04/2007 Current trends in coronal seismology Valery M. Nakariakov University of Warwick United Kingdom http://www.warwick.ac.uk/go/cfsa

Wave and oscillatory processes in the solar corona: Observational evidence of coronal oscillations (or quasi-periodic pulsations) is abundant (major contribution by SOHO,TRACE and NoRH). Possible relevance to coronal heating and solar wind acceleration problems. Possible role in the physics of solar flares. Plasma diagnostics.

Seismological information Mechanisms for (Quasi) Periodicity: Resonance (characteristic spatial scales) Dispersion Nonlinearity / self-organisation Characteristic scales: 1 Mm-100 Mm, MHD speeds: Alfvén speed 1 Mm/s, sound speed 0.2 Mm/s → periods 1 s – several min - MHD waves

(MHD) coronal seismology – diagnostics of solar coronal plasmas with the use of coronal MHD waves and oscillations Main differences with helioseismology: Transparent medium Usually only local diagnostics of the oscillating structures and their nearest vicinity (e.g. magnetic field in the oscillating loop (c.f. time-distance helioseismology). Three wave modes (fast, slow magnetoacoustic and Alfven) – more constrains and more toys to play with. C.f. MHD spectroscopy of tokamaks. Local (various coronal structures) vs Global (AR, CH) (Roberts et al. 1984) (Uchida 1970, Ballai 2004)

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

Dispersion curves of coronal loop: Main MHD modes of coronal structures: sausage (|B|, r) kink (almost incompressible) torsional (incompressible) acoustic (r, V) ballooning (|B|, r)

Observed wave phenomena (to April 2007): Kink oscillations of coronal loops (Aschwanden et al. 1999, Nakariakov et al. 1999) Propagating longitudinal waves in polar plumes and near loop footpoints (De Forest & Gurman, 1998; Berghmans & Clette, 1999) Standing longitudinal waves in coronal loops (Kliem at al. 2002; Wang & Ofman 2002) 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 April 2007):

1. Transverse (kink or m=1) mode: Decaying kink-like oscillations of coronal loops, excited by a nearby flare. Periods are several minutes (e.g. 256 s), different for different loops. Decay times are about a few wave periods.

Estimation of the magnetic field: One of the aims of SDO/AIA

automated detection of oscillations in imaging data cubes Challenges: to minimise the errors automated detection of oscillations in imaging data cubes Recent achievements: (Van Doorsselaere et al. 2007)

Automated detection techniques (for SDO/AIA):

“Periodomap of the active region”

Higher spatial harmonics: apex footpoints Verwichte et al. 2004 along loop

A number of theoretical papers on P2/P1 ratio: Andries et al. (2005) McEwan et al. (2006) Dymova et al. (2007) Estimation of density scale height flux tube divergence

Van Doorsselaere et al. 2007 : The hydrostatic estimation: H = 50 Mm (c.f. Aschwanden et al. 2000: “over-dense loops”)

Hmmm… Mechanism responsible for the decay? enhanced shear viscosity (or shear viscosity = bulk viscosity), phase mixing? dissipationless resonant absorption? Intensive discussion: VS But… Hmmm…

Kink oscillations?

Spectral information is crucial (EIS). Open questions: Excitation mechanism. Options are: a flare-generated coronal blast (fast) wave; a chromospheric wave exciting loop footpoints. Decay mechanisms. Options are: resonant absorption, phase mixing with enhanced sheer viscosity; possibly leakage in the corona in multi-thread systems. Selectivity of the excitation: why some loops respond to the excitation while others do not? The role of nonlinear effects (the displacement is greater than the loop width). Do the oscillations change the loop cross-section shape? Coupling of oscillations of neighbouring loops, oscillations of AR. Spectral information is crucial (EIS).

2. Propagating Longitudinal Waves = Slow Waves Observed near in legs of loops and in plumes: Upwardly propagating perturbations of EUV emission intensity. With constant speed about 25-165 km/s. Amplitude is <12% in intensity (< 6% in density), The periods are about 130-600 s. No manifestation of downward propagation. A number of examples. No correlation between the amplitudes, periods and speeds. From King et al. 2003

Theory: the evolutionary equation: stratification nonlinearity radiative losses - heating dissipation Theory VS Observations:

Main mechanisms affecting the vertical dependence of the amplitude: Stratification (can be estimated, relative density change is needed), Thermal conduction (can be estimated if temperature is known), Magnetic flux tube divergence (can be estimated from images) Radiative damping (can be estimated if temperature is known, e.g. RTV approximation), Unknown coronal heating function. - can be estimated from the observations of the waves!

Multi-strand sub-resolution structuring? Multi-wavelength observations: TRACE 171 A and 195 A: Decorrelation King et al. 2004 Multi-strand sub-resolution structuring?

A probe of the sub-resolution structuring of the coronal temperature

Open questions: What is their origin and driver? (Options: thermal overstability, leakage of p-modes, connection with running penumbra waves). What determines the periodicity and coherency of propagating waves? What is the physical mechanism for the abrupt disappearance of the waves at a certain height (Options: dissipation and density stratification, magnetic field divergence, phase mixing). Are the waves connected with the running penumbra waves?

3. Similar periodicities are often detected in flares: E.g., in microwave emission: (NoRH) Period about 40 s

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

Also, stellar flaring QPP: EQ Peg B flare VL emission (Mathioudakis et al. 2004) :

Suppose that QPP are connected with some MHD oscillations (the same periods!). The model has to explain: the modulation of both microwave and hard X-ray (and possibly WL) emission simultaneously and in phase; (are there any observations which contradict this?) the modulation depth (> 50% in some cases, while the amplitudes of known coronal MHD waves are usually just a few percent); the observed 2D structure of the pulsations.

MHD oscillation in the external loop (very small amplitude) A possible mechanism: periodic triggering of flare by external MHD wave 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., Quasi-periodic modulation of solar and stellar flaring emission by magnetohydrodynamic oscillations in a nearby loop, A&A 452, 343, 2006

Full 2.5D finite-β MHD simulations of the interaction of a fast wave with a magnetic X-point (McLaughlin & Hood, 2004, 2005, 2006; Young et al. 2006): The fast wave experiences refraction. The fast wave energy is accumulated near the separatrix. The current density near the X-point experiences building up. Incoming periodicity is reflected in current periodicity. The amplitude of the generated variations of current density is orders of magnitude higher than the amplitude of the driving fast wave.

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

Current-driven plasma microinstabilities were suggested as a triggering mechanism for fast reconnection (e.g. Ugai, Shibata): Periodic variation of the current density causes periodic triggering of fast reconnection

There is some observational evidence: (Foullon et al., X-ray quasi-periodic pulsations in solar flares as MHD oscillations, A&A 420, L59, 2005) Unseen kink oscillations of the faint trans-equatorial EUV loop cause modulation of the hard X-ray emission near the magnetically conjugate points.

Conclusions: MHD waves are a common feature of the solar corona. The waves contain information about physical parameters in the corona (sometimes unique) – MHD coronal seismology. If understood in the solar corona – very interesting perspectives in stellar coronae. Several MHD modes have been directly observed in solar coronal structures, mainly in EUV. Very interesting perspectives in the microwave band. Flaring QPP can be cause by MHD waves too – there are simple mechanisms for the modulation of hard X-ray and microwave. Nakariakov & Verwichte, Living Reviews of Solar Physics, 2005, http://www.livingreviews.org/lrsp-2005-3