Current trends in coronal seismology

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EGU, Vienna, Austria 20/04/2007. Current trends in coronal seismology. Valery M. Nakariakov University of Warwick United Kingdom. Wave and oscillatory processes in the solar corona:
EGU, Vienna, Austria 20/04/2007Current trends in coronal seismologyValery M. NakariakovUniversity of WarwickUnited Kingdom 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)
  • Basic theory: Dispersion relations of MHD modes of a magnetic flux tube:Magnetohydrodynamic (MHD) equations Equilibrium Linearisation  Boundary conditionsZaitsev & 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)
  • 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 anearby flare.
  • Periods are several minutes (e.g. 256 s), different for differentloops.
  • Decay times are about a few wave periods.
  • Estimation of the magnetic field:One of the aims of SDO/AIAChallenges:
  • 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:apexfootpointsVerwichte et al. 2004along loopA 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”)Mechanism responsible for the decay?enhanced shear viscosity (or shear viscosity = bulk viscosity), phase mixing? dissipationless resonant absorption?Intensive discussion:VSBut…Hmmm…Kink oscillations?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 WavesObserved 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 andspeeds.
  • From King et al. 2003stratificationnonlinearitydissipationradiative losses - heatingTheory: the evolutionary equation: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-wavelength observations:TRACE 171 A and 195 A:DecorrelationKing et al. 2004Multi-strand sub-resolution structuring?A probe of the sub-resolution structuring of the coronal temperatureOpen 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 sOften QPP are seen in both microwave (GS) and hard X-ray : e.g. Asai et al. (2001)Also, stellar flaring QPP:EQ Peg Bflare 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.
  • A possible mechanism: periodic triggering of flare by external MHD waveMHD oscillation in the external loop (very small amplitude)Fast wave perpendicular to B approaches X-pointElectric currents build up (time variant)Current driven micro-instabilitiesAcceleration of non-thermal electrons Anomalous resistivityTriggers fast reconnectionNakariakov et al.,Quasi-periodic modulation of solar and stellar flaring emission by magnetohydrodynamic oscillations in a nearby loop, A&A452, 343, 2006Full 2.5D finite-βMHDsimulations 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 reconnectionThere 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,
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