Current trends in coronal seismology

Centre for Fusion, Space & Astrophysics

Current trends in coronal seismology

Valery M. Nakariakov

University of WarwickUniversity of Warwick

United KingdomUnited Kingdomhttp://www.warwick.ac.uk/go/cfsa

EGU, Vienna, Austria 20/04/2007


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.


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

Seismological information


(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:

2 2 2 2 2 200 0 0

0

'( ) '( )( ) ( ) 0

( ) ( )m m e

e z Ae z A em m e

I m a K m ak C m k C m

I m a K m a

Magnetohydrodynamic (MHD) equations

Equilibrium

Linearisation

Boundary conditions

Zaitsev & Stepanov, 1975- B. Roberts and colleagues, 1981-


Main MHD modes of coronal structures:

• sausage (|B|, )

• kink (almost incompressible)

• torsional (incompressible)

• acoustic (, V)

• ballooning (|B|, )

Dispersion curves of coronal loop:Dispersion curves of coronal loop:


Observed wave phenomena (to April 2007):

1. Kink oscillations of coronal loops (Aschwanden et al. 1999, Nakariakov et al. 1999)

2. Propagating longitudinal waves in polar plumes and near loop footpoints (De Forest & Gurman, 1998; Berghmans & Clette, 1999)

3. Standing longitudinal waves in coronal loops (Kliem at al. 2002; Wang & Ofman 2002)

4. Global sausage mode (Nakariakov et al. 2003)

5. 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)


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



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):


“Per

iodo

map

of

the

activ

e re

gion

”


along loop

Higher spatial harmonics:

apex footpoints

Verwichte et al. 2004


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”)


Mechanism responsible for the decay?

Intensive discussion:

enhanced shear viscosity (or shear viscosity = bulk viscosity), phase mixing?

dissipationless resonant absorption?VS

But…

Hmmm…

4/3PM:

RA:

decay

decay

P

P


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 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. F

rom

Kin

g et

al.

2003


2

2

1 1( ) 0

2 ( ) 2 s

V V VV V S

S H S C

Theory: the evolutionary equation:

stratification nonlinearity

dissipation

radiative losses - heating

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:

Multi-strand sub-resolution structuring?

Decorrelation

Kin

g et

al.

2004


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. 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)

Fast wave perpendicular to B approaches X-point

Electric currents build up (time variant)

Current driven micro-instabilities

Anomalous resistivity

Triggers fast reconnection

Acceleration of non-thermal electrons

Nakariakov et al., Quasi-periodic modulation of solar and stellar flaring emission by magnetohydrodynamic oscillations in a nearby loop, A&A 452, 343, 2006

A possible mechanism: periodic triggering of flare by external MHD wave


• 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.

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):


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):

classical anomalousthreshold classical

threshold anomalous ,,

,

jj

jj

thersholdj

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

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Current trends in coronal seismology