space and astrophysics solar b as a tool for coronal wave studies solar b as a tool for coronal wave...

Space and Astrophysics

Solar B as a Solar B as a tool for coronal tool for coronal wave studieswave studies

Valery M. NakariakovValery M. Nakariakov

University of WarwickUniversity of Warwick

United KingdomUnited Kingdom

The 6th Solar B Science Meeting, 8-11/11/2005


Observational evidence for coronal waves is abundant (SOHO, TRACE, RHESSI, NoRH):

Periods from 1 s to several min.

(Quasi) Periodicity can be connected with:

• Resonance (connected with characteristic spatial scales – e.g. standing modes of coronal structures)

• Dispersion (also connected with characteristic spatial scales but indirectly, through wave dispersion – different spectral components propagate at different

phase and group speeds)

• Nonlinearity / self-organisation (finite amplitude effects and overstabilities – autooscillations, dynamical regimes of reconnection, wave-flow

interactions).

All these mechanisms provide us with seismological information about physical conditions in the corona

2


Already identified coronal MHD modes:

1. Kink oscillations of coronal loops (Aschwanden et al. 1999,2002; Nakariakov et al. 1999; Verwichte et al. 2004)

2. Propagating longitudinal waves in polar plumes and near loop

footpoints (Ofman et al. 1997-1999; DeForest & Gurman, 1998; Berghmans & Clette, 1999; Nakariakov et al. 2000; De Moortel et al. 2000-2004)

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)

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Kink oscillations as a tool for coronal seismology: Determination of coronal magnetic field

Scheme of the method:

4

Nak

aria

kov,

Ofm

an 2

001


Recent development: transverse oscillations in off-limb arcade observed with TRACE:

1/ 20 013

0

1 /7.9 10 en d n n

BP

5

Ver

wic

hte

et a

l. 20

04

2Best fit ( ) cos

ntt Ae tP


First identification of kink second harmonics:

P2 ≈ P1/2, the mode has a node at loop apex.

Andries et al. (2004):

P2 /P1 ~ H (scale height)

P1

P2

A tool for independent estimation of stratification

6


Mechanisms responsible for the decay of kink oscillations are still intensively debated. Two

most popular theories are

• phase mixing with enhanced shear viscosity (or shear viscosity ≈ bulk viscosity), and

• resonant absorption (dissipationless).

Nak

aria

kov

& V

erw

icht

e 20

05

4/3PM:

RA:

decay

decay

P

P

These mechanisms have different scaling of the decay time with oscillation period (Ofman & Aschwanden, 2002):

7


Required resolution in EUV:

Time t < 30 s

Spatial < 1 Mm

DopplerV < 1 km/s

Typical parameters of kink oscillations:

• Oscillation period P: 2-10 min (<P> = 321 s)

• Oscillation duration D: 6-90 min (<D> = 23 min)

• Oscillation amplitude A: 0.1-9 Mm (<A> = 2.2 Mm)

V: 1-70 km/s (<V> = 7 km/s)

Kink oscillations with Solar B:

Quite consistent with XRT (t < 10s, 1 Mm);

Not likely to be detected with EIS (V = 3 km/s)

8

Asc

hwan

den,

200

5


Longitudinal waves as tool for determination of coronal heating function

Observed in coronal fan structures and polar plumes

Distance along

slit

time9

Standard detection method is the time-distance plot for a selected slit on image


Observations vs Theory:

2

2

1 1( ) ( ) 0

2 ( ) 2 s

V V Vz V V z

z H z C

Theory: the evolutionary equation for longitudinal velocity V(z,):

stratification nonlinearity

thermal conduction

radiative losses - heating

Ob

serv

ed a

mplit

ude,

V

• Assume or estimate (z), T(z), hence H(z), Cs(z)

• Obtain (z) by best fitting,

• Estimate radiative losses,

• Obtain the heating function.

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The correlation coefficient of the waves observed in 171Å and 195 Å is found to decrease with distance from source: phase mixing decrease of the wave amplitude

A sum of four waves with different speeds

(80, 110, 140 and 170 km/s) within one pixel

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Probing sub-resolution structuring by longitudinal waves: amplitude evolution with height.

Distance along

slit

time


2sin

sin

si A t

P C

Simulations:

Decorrelation Phase mixing

Sub-resolution structuring?

Fro

m K

ing

et

al.

2003

Probing sub-resolution structuring by multi-wavelength observations of longitudinal waves: decorrelation of waves measured along the same path in different bandpasses.

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Required resolution in EUV:

Time t < 30 s

Spatial < 5 Mm

DopplerV < 1 km/s

Duration of observation: >15-60 min (in sit-and-stare mode with sufficiently large FOV)

Typical parameters of longitudinal waves:

• Oscillation period P: 2.5-9 min (<P> = 282 s)

• Oscillation duration D: > 30-60 min

• Wavelength : (15-100)*sin(LOS) Mm

• Oscillation amplitude : 0.7-14.6% (<> = 4.1%)

V: 0.1-0.15 Cs (<V> = 4-8 km/s)

Longitudinal oscillations with Solar B:

Quite consistent with XRT (t < 10s, 1 Mm);

Not likely to be detected with EIS (V = 3 km/s)

13

De

Moo

rtel

. et a

l. 20

02


How can EIS be useful for coronal wave studies?

• Search for torsional modes (not identified in the corona yet):

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They can be observed as periodic Doppler broadenings of coronal spectral lines; possible amplitude can be of the same order as the amplitude of kink oscillations (e.g. <5%) V/CA ≈ 0.05 V ≈ 20-30 km/s. The period of an N-th standing torsional mode is 2L/CAN , for a typical active regions, the longest periods are a few min – well resolvable with EIS. (See Nakariakov & Verwichte 2005 for more detail, and Williams 2004 for forward modelling).

• Standing acoustic modes (well resolved by SUMER):

Observational challenges:• Imaging observation (e.g. 1st or 2nd harmonics?),• Density perturbations?• Cooler lines?,• Identification in flaring light curves W

ang

et a

l.. 2

003


Conclusions:Conclusions:• Coronal waves provide us with a unique tool for the estimation of coronal magnetic fields, heating function, transport coefficients, independent estimation of stratification, and for probing coronal fine structuring.

• XRT will be a primary tool for detection and study of kink oscillations and propagating longitudinal waves. Also, detection of standing longitudinal modes would be very likely.

• EIS can be used for the search for torsional modes and for detailed study of standing longitudinal modes.

http://www.warwick.ac.uk/go/space

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References:1. Andries, J., Arregui, I, Goossens, M., determination of the coronal density stratification from the

observations of harmonic coronal loop oscillations, ApJ 624, L57, 2005

2. De Moortel, I.; Ireland, J.; Walsh, R. W.; Hood, A.W., Longitudinal intensity oscillations in coronal loops observed with TRACE - I. Overview of measured parameters, Solar Phys. 209, 61, 2002

3. King, D.B., Nakariakov, V.M., Deluca, E.E., Golub, L., McClements, K.G., Propagating EUV disturbances in the Solar corona: Two-wavelength observations, A&A 404, L1, 2003

4. Nakariakov, V.M., Ofman, L., Determination of the coronal magnetic field by coronal loop oscillations, A&A 372, L53, 2001

5. Nakariakov, V.M., Verwichte, E., Coronal waves and oscillations, Living Rev. Solar Phys., 2, 3, 2005

6. Ofman, L.; Aschwanden, M. J., Damping time scaling of coronal loop oscillations deduced from Transition Region and Coronal Explorer observations, ApJ 576, L153, 2002

7. Verwichte, E., Nakariakov, V.M., Ofman, L., Deluca, E.E., Characteristics of transverse oscillations in a coronal loop arcade, Solar Phys. 223, 77, 2004

8. Wang, T. J et al., Hot coronal loop oscillations observed with SUMER: Examples and statistics, A&A 406, 1105, 2003

9. Williams, D.R., Diagnosing MHD wave detections in solar coronal loops: torsional effects, Proc.

SOHO-13, ESA SP-547, 2004

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space and astrophysics solar b as a tool for coronal wave studies solar b as a tool for coronal wave...

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