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PLASMA HEATING DURING THE PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS MAGNETIC LOOPS K.G.Kislyakova 1,2 , V.V.Zaitsev 2 1 Lobachevsky State University of Nizhni Novgorod 2 Institute of Applied Physics, Russian Academy of Sciences Puschino, 2010 Puschino, 2010

PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

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Page 1: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

PLASMA HEATING DURING THE PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF PARAMETRIC EXCITATION OF

ACOUSTIC WAVES IN CORONAL ACOUSTIC WAVES IN CORONAL

MAGNETIC LOOPSMAGNETIC LOOPS

K.G.Kislyakova1,2, V.V.Zaitsev2

1 Lobachevsky State University of Nizhni Novgorod2 Institute of Applied Physics, Russian Academy of Sciences

Puschino, 2010Puschino, 2010

Page 2: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

Types of coronal magnetic loopsTypes of coronal magnetic loops

● CML: coronal magnetic loops (photo by TRACE)

Variety in parameters:

1. Warm loops: ,

2. Flare loops: ,

3. Quasistationary X-ray loops:

intermediate values

KT 610)25.1( cmL 1010)75.1( KT 7104 cmL 98 105105

)()()()( tctptBtI s

Page 3: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

Various mechanisms of plasma heating in the Solar corona

● Heating by currents:

BUT: observed currents in the magnetic loops

● Tearing instability, reconnection, microflares:Typical energy release during a separate microflare in comparison to the energy required to explain coronal temperatures and the required microflares occurrence rate:

● Heating by Alven waves: period

Dissipation(Braginskii 1963)

Heating function:

Dissipation is too small to compensate the radiation loss.

AITnj

qJ15

//2

2// 10)(

//

)1988,(1010 1110// HaguardAI

ssergsergsP 1001010/10 125...2426

)103B,103n,102L(30/2 23910 GcmcmsVLT AA

1182222/1e

2

1162222

106,0/)/m(

105,0/

sLvm

sLc

BieiTiiviscÀ

peeiJouleÀ

sergTq JÀ

JouleA

342132 /cm106)(n 1028/h

Page 4: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

Coronal heating due to the dissipation of the sound waves

● Sound waves: period

Dissipation (Braginskii 1963):- due to conductivity

- due to viscosity

- due to thermal conductivity

min203/2 ss cLT

● Heating function:

Heating function may be in the order of the radiative loss if

1.003,0)/( TnkW Bs

kc

cc

A

sJ 2

2

4

eV 218,0

semm

T e

i 32 105,112,0

13423 106)(10)206( scmergTnTnk

WWq

B

ssTs

● BUT: how do the sound waves penetrate into the corona?One of the possible explanations – parametric resonance which could serve as an effective mechanism of coronal plasma heating.

Page 5: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

Parametric resonance in the Solar Corona

● Frequency of forced oscillations: appr.3 mHz (pumping by the global 5-min oscillations of the photosphere)

● PR can serve as an effective mechanism of coronal plasma heating

● Spectral peculiarities: typical frequencies for PR (pumping frequency, subharmonic, and the first upper frequency), distinctive correlation between intensity and emergence frequency of individual harmonics

...3,2,1,2

nn

n

See [1] for details about PR

Page 6: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

Realisation (fit subtracted) and mean spectrum of sun burst on April 11 2001

● Observations at 11,7 GHz

Page 7: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

Realisation and dynamical spectrum of sun burst on June 27 1993

● Observations at 37 GHz

(Observations by the Metsahovi observatory, Finland)

Page 8: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

Energy and dissipation of sound waves in CML

● Mean energy of the sound oscillations in CML:

and,1

18

16

2

2

0

2

22

20

200

20

I

I

rc

I

c

vW

ss

22

0

3

4

rc

IIp

,474

ln,22 0

2

rl

mncr

I

iRLC

● Eigen frequency of an equivalent electric circuit:

0~ / socpv

● Heating rate andthe damping decrement: ,ssWH thermvisjoules

● Parametric resonance can be an effective heating source for loops with resonant lengths: cm

cl s

02

● Frequencies of 5-min photosperic oscillations:

1212 106105.1 ss => cmlcm 109 102102

2

0

10

LRC

LRC

I

I

Page 9: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

CML plasma heating

● Heat balance equation of a stationary loop and heat conduction coefficient: , where

● Boundary conditions:

● After some conversions and integration we get:

● After the pressure is eliminated we get dependence of temperature in the apex of the loop from its length:

● After calculation we get the temperature in the apex of the loop:

HTns

TT

s e

)(22/5

2/7761092.0 Kcmerge

),2

(0),,0(0 10 TTl

sdsdT

TTsdsdT

2/10)( TT

2/1

51

52/1

2

202 1

2

T

T

k

p

ds

dTT

eB

7/47/27/2

7/2

0

7/4

7/2

0

7/4

7/1

42

20

1 7)(5.924

BlV

rh

lBLrhV

lBA

bT

e

MKT 631 7/21 )( lICT

Page 10: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

Evidences of PR on late-type stars

● It is generally accepted that the coronas of active stars are filled with magnetic loops, quite similar to the solar corona. This is supported, in particular, by observations of pulsating optical and X-ray emission from active stars, associated with oscillations of magnetic loops in the stellar coronas.

● Soft X-ray oscillations have been observed for several dMe stars; these oscillations have periods ranging from several tens to several hundreds of seconds, which are not associated with any flares.

● These pulsations can probably be excited by photospheric convection in the presence of parametric resonance between the oscillations in the velocity of the photospheric plasma and the free acoustic oscillations of magnetic loops.

Page 11: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

Conclusions

● The parametric resonance can serve as an effective channel of transporting the energy of photospheric oscillations into the upper layers of the solar atmosphere. This effect opens up the important prospects in understanding the mechanisms of coronal plasma heating.

● The energy of acoustic waves excited in the coronal magnetic loop, rate of dissipation of acoustic waves, and rate of heating of the coronal plasma can be determined

● The proposed mechanism can explain the origin of quasi-stationary X-ray loops with temperatures of 3–6 MK. The lengths of these loops are resonant for acoustic waves excited by the 5-min photospheric oscillations.

● Proposed mechanism can also be used to the X-ray loops heating on stars of late spectral classes.

Page 12: PLASMA HEATING DURING THE PARAMETRIC EXCITATION OF ACOUSTIC WAVES IN CORONAL MAGNETIC LOOPS K.G.Kislyakova 1,2, V.V.Zaitsev 2 1 Lobachevsky State University

Basic papers:• Parametric Resonance in the Solar Corona. Cosmic Research, 2008, Vol. 46, No. 4,

pp. 301–308. © Pleiades Publishing, Ltd., 2008. Original Russian Text © V.V. Zaitsev, A.G. Kislyakov, K.G. Kislyakova, 2008, published in Kosmicheskie Issledovaniya, 2008, Vol. 46, No. 4, pp. 310–317.

• Plasma Heating during the Parametric Excitation of Acoustic Waves in Coronal Magnetic Loops. Astronomy Reports, 2010, Vol. 54, No. 4, pp. 367–373. Pleiades Publishing, Ltd., 2010. Original Russian Text V.V. Zaitsev, K.G. Kislyakova, 2010, published in Astronomicheskiy Zhurnal, 2010, Vol. 87, No. 4, pp. 410–416.

• Detection of large-scale kink oscillations of coronal loops manifested in modulations of solar microwave emission. M.L. Khodachenko, K.G. Kislyakova , T.V. Zaqarashvili, A.G. Kislyakov, M. Panchenko, V.V. Zaitsev and H.O. Rucker. Submitted to A&A, March 2010

• Methods of intermodulation effects decrease in Wigner-Ville transform. Shkelev, E.I., Kislyakov, A.G., Lupov, S, Yu., Radiophys. & Quant. Electronics, 45, 433, 2002.