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 of Nizhni Novgorod 2 Institute of Applied Physics, Russian Academy of Sciences Puschino, 2010

2. Types 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

3. 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.

4. 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 ● Heating function: Heating function may be in the order of the radiative loss if ● 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.

5. 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 See [1] for details about PR

6. Realisation (fit subtracted) and mean spectrum of sun burst on April 11 2001 ● Observations at 11,7 GHz

7. Realisation and dynamical spectrum of sun burst on June 27 1993 ● Observations at 37 GHz (Observations by the Metsahovi observatory, Finland)

8. Energy and dissipation of sound waves in CML ● Mean energy of the sound oscillations in CML: and ● Eigen frequency of an equivalent electric circuit: ● Heating rate and the damping decrement: ● Parametric resonance can be an effective heating source for loops with resonant lengths: ● Frequencies of 5-min photosperic oscillations: =>

9. 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:

10. 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.

11. 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.

12. 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.