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RADIAL OSCILLATIONS OF CORONAL LOOPS AND FLARE PLASMA DIAGNOSTICS

Yu.G . Kopylova , A . V . Stepanov , Yu . T.Tsap, A.V.Melnikov. Pulkovo Observatory, St.Petersburg. RADIAL OSCILLATIONS OF CORONAL LOOPS AND FLARE PLASMA DIAGNOSTICS. The main structural elements of the Sun and late type stars coronae are magnetic loops. TRACE, UV : direct

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RADIAL OSCILLATIONS OF CORONAL LOOPS AND FLARE PLASMA DIAGNOSTICS

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  1. Yu.G.Kopylova,A.V.Stepanov, Yu.T.Tsap, A.V.Melnikov Pulkovo Observatory, St.Petersburg RADIAL OSCILLATIONS OF CORONAL LOOPS AND FLARE PLASMA DIAGNOSTICS

  2. The main structural elements of the Sun and late type stars coronae are magnetic loops TRACE, UV: direct observation of the MHDloops oscillations

  3. Modulation of Flare Emission 1. MHD waves in coronal loops; 2. Pulsating regime of magnetic reconnection; 3. Non-linear wave-wave or wave-particle interaction; 4. Modulation of the electric current in flare loops. Rosenberg suggested to associating pulsations of the radio emission with loop oscillations Coronal seismology Loop plasma diagnostic

  4. The eigenmodes of coronal loops (RADIAL) The emission in many wavelength ranges is effectively modulated by radial oscillations

  5. The coronal magnetic tube model Axisymmetric magnetic flux tube outside index Inside the tube index Perturbed quantities Solutions inside the tube outside

  6. About the oscillation period estimation First analytical solution was obtained by Zaitsev and Stepanov (1975) ??? Edwin and Roberts (1983) numerical calculations Trapped modes, no emission of MHD waves Solution outside the tube Nakariakov et al.(2003) ?

  7. ain general case is complex quantity Solution of dispersion equation for complex argument aincludes both leaky and trapped modes

  8. Dispersion curves ofradial FMA oscillations Trapped modes coincide with curves obtained by Edwin and Roberts (1983) Leaky modes Zeros of

  9. .s The period of the modesaccompanied by the emission of MHD waves into the surrounding mediumis determined by the radius of the tubea, not by its lengthL.

  10. THE MODULATION OF FLARE EMISSION BY THERADIAL OSCILLATIONS OF CORONAL LOOPS The modulation of nonthermal gyrosynchrotron emission From the Dulk formulae for emission coefficient of trapped electrons in optically thin1 and thick2 sources: Ff1 increases with decreasing Ff2 Pulsation are out of phase The magnetic field Вand spectral index estimation from ratio of modulation depths for optically thin and thick sources.  

  11. The Flare of May 30, 1990 Pulsation of the microwave emission with period P =1.5 s on the time profiles at 15 and 9.375 GHz vary out of phase, M1 = 2.5%, M2 = 5%,. Assumptions: 1) Radial oscillations of the flare loop caused the emission modulation 2) The emission source at 15 GHz was optically thin but at 9.375 GHz optically thick Spectral index of electrons= 4.4 Magnetic fieldB ~200 G

  12. Plasma diagnostic using of the observable characteristics of the pulsations (the modulation depthM, the Q-factor, and the periodP) Zaitsev and Stepanov, 1982 (X-ray pulsations) For microwave emission of solar flares nonthermalgyrosynchrotron mechanism is responsible ξ = 0.9δ − 1.22 Q=/?

  13. The damping of radial FMA oscillations I. Acoustic damping mechanism • Analytical solution of the dispersion equation. 2.Energy method of the acoustic decrement calculation. 3.Numerical solution of the dispersion equation Comparison analysis of three methods have shown that for rarefied loops this mechanism defines oscillation damping Analytical solution Z-S Energy method Numerical calculations Dependences of the Q factor on ratio of the Alfven speeds inside and outside the magnetic loop

  14. The solar flare of May 16, 1973 McLean and Sheridan(1973) have detected pulsations with P=4 s and rapid amplitude decrease. Upper limit for electron density Acoustic damping mechanism of loop radial oscillations We’ll assume that density in the external region varies with height h in accordance to the Baumbach–Allen formula for electron density distribution

  15. The damping of radial FMA oscillations I. Dissipative processes The comparison analysis of the dissipative processes decrements Joulelosses radiative losses Electron conductivity Ion viscosity Total decrement. So the ion viscosity and thermal electron conductivity make a major contribution to the damping

  16. Taking into account expression for total decrement we modified the diagnostic method on a case of pulsations of the gyrosyncrotron emission χ= 10ε/3 + 2, T [K], n [cm-3], B [G] The expression for determining the flare plasma parameters

  17. The Flare of August 28, 1999 Observations: NoRH (17 ГГц) АО NOAA № 8674 (Yokoyama et al.,2002) Flare region consisted of 2 emission sources The results of wavelet analysis for the emission intensity: 3 oscillation branches with 14, 7 and 2.4 s

  18. Loop-loop interaction model: Ballooning oscillations: P≈ 14 and 7 s Sausage oscillations: P ≈ 2.4s Parameters Extended loopCompact loop T ,K 2.5 × 107 5.2 × 107 n, cm-3 1.5 × 1010 4× 1010 B, G 150 230 β 0.04 0.11 ________________________________ 14 s 7 s FLARE SCINARIO 2.4 s Ballooning mode or plasma tongue oscillations excite in dense compact loop. Due to gas pressure rise the violation of oscillation conditions appears and ballooning instability develops. Development of ballooning instability results in the time gap. Injection of hot plasma from compact into extended loop occurs. Radial oscillation with 2.4 s of the large loop caused by the gas pressure rise are excited. As soon as the compact loop was liberated from excess pressure the oscillations of plasma tongues with 14 and 7 s resumed. 14 and 7 s pulsations have time gap: 1 and 2 harmonicas of ballooning modes

  19. Modulation of nonthermal bremsstralung from loop footpoints (optical, hard X-ray emission) The emission flux determined by the variations of the fast electrons flux . Based on the model proposed by Zaitsev and Stepanov for radial modes excitation and taking into account total damping decrement we have derived expression for T,n,B estimation.

  20. Oscillations of Optical Emissionon the star EV Lac During simultaneous observations of three flares on EV Lac: Terskol Peak (Northern Caucasus), Stephanion Observatory (Greece), Crimean Observatory, Belogradchik (Bulgaria) in-phase oscillations with Р = 10-30 s were detected in the U and B bands Zhilyaev et al. (2000), U: ΔF 0.2, B: ΔF 0.05, (flare 11.09.98) • Assumptions • Optical emission occurs due to nonthermal bremsstalung mechanism. • Pulsations of flares emission are produced bythe excitation of sausage loop oscillations P=13 c, Q=50, M=0.2

  21. The Flareon November 4, 2003 on EQ Peg B (M5E) (ULTRACAM) Taking T, B, n, L from Haisch scaling laws (Mullan et al., 2006) Mathioudakis et al. have connected pulsation with trapped sausage mode. P =10 s, Q=30, ΔF=0.1 Mathioudakis et al.(2006) non-leaky (trapped) radial oscillations We assume that leaky radial oscillations were excited. ?

  22. Change of oscillation period in time P3 12 s P211 s P18 s The period drifts to longer values during the flare P1 P2P3 L~ 1010сm Parameters decreased during the flare

  23. Conclusions: The radial oscillations of solar and stellar coronal loops in most casesare leaky. The period of the leaky modes is determined by the radius of the tube, not by its length.For dense flare loops dissipation of radial oscillations is determined by ion viscosity and the electron thermal conductivity. For rarefied loops acoustic damping mechanism plays the main role. Methods of diagnostics for the flare loop parameters based on the observed period, quality-factor, and modulation depth of the nonthermal emission pulsations are suggested and applied to the analysis of several solar and stellar flareevents. Kopylova Yu.G., Stepanov A.V., Tsap Yu.T.,Ast. Lett., 2002, V.28, №11, p.783-879.Stepanov A.V., Kopylova Yu.G., Tsap Yu.T., et al., Ast.Lett., V.30, № 7, 2004, p.480-488. Stepanov A.V., Kopylova Yu.G., Tsap Yu.T, Kuprianova E.G., Ast.Lett., V.30, № 9, 2005, p.612-619. Kopylova Yu.G., A.V. Melnikov, Stepanov A.V. et al.,Ast.Lett., V.33, 2007, №10, p.706–713. Publications:

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