Ограничения на модели ускорения электронов в солнечных вспышках

1. ИКИ РАН, Конференция по физике плазмы в солнечной системе, 08 февраля 2010г) Ограничения на модели ускорения электронов в солнечных вспышках Мельников В.Ф., Пятаков Н.П. (ГАО РАН, ФГНУ НИРФИ)

2. Particle Acceleration Processes There exists a wide variety of acceleration mechanisms: (1) electric DC-field acceleration (current sheets, twisted loops) (2) stochastic acceleration (wave turbulence, microflares) (3) shock acceleration (propagating MHD shocks; standing MHD shocks in reconnection outflows) (4) betatron acceleration (in collapsing magnetic traps) Their properties are not the same. They may act in different places inside a flaring loop, and they may produce electrons with different types of pitch-angle distribution, Possibly, all of them can operate in solar flares!

3. Loop top Acceleration in a Current Sheet (X-type reconnection) Energy gained: W = E x Lz Large-scale electric field in Sweet-Parker current sheet Injection across the loop axes (e.g. Syrovatskii, 1976; Litvinenko & Somov, 1995; Somov & Kosugi, 1997; Shibata 2000- …) Zharkova & Gordovsky: injection along the MFL???

4. Betatron Acceleration in a Collapsing Magnetic Trapacross the loop axes (Bogachev and Somov, 2004; Karlicky, Kosugi, 2004)

5. Looptop E E DC-Acceleration in Twisted Magnetic Loops (Zaitsev, Urpo, Stepanov 2000; Zaitsev & Stepanov2008) Acceleration along the loop axes Acceleration can be in the loop top (due to prominence) or near a footpoint Footpoint

6. Stochastic acceleration in micro-current sheets (L. Vlahos et al, 2004; J. Brown et al 2009; R. Turkmani et al 2009) Acceleration is isotropic or partly across the magnetic field lines. Acceleration sites are distributed along a whole loop(s)

7. Are there any constraints from observations? The properties of the electron source in a flaring loop are not the same. They may act in different places inside a flaring loop, and they may produce electrons with different types of pitch-angle distribution, Possibly, all of them can operate in solar flares! Only observations can tell us which mechanism is dominant in a specific flare configuration. The purpose of this talk is to show that modern spatially resolved observations can provide us with data about the key questions: acceleration site and pitch-angle anisotropy and, therefore, give us valuable constraints on acceleration models.

8. Transport effects It is clear from a simple collisionless consideration that electron distribution along a magnetic loop must depend on a specific position and pitch-angle distribution of the acceleration/ injection. The loss-cone condition:  < arcsin (Bs/Bm)

9. Kinetics of Nonthermal Electrons in Magnetic Loops In a magnetic loop, a part of injected electrons are trapped due to magnetic mirroring and the other part directly precipitates into the loss-cone. The trapped electrons are scattered due to Coulomb collisions and loose their energy and precipitate into the loss-cone. A real distribution strongly depends on the injection position in the loop and on the pitch-angle dependence of the injection function S(E,,s,t), and also on time (Melnikov et al. 2006; Gorbikov and Melnikov 2007). Non-stationary Fokker-Plank equation (Lu and Petrosian 1988):

10. m = m S ( E , , s , t ) S ( E ) S ( ) S ( s ) S ( t ), 1 2 3 4 Initial and boundary conditions Initial condition (no electrons at moment t = 0) Boundary condition,s (precipitated electrons do not come back into the magnetic loop) Injection function: In the case of isotropic injection: . (35)

11. near a footpoint homogeneous at the looptop longitudinal isotropic perpendicular Different acceleration models give three basic predictions on the position of the acceleration site and pitch angle distribution

12. For illustration, consider transport effects on the example of two simple models: • Case 1: • Isotropic injection in the center of a magnetic trap. • Case 2: • Isotropic injection near the footpoints of a magnetic trap.

13. Case 1:Injection at the looptop Case 2: Injection near the right footpoint s=0 corresponds theloop center. Injection is isotropic. Mirror ratio к=5. Plasma densityn0=5*1010 cm-3 throughout the loop Dynamics of the high energy electron distribution along a flaring loop (Melnikov 2006; Gorbikov & Melnikov 2007)

14. Dynamics of the pitch-angle distribution.Case 1: isotropic injection at the loop top Decreasing of the perpendicular anisotropy at the center of the loop, and increasing of it near a footpoint Mirror ratio к=2. Plasma densityn0=5*1010 cm-3 throughout the loop

15. Evolution of the pitch-angle distributionCase 2: injection near a footpoint Formation of the oblique anisotropy at the center of the loop in the rise and maximum phase of injection, and formation of perpendicular anisotropy near a footpoint looptop Leg near a footpoint

16. Properties of Gyrosynchrotron Emission from a Realistic Radio Source • Taking into account: • influence of the enhanced plasma density on the energy spectrum of trapped electrons and gyrosynchrotron emissivity, • influence of magnetic mirroring and change of the pitch-angle distribution along a loop, • influence of electron pitch-angle anisotropy on the parameters of GS emission, • influence of the magnetic loop curvature, • Influence of inhomogeneities of magnetic field and plasma density. (Fleishman, Melnikov 2003; Melnikov, Pyatakov, Gorbikov 2006-2010)

17. GS emission and absorption coefficients, exact expressions Calculations are done using Fleishman’s code (Fleishman & Melnikov, ApJ 2003)

18. Case 2 Case 1

19. Radio brightness distribution Case 2: Injection near a footpoint Case 1: Injection at the loop top 17 GHz

20. Distribution of the optical depth Case 2: Injection near a footpoint Case 1: Injection at the loop top Tau << 1

21. Spatial profiles of brightness at 34 GHz at the burst maximum (Melnikov, Reznikova, Shibasaki, 2002, 2006)

22. Reznikova et al. ApJ 2009 : Footpoint sources exist on the rise and peak phases, and even in the beginning of the decay phase. Brightness distribution dynamics, 24 August 2002 (main peak, 34 GHz)

23. Distribution of the polarization degree Case 2: Injection near a footpoint Case 1: Injection at the loop top Ordinary mode circular polarization  Signature of the longitudinal anisotropy Increase in X-mode polarization degree  signature of the perpendicular anisotropy

24. Case 2: Injection near a footpoint Case 1: Injection at the loop top Spectral steepening  signature of the longitudinal anisotropy Distribution of the spectral index (Limb Loop) Spectral flattening  Signature of the perpendicular anisotropy

25. Case 2: Injection near a footpoint Case 1: Injection at the loop top Spectral steepening  Signature of the perpendicular anisotropy Spectral steepening  Signature of the longitudinal anisotropy Distribution of the spectral index (solar disk, Theta = 45 deg)

26. High frequency spectral index variations along a loop. Yokoyama et al. 2002, ApJ, 576, L87. Microwave spectrum near footpoints is considerably softer (by ~ 0.5-1) than near the loop top during the main peak of bursts

27. Радиопризнаки продольной питч-угловой анизотропии ускоренных электронов во вспышечной петле установлены недавно в работах: 1) Altyntsev A.T.et al. (Astrophys. J. 2008, 677, p.1367) 2) Reznikova V.E. et al. (Astrophys. J. 2009, V.697, p.735)

28. Новый взгляд на Солнце Microwave diagnostics of the position of an acceleration site and pitch-angle anisotropy of energetic electrons in the flare 24 Aug 2002 Фильмы, полученные с помощью радиоинтерферометров - Сибирского Солнечного Радиотелескопа (Иркутск) и радиогелиографа Нобеяма (Япония), а также с помощью приборов на космических аппаратах Yohkoh, HESSI (мягкий и жесткий рентген), SOHO (оптика), TRACE (ультрафиолет) поражают воображение и меняют наши представления о физике явлений в солнечной короне. Резникова В.Э.1,2, Мельников В.Р.2,3 , Пятаков Н.П. 2 1Nobeyama Solar Radio Observatory/NAOJ, Nagano 384-1305, Japan 2ФГНУ НИРФИ, Нижний Новгород, 603950, Россия 3ГАО РАН, Санкт-Петербург, 196140, Россия

29. Influence of electron pitch-angle anisotropy on parameters of gyrosynchrotron emission

30. Gyrosynchrotron emission directivity The angular width of the emission beam:  ~ -1 = mc2/E

31. Influence of the electron distribution anisotropy on the frequency spectrum The angular width of the emission beam:  ~ -1 = mc2/E fmax  fB (E/mc2)2 For solar flare conditions, the broad band microwave emission are mainly generated by mildly relativistic electrons At low frequencies the beam is wide, and at the high fs it is large.  the anisotropydoes influence the emission spectrum

32. Observational evidence for electron pitch-angle anisotropy in a microwave GS source Radio waves’ Quasi-longitudinal propagation Quasi-transverse propagation Quasi-longitudinal propagation Differences in: - intensity, - spectrum and - polarization

33. Quasi-longitudinal Quasi-transverse Results of simulations:Electron pitch-angle distribution of the loss-cone type: • f2() ~ exp{-2/ 02} = cos(),  =B^V. •  considerable change of microwave parameters for the quasi-parallel propagation • ( =0.8): • Decrease of intensity; • Increase of polarization degree • Increase of the spectral index • (Fleishman & Melnikov 2003)

34. Quasi-longitudinal Quasi-transverse Results of simulations: Electron pitch-angle distribution of the beam type: • f2() ~ exp{-(- 1 )2/ 02} = cos(),  =B^V. •  considerable change of microwave parameters for the quasi-transverse propagation • ( =0.2): • Decrease of intensity; • Change of polarization degree to O-mode • Increase of the spectral index (Fleishman & Melnikov, ApJ 2003)

35. Заключение 1) Показано, что для разных характеристик источника электронов (положение области ускорения/инжекции в петле, тип анизотропии) можно получить сильно отличающиеся характеристики пространственного распределения интенсивности, поляризации и частотного спектра микроволнового излучения вспышечной петли. 2) Установлено, что эти отличия могут быть надежно зарегистрированы с помощью современных радиогелиографов сантиметрового-миллиметрового диапазонов и могут быть использованы для выбора наиболее подходящей модели ускорения, реализующейся в той или иной конкретной вспышечной петле. 3) Заложены основы нового метода диагностики положения области ускорения/инжекции в петле и типа анизотропии ускоренных электронов.

36. Спасибо за внимание!

37. References • Melnikov V.F., K. Shibasaki, V.E. Reznikova. "Loop-top nonthermal microwave source in extended flaring loops." - ApJ, 2002, V.580, pp.L185-L188 • Fleishman G.D. & Melnikov V.F. Gyrosynchrotron Emission from Anisotropic Electron Distributions - ApJ, 2003, V. 587, PP. 823–835 • Melnikov V.F. Electron Acceleration and Transport in Microwave Flaring Loops.In: "Solar Physics with the Nobeyama Radioheliograph", Proc. Nobeyama Symposium (Kiosato, 26-29 October 2004), Ed. K.Shibasaki, NSRO Report No.1, p.9-20, 2006 • Melnikov V.F., Gorbikov S.P., Reznikova V.E., Shibasaki K. Relativistic Electron Spatial Distribution in Microwave Flaring Loops. – Izv. RAN, ser.fiz., 2006, V.70, pp.1472-1474 • Gorbikov S.P., Melnikov V.F. Numerical solution of the Fokker-Plank equation for modeling of particle distribution in solar magnetic traps. - Mathematical Modeling, 2007, V.19, No.2, pp.112-123 • Reznikova V.E., Melnikov V.F., Shibasaki K., Gorbikov S.P., Pyatakov N.P., Myagkova I.N., Ji H. 2002 August 24 limb flare loop: dynamics of microwave brightness distribution. – ApJ, 2009, V.697, pp.735–746.

38. Аннотация Различные теоретические модели ускорения частиц в солнечных вспышках предсказывают различия в положении области ускорения и в типах питч-углового распределения ускоренных электронов. В данной работе проведено решение нестационарного кинетического уравнения Фоккера-Планка при различных предположениях о характеристиках инжекции энергичных электронов в магнитную петлю с тем, чтобы определить их пространственное, энергетическое и питч-угловое распределения и рассчитать соответствующие характеристики гиросинхротронного излучения. Показано, что для разных характеристик источника электронов (положение области ускорения/инжекции в петле, тип анизотропии) можно получить сильно отличающиеся характеристики пространственного распределения интенсивности, поляризации и частотного спектра микроволнового излучения вспышечной петли. Установлено, что эти отличия могут быть надежно зарегистрированы с помощью современных радиогелиографов сантиметрового-миллиметрового диапазонов и могут быть использованы для выбора наиболее подходящей модели ускорения, реализующейся в той или иной конкретной вспышечной петле. Приведены результаты диагностики, полученные на основе данных наблюдений Радиогелиографа Нобеяма.