Ограничения на модели ускорения электронов в...
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Ограничения на модели ускорения электронов в солнечных вспышках
Мельников В.Ф., Пятаков Н.П.
(ГАО РАН, ФГНУ НИРФИ)
ИКИ РАН, Конференция по физике плазмы в солнечной системе, 08 февраля 2010г)
2009 г.2009 г. 22
Particle Acceleration ProcessesParticle 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!
2009 г.2009 г. 33
Acceleration in a Acceleration in a Current Sheet Current Sheet
(X-type reconnection)(X-type reconnection)
Energy gained:
W = E x Lz
Large-scale electric field in Sweet-Parker current sheet
(e.g. Syrovatskii, 1976; Litvinenko & Somov, 1995; Somov & Kosugi, 1997;Shibata 2000- …)
InjectionInjection acrossthe loop axes
Loop top
Zharkova & Gordovsky: injection along the MFL???
2009 г.2009 г. 44
Betatron Acceleration in a Collapsing Betatron Acceleration in a Collapsing Magnetic TrapMagnetic Trap
across the loop axesacross the loop axes
(Bogachev and Somov, 2004(Bogachev and Somov, 2004; Karlicky, Kosugi, 2004); Karlicky, Kosugi, 2004)
2009 г.2009 г. 55
DC-Acceleration in Twisted Magnetic LoopsDC-Acceleration in Twisted Magnetic Loops
(Zaitsev, Urpo, (Zaitsev, Urpo, Stepanov 2000;Stepanov 2000;Zaitsev & StepanovZaitsev & Stepanov 20082008))
Acceleration along the loop axes
Acceleration can be in the loop top (due to prominence) or near a footpoint
Footpoint
Looptop
E
E
2009 г.2009 г. 66
Stochastic acceleration in micro-Stochastic acceleration in micro-current sheetscurrent 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)
2009 г.2009 г. 77
Are there any constraints from Are there any constraints from observations?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.
2009 г.2009 г. 88
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. cos
The loss-cone condition:
< arcsin (Bs/Bm)
2009 г.2009 г. 99
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):
f
E
cf
ds
Bdc
s
fc
t
f
0
2
2
1ln
),,,(1 223
0
tsESfc
Kinetics of Nonthermal Electrons in Kinetics of Nonthermal Electrons in Magnetic Magnetic LoopsLoops
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Initial and boundary conditionsInitial and boundary conditions
.0)0,,,( sEf
,0),,0,( min tsEf .0),,0,( max tsEf
Initial condition
Boundary condition, s
(precipitated electrons do not come back into the magnetic loop)
Injection function:
(no electrons at moment t = 0)
)/()( 01 EEES
constS )(2
]/)(exp[)( 20
213 ssssS
]/)(exp[)( 20
214 ttttS
In the case of isotropic injection:
]/)(exp[)( 20
212 S
),()()()(),,,( 4321 tSsSSEStsES
Different acceleration models give three basic predictions on
the position of the acceleration site and pitch angle distribution
homogeneous at the looptop near a footpoint
isotropic longitudinal perpendicular
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For illustration, consider transport effects on For illustration, consider transport effects on the example of two simple models: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.
2009 г.2009 г. 1313
Dynamics of the high energy electron Dynamics of the high energy electron distribution along a flaring loopdistribution along a flaring loop
s=0 corresponds the loop center. Injection is isotropic. Mirror ratio к=5. Plasma density n0=5*1010 cm-3 throughout the loop
Case 1: Injection at the looptop Case 2: Injection near the right footpoint
(Melnikov 2006; Gorbikov & Melnikov 2007)
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Dynamics of the pitch-angle distribution.Dynamics of the pitch-angle distribution.
Case 1: isotropic injection at the loop topCase 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 density n0=5*1010 cm-3 throughout the loop
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Evolution of the pitch-angle distributionEvolution of the pitch-angle distribution
Case 2: injection near a footpointCase 2: injection near a footpoint
looptop Leg 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
Properties of Gyrosynchrotron Emission from a Realistic
Radio Source
Taking into account: 1) influence of the enhanced plasma density on the energy
spectrum of trapped electrons and gyrosynchrotron emissivity, 2) influence of magnetic mirroring and change of the pitch-angle
distribution along a loop, 3) influence of electron pitch-angle anisotropy on the parameters
of GS emission, 4) influence of the magnetic loop curvature,5) Influence of inhomogeneities of magnetic field and plasma
density.
(Fleishman, Melnikov 2003;Melnikov, Pyatakov, Gorbikov 2006-2010)
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GS emission and absorption GS emission and absorption coefficients, exact expressionscoefficients, exact expressions
Calculations are done using Fleishman’s code
(Fleishman & Melnikov, ApJ 2003)
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Case 1Case 1 Case 2Case 2
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Radio brightness distributionRadio brightness distribution
CCase ase 11: Injection at the loop top: Injection at the loop top CCase ase 22: Injection near a footpoint: Injection near a footpoint
17 GHz
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Distribution of the optical depthDistribution of the optical depth
CCase ase 11: Injection at the loop top: Injection at the loop top CCase ase 22: Injection near a footpoint: Injection near a footpoint
Tau << 1
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Spatial profiles of brightness at 34 GHz at the burst Spatial profiles of brightness at 34 GHz at the burst maximummaximum
(Melnikov, Reznikova, Shibasaki, 2002, 2006)
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Brightness distribution dynamics, Brightness distribution dynamics, 24 August 2002 (main peak, 34 GHz)24 August 2002 (main peak, 34 GHz)
Reznikova et al. ApJ 2009 : Footpoint sources exist on the rise and peak phases, and even in the beginning of the decay phase.
2009 г.2009 г. 2323
Distribution of the polarization degreeDistribution of the polarization degree
CCase ase 11: Injection at the loop top: Injection at the loop top CCase ase 22: Injection near a footpoint: Injection near a footpoint
Ordinary mode circular polarization Signature of the longitudinal anisotropy
Increase in X-mode polarization degree signature of the perpendicular anisotropy
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Distribution of the spectral index (Limb Loop)Distribution of the spectral index (Limb Loop)
CCase ase 11: Injection at the loop top: Injection at the loop top CCase ase 22: Injection near a footpoint: Injection near a footpoint
Spectral steepening signature of the longitudinal anisotropy
Spectral flattening Signature of the perpendicular anisotropy
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Distribution of the spectral indexDistribution of the spectral index(solar disk, Theta = 45 deg)(solar disk, Theta = 45 deg)
CCase ase 11: Injection at the loop top: Injection at the loop top CCase ase 22: Injection near a footpoint: Injection near a footpoint
Spectral steepening Signature of the perpendicular anisotropy
Spectral steepening Signature of the longitudinal anisotropy
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High frequency spectral index variations along a High frequency spectral index variations along a loop.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
2009 г.2009 г. 2727
Радиопризнаки Радиопризнаки продольной питч-угловой анизотропии ускоренных ускоренных электронов во вспышечной петлеэлектронов во вспышечной петле
установлены недавно в работах:установлены недавно в работах:
1) 1) Altyntsev A.T.Altyntsev A.T. et al. (Astrophys. J. 2008, et al. (Astrophys. J. 2008, 677, p.1367))
2) Reznikova V.E. et al. (Astrophys. J. 2009, 2) Reznikova V.E. et al. (Astrophys. J. 2009, V.697, p.735))
2009 г.2009 г. 2828
Новый взгляд на СолнцеНовый взгляд на Солнце
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.
Microwave diagnostics of the position of an acceleration site and pitch-angle anisotropy of energetic electrons in
the flare 24 Aug 2002
Резникова В.Э.1,2, Мельников В.Р.2,3 , Пятаков Н.П. 2
1Nobeyama Solar Radio Observatory/NAOJ, Nagano 384-1305, Japan2ФГНУ НИРФИ, Нижний Новгород, 603950, Россия
3ГАО РАН, Санкт-Петербург, 196140, Россия
Influence of electron pitch-angle anisotropy on parameters of gyrosynchrotron emission
2009 г.2009 г. 3030
Gyrosynchrotron emission directivityGyrosynchrotron emission directivity
The angular width of the emission beam:
~ -1 = mc2/E
2009 г.2009 г. 3131
Influence of the electron distribution Influence of the electron distribution anisotropy on the frequency spectrumanisotropy 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 anisotropy does influence the emission spectrum
2009 г.2009 г. 3232
Observational evidence for electron pitch-angle Observational evidence for electron pitch-angle anisotropy in a microwave GS sourceanisotropy in a microwave GS source
Quasi-longitudinal propagation
Quasi-transverse propagation
Radio waves’Quasi-longitudinal propagation
Differences in:Differences in:- intensity, - intensity, - spectrum and - spectrum and - polarization- polarization
2009 г.2009 г. 3333
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)
Results of simulations:
Electron pitch-angle distribution of the loss-cone type:
Quasi-longitudinal Quasi-transverse
2009 г.2009 г. 3434
f2() ~ exp{-(- 1 ) 2/ 0
2}
= 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)
Results of simulations:Results of simulations:
Electron pitch-angle distribution of the beam type:
Quasi-longitudinal Quasi-transverse
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.
2009 г.2009 г. 3636
Спасибо за внимание!Спасибо за внимание!
2009 г.2009 г. 3737
ReferencesReferences
1. Melnikov V.F., K. Shibasaki, V.E. Reznikova. "Loop-top nonthermal microwave source in extended flaring loops." - ApJ, 2002, V.580, pp.L185-L188
2. Fleishman G.D. & Melnikov V.F. Gyrosynchrotron Emission from Anisotropic Electron Distributions - ApJ, 2003, V. 587, PP. 823–835
3. 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
4. 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
5. 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
6. 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.
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.