Ограничения на модели ускорения электронов в солнечных вспышках

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

2009 г.2009 г. 1010

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

2009 г.2009 г. 1212

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)

2009 г.2009 г. 1414

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

2009 г.2009 г. 1515

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)

2009 г.2009 г. 1717

GS emission and absorption GS emission and absorption coefficients, exact expressionscoefficients, exact expressions

Calculations are done using Fleishman’s code

(Fleishman & Melnikov, ApJ 2003)

2009 г.2009 г. 1818

Case 1Case 1 Case 2Case 2

2009 г.2009 г. 1919

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

2009 г.2009 г. 2020

Distribution of the optical depthDistribution of the optical depth


Tau << 1

2009 г.2009 г. 2121

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)

2009 г.2009 г. 2222

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


Ordinary mode circular polarization Signature of the longitudinal anisotropy

Increase in X-mode polarization degree signature of the perpendicular anisotropy

2009 г.2009 г. 2424

Distribution of the spectral index (Limb Loop)Distribution of the spectral index (Limb Loop)


Spectral steepening signature of the longitudinal anisotropy

Spectral flattening Signature of the perpendicular anisotropy

2009 г.2009 г. 2525

Distribution of the spectral indexDistribution of the spectral index(solar disk, Theta = 45 deg)(solar disk, Theta = 45 deg)


Spectral steepening Signature of the perpendicular anisotropy

Spectral steepening Signature of the longitudinal anisotropy

2009 г.2009 г. 2626

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.

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Ограничения на модели ускорения электронов в солнечных вспышках