Possibilities for constraining acceleration models from microwave observations

Transcription

1 IX RHESSI workshop (1-5 September 2009, Genova) Possibilities for constraining acceleration models from microwave observations Melnikov, V.F., (Pulkovo Astronomical Observatory; Nobeyama Solar Radio Observatory)

2 Plan of the talk 1. Motivation: Why the position of the acceleration site and pitchangle anisotropy of accelerated electrons are important? 2. Basic effects useful for the microwave diagnostics: Influence of the pitch-angle anisotropy on characteristics of GS emission; Transport effects of electrons in a magnetic loop. 3. Modeling: Electron distributions GS-emission distributions 4. Conclusion 2009 г. 2

3 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! 2009 г. 3

4 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 Loop top (e.g. Syrovatskii, 1976; Litvinenko & Somov, 1995; Somov & Kosugi, 1997; Shibata ) Zharkova & Gordovsky: injection along the MFL??? 2009 г. 4

5 Betatron Acceleration in a Collapsing Magnetic Trap across the loop axes (Bogachev and Somov,, 2004; Karlicky, Kosugi,, 2004) 2009 г. 5

6 Acceleration in the Termination Shock along the loop axes (Miteva et al,, 2009, this RHESSI workshop) 2009 г. 6

7 DC-Acceleration in Twisted Magnetic Loops (Zaitsev, Urpo, Stepanov 2000; Зайцев, Степанов, УФН 2008) E Looptop Acceleration along the loop axes Acceleration can be in the loop top (due to prominence) or near a footpoint E Footpoint 2009 г. 7

8 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) 2009 г. 8

9 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 г. 9

10 Influence of electron pitch-angle anisotropy on parameters of gyrosynchrotron emission

11 Influence of the electron distribution anisotropy on the frequency spectrum The angular width of the emission beam: θ ~ γ -1 = mc 2 /E f max f B (E/mc 2 ) 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. 11

12 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 2009 г. 12

13 Results of simulations: Quasi-longitudinal Quasi-transverse Electron pitch-angle distribution of the loss-cone type: f 2 (μ) ~ exp{-μ 2 / μ 02 } μ = cos(ϕ), ϕ =B^V. considerable change of microwave parameters for the quasi-parallel propagation (η =0.8): - Decrease of intensity; - Increase of polarization degree - Increase of the spectral index (Fleishman & Melnikov 2003) 2009 г. 13

14 Results of simulations: Electron pitch-angle distribution of the beam type: Quasi-longitudinal Quasi-transverse f 2 (μ) ~ exp{-(μ- μ 1 ) 2 / μ 02 } μ = cos(ϕ), ϕ =B^V. considerable change of microwave parameters for the quasitransverse propagation (η =0.2): - Decrease of intensity; - Change of polarization degree to O-mode - Increase of the spectral index (Fleishman & Melnikov, ApJ 2003) 2009 г. 14

15 Transport effects μ = cosθ What types of anisotropic distributions in different parts of a flaring magnetic loop are expected for various models of acceleration/ injection? The loss-cone condition: θ < arcsin (Bs/Bm) 2009 г. 15

16 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,μ,s,t), and also on time (Melnikov et al. 2006; Gorbikov and Melnikov 2007). Non-stationary Fokker-Plank equation (Lu and Petrosian 1988): f t f = cβμ s + d cβ ln B ds 2 1 μ μ 2 f + c λ 0 E f β + + c ( 1 μ ) + S( E, μ, s, t) г. 0 μ μ λ β γ 16 f

17 Initial and boundary conditions Initial condition f ( E, μ, s,0) = 0. (no electrons at moment t = 0) Boundary condition, s f ( E, μ > 0, smin, t) = 0, f ( E, μ < 0, smax, t) = 0. (precipitated electrons do not come back into the magnetic loop) Injection function: S 1( E0 E) = ( E / ) δ S E, μ, s, t) = S1( E) S2( μ) S3( s) S ( t), ( S2 ( μ) = exp[ ( μ μ1) / μ0 ] 2 S3( s) = exp[ ( s s1 ) / s 2 S4 ( t) = exp[ ( t t1) / t ] ] In the case of isotropic injection: S 2 ( μ) = const 2009 г. 17

18 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

19 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 г. 19

20 Dynamics of the high energy electron distribution along a flaring loop Case 2: Injection near the right footpoint Case 1: Injection at the looptop s=0 corresponds the loop center. Injection is isotropic. Mirror ratio к=5. Plasma density n 0 =5*10 10 cm -3 throughout the loop (Melnikov 2006; Gorbikov & Melnikov 2007) 2009 г. 20

21 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 density n0=5*10 10 cm -3 throughout the loop 2009 г. 21

22 Evolution of the pitch-angle distribution Case 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 2009 г. 22

23 Case 1 Case г. 23

24 Magnetic field strength and viewing angle distributions along the loop 2009 г. 24

25 Radio brightness distribution Case 1: : Injection at the loop top Case 2: : Injection near a footpoint 17 GHz 2009 г. 25

26 Discovery of looptop microwave sources in optically thin part of the frequency spectrum Kundu et al 2001 Melnikov et al 2002 Statistical results: Martynova, Melnikov, Reznikova 2006 Tzatzakis, Nindos, Alissandrakis г. 26

27 Spatial profiles of brightness at 34 GHz at the burst maximum (Melnikov, Reznikova, Shibasaki, 2002, 2005) 2009 г. 27

28 Statistics of brightness distribution at 34 GHz 17 N = 21 N = фаза роста фаза максимума фаза спада два основания одно основание вершина Martynova, Melnikov, Reznikova г. 28

29 Brightness distribution dynamics, 24 August 2002 (main peak, 34 GHz) Reznikova et al. ApJ г. 29

30 Influence of electron pitch-angle anisotropy on the distribution along the loop of the polarization degree and local spectral index of gyrosynchrotron emission New methods of direct diagnostics of the injection/acceleration site and mechanism (Melnikov, Gorbikov, Pyatakov 2009)

31 Distribution of the polarization degree Case 1: : Injection at the loop top Case 2: : Injection near a footpoint 2009 г. 31

32 Gyrosynchrotron emission polarization properties Looptop Footpoint Case 1 (injection in the loop top) Looptop Footpoint Case 2 (injection near a footpoint) 2009 г. 32

33 Distribution of the spectral index Case 1: : Injection at the loop top Case 2: : Injection near a footpoint 2009 г. 33

34 Gyrosynchrotron emission spectral slope properties Looptop Footpoint Case 1 (injection in the loop top) Looptop Footpoint Case 2 (injection near a footpoint) 2009 г. 34

35 Summary of microwave emission properties Case 1, Injection at the looptop: Electrons The shape of the spatial distribution does not change much with time. During all the burst phases the distribution remains anisotropic perpendicular to magnetic field lines. Near footpoints the anisotropy degree increases on the decay phase. Microwaves At frequencies where a source is optically thin, there is a peak of the microwave brightness distribution at the looptop; the spectrum slope is steeper near footpoints; polarization is X-mode everywhere in the loop. Case 2, Injection near a footpoint: The shape of the spatial distribution changes with time dramatically: from peaks near footpoints to a single peak at the looptop. Such a distribution produces two well pronounced radio brightness peaks near the footpoints in the rise and maximum phase of a burst, and a single peak at the looptop in the decay phase of a radio burst. Oblique pitch-angle distribution at the looptop leads to the O-mode polarization from the looptop!!! 2009 г. 35

36 Conclusions Consideration of pitch-angle, energy and time distributions of mildly relativistic electrons in different parts of a single magnetic loop on the basis of the non-stationary Fokker-Planck equation show that GSproperties depend very much on the position of the electron injection site in the magnetic flaring tube. It is shown that spatially resolved microwave observations are able to provide us with new knowledge on acceleration sites, energy, and pitch-angle distributions of accelerated electrons in flaring magnetic loops. As a consequence they may provide us with new constraints on particle acceleration mechanisms and models. Building new radio instruments with high spatial, spectral and temporal resolution is crucially important for solving the key problems in the physics of solar flare particle acceleration. VLA NoRH FASR, SSRT, CSRH 2009 г. 36

37 Thank You! 2009 г. 37