On the some problems of particle acceleration on the Sun and stars

1. On the some problems of particle acceleration on the Sun and stars A.Stepanov Pulkovo Observatory 10th Finnish-Russian Symposium on Radioastronomy Orilampi, Finland 1-5 Sep. 2008

2. OUTLINE of the TALK • Mechanisms of particle acceleration in astrophysics • Acceleration in DC-electric field • Particle injection into acceleration mechanism • Colgate paradox (problem of very high electric current) • Plasma turbulence and energetic particle propagation We will discuss these points in the frame of coronal magnetic loops – the fundamental structure of the solar atmosphere

3. TRACE and VLBA/VLA: magnetic loops are fundamental structures of coronae of the Sun and late type stars UV Ceti B (Feb 4,1996)VLBA/VLA at 3.6 cm.White circle ~ 0.8 milliarcsec The Sun

4. Artist impression of corona of Algol (Lestrade et al 1988) Magnetic fields around UV Ceti (Kellet et al 2002)

6. Parameters of flaring magnetic loops Parameter the Sun red dwarf ---------------------------------------------------------------- Loop length, L cm(1-10)109 2109 - 31011 Loop radius, r cm≥108 108 – 109 Plasma density, n cm-31010 - 1011 1010 - 1012 Plasma temperature, T K106 - 107 3106 – 108 Magnetic field, B G102 - 103 102 – 3103 Magnetic mirror ratio, 2 – 100 Alfven velocity, VA cm/s108≥ 108 Emission measure, EM cm-31047 - 1050 1050 - 1053

8. Mechanisms of charged particle acceleration in astrophysics • Fermi (first order) • Stochastic acceleration by waves (Fermi - second order) • Betatron acceleration, V^2/B = const • Magnetic pumping (Alfven) • Acceleration in shock waves • In DC-electric field - the most direct way

10. Fermi & Betatronacceleration in collapsing magnetic trap(Somov & Kosugi 1997; Karlicky & Barta 2004)

11. Disadvantages of collapsing trap model • No specific of distribution of accelerated particles were take into account in the integral of collisions. • No wave-particle interaction were take into account • Productivity of the mechanism ~ 10^28 – 10^29 el/s which is much less than revealed from hard X-ray data: ~ 10^35 – 10^36 el/s (Miller et al 1999) • Sui, Holman, Dennis (2008) TRACE & RHESSI: Most of impulsive HXR (>25 keV) emitted before the cusp was seen→ Electron acceleration predominantly occur before a casp is present

12. Stochastic acceleration in micro-current sheets (L. Vlahos, 2004) From one current sheet to millions Acceleration is preferably in the direction transverse to the magnetic field lines.

14. Electron acceleration by large-scale Alfven wavesFletcher & Hudson ApJ v.675 (2008)

15. Flare loop as an equivalent electric circuit Severny (1964): vertical currents I ~ 31011 A near sunspot Electric circuit approach: Alfven & Carlquist (1967): electric circuit analog of a flare Stenflo (1969), Spicer (1977), Ionson (1982), Zaitsev & Stepanov (1991), Melrose (1995),Wheatland & Melrose (1995), Zaitsev et al. (2000), Tan & Huang (2005)

16. Electric circuit model: Particle acceleration in DC electric fields From generalized Ohm’s law (Zaitsev, Urpo, Stepanov A&A 2000): , ξ= σF2/(2- F)c2nmiνia Number of runaway electrons per second (Knoepfel & Spong 1979): x = ED/E|| >>1, ED = mνeiVTe/eis the Dreicer field Under solar flare loop condition dN(>100 keV)/dt ≈ 1035 el/s forx = ED/E|| = 25. Electron and ions should be accelerated in opposite directions !

17. Size of Earth First Gamma-Ray Image of a Solar Flare23 July 2002 • Limb of Sun • Plasma in loops at ~2 106 K • 2.223 MeV gamma-rays from ions- centroid displaced by20 ± 6 arcsec from X-rays • X-rays at footpoints from electrons ~100,000 km

18. Hurford, Krucker, Lin et al (ApJ 2006)

19. RHESSI observationsblue: 50-100 keV, red: gamma emission(Kosovichev ApJ v.670, 2007)

20. Direction of linear polarization CORONAS-F:Solar Hard X-Ray Polarization Spectropolarimeter SPR-N Solar Flare October 29, 2003. 15-40 keV Background 20-40 keV 40-60 keV 60-100 keV 

21. Helioseismic responses to flaring high energy electronsKosovichev ApJ v.670 (2007) Flare of 2002 July 23 SOHO/MDI & RHESSI

22. Two problems of particle acceleration(Miller et al JGR,1999) (1) Acceleration rate dNe/dt≈ 1037el/s gives electron quantityNe(>20 кэВ) ≈ 1039. Bulk plasma in a loop must be in acceleration regime? Additional sources of particles: • Plasma of chromosphere • Prominence matter driver: ballooning instability (2) Even dNe/dt≈ 1035el/s gives current I≥ 1015A→ B≥106G Ways out: current filamentation? reverse current? Holman 1985; van der Oord 1990: Filaments (≥ 104) with opposite current direction

23. Lee &Sudan(Phys.Fluids 1971)Zaitsev & Stepanov (Phys.Uspekhi 2008) Bφ in front of electron beam is changed. Ez appears and produces current directed opposite electron beam (Lenz law).

24. Loop-loop interaction (Hanaoka 1999)

25. A&A 480 489 (2008)

26. Wave-particle interaction Consequences of turbulent propagation of energetic particles

27. Coronal loop as a magnetic mirror trap • Gyroradius of ~100 keV electrons rc = v/ωe≈ 10 cm • Mean free path of ~100 keV electrons lfr ≈ 1010-1011 cm • Loop typical scale ≈ 108 – 1010 cm Loss cone: no particles with (V┴/V││)2 < σ -1 → Anisotropy → A number of wave instabilities under cyclotron resonance condition:  - k V - sc= 0 Instabilities in coronal loops are important for energetic particle dynamics For quite powerful source of energetic particles the strong diffusion regime of particles on waves is realized,

28. Main effects of strong diffusionBespalov & Trakhtengerts (Rev. Plasma Theory,10,1980) • Particle distribution function is almost isotropic Pitch-angle diffusion rate is much large that the momentum diffusion rate (/)/(p/p)=(kp/m -1)>>1 because kp/mωc>> (Melrose 1980) • A particle interacting with small-scale waves stochastically changes its velocity direction, i.e. the particle motion along the loop axis can be described as diffusion. An anomalous viscosity appears resulting from wave turbulence and slowing down the particle motion. Therewith the particle propagation velocity is about the wave phase velocity

29. I. Consequences of strong diffusionSimultaneous acceleration:Time delay of gamma-ray vs HXR emissionBespalov, Zaitsev, Stepanov (ApJ. 1991) Propagation time of high-energy electrons: V is particle velocity, A is Alfven velocity, L is loop length, σ is mirror ratio Propagation time of high-energy protons:

30. III. Consequences of strong diffusion:Turbulent propagation of relativistic electronsStepanov, Yokoyama, Shibasaki et al. (A&A 2007) NoRH: ~ 1 MeV electrons generating gyrosynchrotron emission at 17 GHz propagate along loop axis with the velocity of about 104 km/s, which is 30 times less(!) than the light velocity. Reason: Electrons generate low-frequency whistlers and undergo strong resonant scattering. Emission front propagates with the wave phase velocity, which is much lower than particle velocity. “Turbulent wall” is formed and “turbulent “viscosity appears.

31. IV. Consequences of strong diffusion:Linear polarization in Hα emission of solar flares Impact polarization. Observations: • Firstova & Boulatov (1996) - 20% • Vogt, Sahal-Brechot, Henoux (2002) - 3-5% • Xu, Henoux, Chambe et al (2005) – 4% • Bianda, Benz, Stenflo et al (2005): Observations of 30 flares (July 4,2002 – October 28,2003) with ZIMPOL. GOES class:from С2.1 to Х17.1 All events were associated withhard X-rays (RHESSI), one of them (October 28,2003) in gamma-ray lines. Max linear polarization: 0.07% in 10’’×10’’ area during integration time of 40 s.

32. Vogt & Henoux (1996): No linear polarization if proton distribution function is isotropic ∂f/∂Ө = 0. Reasons for the absence of linear polarization (Bianda et al 2005): (1) Instability of Alfven waves driven by energetic protons and isotropization (Wentzel 1974) (2) Isotropization due to proton-neutral collisions. (3) Defocusing by the converging magnetic field (Bianda et al 2005): factors (2) and (3) are most important (?)

33. OUR MODEL (Stepanov & Tsap 2008) The main reason:Wave-particle interaction High-energy protons propagate toward loop footpoints and penetrate into the level of Hαemission Ion-cyclotron resonance: , ω = k||A High degree of particle isotropy is due to excitation of small-scale Alfven waves by protons and effective pitch-angle scattering of particles

34. Strong diffusion case Diffusion time of ~ 1 MeVprotonsτd= 5×10-3s << L/v ~ 1 s – time of free flight of flare loop with the length L ~ 109 cm. This is necessary condition for strong diffusion. Sufficient condition(Bespalov & Trakhtengerts 1980): Particle flux ≈ 5×1012pr/cm2s Solar flares: Acceleration rate of ~ 1 MeVprotons~ (1033 - 1034) pr/s(Miller et al 1997) for the loop cross section S~ 1017 cm2gives J~ (1016 – 1017) pr/cm2s >> J* In the case lower level of Alfven wave turbulence (BA2/B2 < 10-5) strong diffusion is not realized and Hαemission is linearly polarized

35. conclusions • Coronal magnetic loop – place of particle acceleration • To supply sufficient number of accelerated particles (≥ 10^38) additional injection in acceleration regime are needed • The sources of additional injection : chromosphere plasma and/or prominence matter • Various mechanisms work in flares, but acceleration in DC-electric field is the most direct way to gain particle energy • Wave-particle interaction plays important role in dynamics and emissions of high-energy particles in a loop