1. FLARING ENERGY RELEASE Lyndsay Fletcher University of Glasgow EPS Plasma Meeting, Sofia, June 2009 1

2. Overview Flare observations: fast electrons, radiation source characteristics Theoretical basics: Energy storage and release, ‘standard’ flare model, electron acceleration Challenges to the ‘standard’ model and a new idea Electron beams or Alfvén waves? Alfvén waves – preliminary calculations Conclusions 2

3. Solar magnetism and coronal activity Convective and rotational energy of solar interior is transferred to solar atmosphere via stressing of the magnetic field. Magnetic energy is dissipated in flares, leading to motion of the bulk plasma, heating and particle acceleration. 3

4. Electrons in flares Flare X-ray spectrum: e - - p + bremsstrahlung Green: hot plasma (Fe emission lines) Red : 12-25keV (thermal X-rays) Blue : 25-50keV (nonthermal X-rays) Movie: Peter Gallagher Movie: Gordon Holman As much as 50% of all the flare energy released goes into accelerating electrons (Emslie et al ‘04, ‘05) These electrons 4

5. Flare Radiation Flare in total solar irradiance Flare energy = 6 x 10 25 J Woods et al 2005 X-rays are important diagnostics, but flare radiation is mostly optical/UV (lines & continuum), from compact sources. In some large flares this is visible in the integrated brightness. flare G-band (CH molecule) Fe (stokes I) Fe (Stokes V) Isobe et al 2007 Spatially resolved observations Source FWHM = 5 x 10 5 m Power ~ 10 22 WPower per unit area ~ 10 9 W m -2 5

6. Flare footpoints Typically two strong hard X-ray footpoints. HXR and optical emission are spatially and temporally correlated Orange = HXR Blue = optical grey = Hard X-ray black= optical Fletcher et al. 2007 Krucker et al. 2008 Non-thermal electrons collide in chromosphere, heat and ionise to produce the optical/UV. 6

7. Energy storage Energy is stored in the coronal magnetic field, as currents. Magnetic reconnection allows magnetic field to reconfigure to a lower energy state. Red = location of strong currents (Schrijver et al 2008) Before flareAfter flare Pre-flare currents stored less than 12,000 km above photosphere, concentrated around polarity inversion line. Magnetic field and current distribution 7

8. Energy release and eruption 8 Török & Kliem 2005 There are many models for a flare eruption. Most involve a driven ideal MHD instability followed by a resistive instability e.g. Kink instability Twisted field embedded in overlying field (green) Kink instability embedded in an overlying field (green)

9. The ‘standard’ flare model 2D ‘standard model’ Ejected plasmoid Slow shock Upward reconnection outflow Reconnection region Reconnection inflow Reconnection outflow (turbulent) Stand-off shocks Slow or fast shock Post-flare loops Ribbons/footpoints electron beams The observations are interpreted in a framework called the standard flare model 1) Magnetic energy liberated via magnetic reconnection. 2) Electrons accelerated in corona carry flare energy to the chromosphere. 3) Most of energy radiated by chromosphere (opt-UV). 4) Chromosphere is heated and expands into corona  dense, hot flare loops. 9

10. Electron acceleration in the corona L~10 7 m E or.. 1) Acceleration in reconnection E 2) Stochastic acceleration in turbulent E Liu et al 2008. There are two main models for coronal acceleration: (Shock acceleration of flare electrons not thought so likely) High efficiency, low volumeLow efficiency, high volume 10

11. Coronal electrons Krucker et al. 06 Coronal source volume ~ 3 × 10 21 m 3 11 Pre-flare coronal electron density is ~ 10 15 m -3 Coronal X-rays flux implies ~ 1-10% are accelerated to >20keV (energetically, non-thermal electrons dominate thermals).

12. Chromospheric electrons: standard model Accelerated electrons originate in corona. Electron beam travelling along coronal B carries flare energy to chromosphere UV, opt., HXR chromosphere accelerator electrons 10 35 - 10 36 electrons/s accelerated. Coronal n e = 10 15 cm -3, so each second, all electrons in V = 10 20 - 10 21 m 3 accelerated. Holman et al 03 Time (mins) Electrons in the chromosphere 510 15 0 12 July 23 2003 Photon spectrum Source-averaged electron spectrum

13. Electron number and current Standard model beam rate is ~ 10 36 el. s -1 (leaving corona) Beam area from HXR and optical is < 10 13 m 2 Beam flux ~ 10 23 el. m -2 s -1 Beam speed v beam ~ 1-2 × 10 8 m s -1 (electrons at 30-100 keV) Beam density n beam ~ few × 10 14 m -3 (large fraction of n corona ) Self field ~ 10 4 T (~ 10 5 - 10 6 x ambient) Return current n beam v beam = n corona v rc So v rc ~ few × 10 7 ms -1 c s = 3×10 5 ms -1 and v th,e ~ 1.2 ×10 7 m s -1  beam instability. 13

14. Energy transport in our magnetosphere Following substorm reconnection, energy stored in the Earth’s magnetic field propagates as Alfvén waves. - Cascades to small k  - Generates field-aligned electric field which accelerates auroral electrons. (e.g. Chaston et al. 2008) - Energy ultimately dissipates in the ionosphere Could there be an analogous process in flares? 14

15. Flare energy transport by Alfvén pulse Before the flare, energy is stored in twisted magnetic field. Field reconfigures, twist redistributes and energy is released Wave pulse carries energy as Poynting flux Nb. twist greatly exaggerated in this cartoon. 15

16. Wave speed and Poynting flux 10,000 km |B| measured from gyrosynchrotron emission: Typical magnetic field strength at 10,000 km altitude: ~ 0.05T (500 G) average over region ~ 0.1T (1kG) above a sunspot Brosius & White 2006 Pre-flare coronal density ~ 10 15 m -3  v A ~ 0.1c – 0.3c Observed chromospheric output = 10 9 W m -2 Needs a wave Poynting flux with  B ~ 0.006T (60G ) Gyrosynchrotron emission (contours) above a sunspot 16

17.  v th in flare corona and upper chromosphere So waves are in ‘inertial’ regime and generate an E || where For typical solar k || and k , the E || is small. But if || ~ 100 km,  ~ 10 km then E || > Dreicer field and electrons can be accelerated. Electrons unable to surmount wave potential barrier reflect and are energised to 2mv A 2 ~ 25 - 100 keV. Inertial Alfven waves 17

18. Electron acceleration in a shear pulse Uniform equilibrium with B = (0,0,B 0 ), electric potential  = 0. Shear wave perturbation in magnetic potential A is Solutions: 18 Modification for electron inertia Choose: giving (McClements & Fletcher 2009)

19. T = 4  10 6 K T = 3  10 6 K T = 2  10 6 K T = 10 6 K Calculate fraction of initially Maxwellian electrons reflected by this pulse and accelerated: n e = 10 15 m -3, B 0 = 0.1T,  B = 0.01T Accelerated fraction and distribution T = 4  10 6 K T = 3  10 6 K T = 2  10 6 K T = 10 6 K  x = 3m, initially Maxwellian Electron distribution in this simple case does not look like the observed power-law. Can try spatially varying plasma and field properties, and broader spectrum wave pulse. 19

20. MHD simulations of wave propagation 3D MHD simulations of reconnection in coronal field Diffusion region assumed small Poynting flux and enthalpy flux tracked. Sheared low-  arcade, erupting y=0 plane: Poynting flux in x direction y = 0 plane Poynting flux in z direction Photospheric projection: Temperature (grey) Poynting flux (red) x z (Birn et al. 2008) 20

21. Wave dissipation in the chromosphere Ion-neutral damping is strong in low chromosphere  heating and WL, UV production (Emslie & Sturrock 82) Also with higher viscosity and higher gradients, a (perpendicular) turbulent wave cascade may develop as wave pulse crosses chromosphere.  stochastic electron acceleration in the chromosphere? (e.g. Hamilton & Petrosian 1992). e.g. Transit time acceleration optimal when v A ~ v th,e, which happens in upper chromosphere. 21

22. Conclusions During a flare, stored magnetic energy is distributed through corona and efficiently converted to KE of fast particles. Flare ‘standard model’ does a pretty good job at providing a framework for the whole flare phenomenon. However, theory of energy transport by electron beams runs into some trouble compared with recent observations. Proposal – energy transport by Alfven wave pulse Much remains to be worked out…. Electron acceleration in wave E field? Pulse dissipation in chromosphere & local acceleration? 22