ALFVEN WAVE ENERGY TRANSPORT IN SOLAR FLARES

1. ALFVEN WAVE ENERGY TRANSPORT IN SOLAR FLARES Lyndsay Fletcher University of Glasgow, UK. RAS Discussion Meeting, 8 Jan 2010

2. Flare ‘cartoon’ It is clear that the energy for a solar flare is stored in stressed coronal magnetic field (currents). Unconnected, stressed field 1) Field reconfigures and magnetic energy is liberated via magnetic reconnection. 2) Energy transmitted to the chromosphere, where most of the flare energy is radiated (optical-UV). How does the energy transport happen? Post-reconnection, relaxing field - shrinking and untwisting Energy flux relaxed field – ‘flare loops’ Footpoint radiation, fast electrons, ions

3. Particle beams or waves? In the ‘standard’ flare model an electron beam accelerated in the corona transports energy to the chromosphere. Here we propose a wave-based alternative, motivated by the following: • Pre-flare energy storage => twisted field, so energy release => untwisting – i.e. an Alfvenic pulse. Consequences? • Earth’s magnetosphere provides an example of efficient particle acceleration by Alfven waves, generated in substorms. • Since the (1970s) it is clear that the corona contains insufficient electrons to explain chromospheric HXRs (Hoyng et al. 1973, Brown 1976). Overall flare beam/return currents electrodynamics in a realistic geometry is far from understood.

4. Flare energy requirements Flare total irradiance Power directly measured in the optical can be up to 1029 erg s-1 Power in fast electrons inferred from hard X-rays is around the same. flare Woods et al 2005 Flare energy = 6 x 1032 ergs over ~ 1000 sec. G-band (CH molecule) Flare energy radiated from a small area: HXR footpoints ≈1017 cm2, (WL footpoints can be smaller.) Isobe et al 2007 Fe (stokes I) Fe (Stokes V) Source FWHM = 5 x 107 cm Power per unit area ≈ 1011-12 erg cm-2

5. Flare electrons Flares are very good at accelerating and heating electrons. Radiation from non-thermal electrons is observed in the corona and chromosphere. So a wave model must also accelerate electrons. Krucker et al. 2008 Coronal X-rays imply≈ 1-10% of electrons are accelerated and decay approx. collisionally (e.g. Krucker et al 2008). Chromospheric X-rays require a ‘non-thermal emission measure’ cm-3 (e.g. Brown et al 2009)

6. Wave speed and Poynting flux The flare corona is quite extreme…. Coronal |B| deduced from gyrosynchrotron: Active region magnetic field strength at 10,000 km altitude (≈ filament height): ≈ 500 G average ≈ 1kG above a sunspot Brosius & White 2006 e.g. Lee et al (98) Brosius et al (02) Gyrosynchrotron emission (contours) above a sunspot Coronal density ~ 109 m-3  vA≈ 0.1 - 0.3c Transit time through corona = 0.1 – 0.3 s ‘Poynting Flux’ So flare power ≈ 1011 erg cm-2needs B ≈ 50 G (though note, reflection coeff ~ 0.7 initially) 10,000 km

7. MHD simulations of Alfven pulse propagation 3D MHD simulations of reconnection/wave propagation Diffusion region assumed small Track Poynting flux and enthalpy flux. (Birn et al. 2009) Sheared low-b coronal field, erupting x Inwards Poynting flux z Downwards Poynting flux Photospheric projection: Temperature (grey) Poynting flux (red) Time development of energy fluxes y=0 plane: ‘Poynting flux’ in x direction y = 0 plane ‘Poynting flux’ in z direction

8. Wave propagation in low-b plasma VAL-C In corona & upper chromosphere, vA≈ vth,ei.e., b≈ me/mp The wave has an EII and can damp by electron acceleration (e.g. Bian talk) b = me/mp T = 4 106 K T = 3 106 K T = 2106 K 1.0 T = 106 K Case of b << me/mp(‘inertial’ regime) requires k large - i.e. l≈ 3m to get acceleration to 10s of keV. (McClements & Fletcher 2009) 0.5 Accelerated fraction 1.0 3.0 5.0 l

9. Wave propagation in b ≥ me/mp plasma Case of b ≥ me/mp(kinetic regime): Wave can damp for larger transverse scales– order of rs = c/wpi Damping by Landau resonance (electron acceleration, Bian & Kontar 2010) – damping rate (s-1) is: (Bian) Sample values, assuming l|| = 100km So, still need to generate quite small transverse scales by phase mixing/turbulent cascade

10. Heating & acceleration in the chromosphere • Electron acceleration needs tacc < te-e • In chromosphere, electron heating first (c.f. Yohkoh SXT & EIS impulsive footpoints @ 107K, Mrozek & Tomczak 2004, Milligan & Dennis 2009) • electrons heat, tscattering increases, and non-thermal tail produced. • Electron acceleration timescale is that on which large k is generated, • e.g. by turbulent cascade: • Take lmax=10km, dB/B = 10%, vA = 5000 km/s then tturb≈ 0.02s • e.g. @107K, 1% of electrons have E > 5keV. • at 1011 cm-3 , 107K, 5keV electrons have te-e = 0.02s => acceleration. e.g. Lazarian 04

11. Electron number estimates Look at upper/mid VAL-C chromosphere: heating of chromosphere within 1/g(kinetic) = 1s T increases, tail becomes collisionless – within 1/tturb ~ 0.02s Non-thermal emission measure in chromosphere Accelerated fraction f ~ 0.01 ne ~ 1011 cm-3 nh ~ 1012 cm-3 (ionisation fraction ~ 10%) So volume V = 1025 cm3 If h = 1000km, needs A = 1017cm2 - similar to HXR footpoint sizes. A h Chromospheric accelerating volume

12. Conclusions During a flare, magnetic energy is transported through corona and efficiently converted to KE of fast particles in chromosphere. Proposal – do this with an Alfven wave pulse in a very low b plasma Small amount of coronal electron acceleration in wave E field Perpendicular cascade in chromosphere & local acceleration Overall energetics and electron numbers look plausible Many interesting questions concerning propagation & damping of these non-ideal (dispersive) waves in ~ collisionless plasmas. RAS Discussion Meeting, 8 Jan 2010 12