Conditions of Electron Acceleration by Magnetic Reconnection During Solar Flares

1. Conditions of Electron Acceleration by Magnetic ReconnectionDuring Solar Flares Gottfried Mann and Alexander Warmuth Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany e-mail: GMann@aip.de RHESSI‘s aim: How are electrons accelerated up to high energies (> 30 keV) within a fraction of a second? Aim of the talk: To study the conditions of the generation of energetic electrons without making any assumptions about the acceleration mechanism.

2. RHESSI Results 1138 photon spectra obtained in 18 flares (C5.5 – X17.2 GOES class) are converted into spectra of injected non-thermal electrons by a forward-fitting method as developed by Holman et al. (2003)

3. The Standard Model – Magnetic Reconnection (Carmichael 1964, Sturrock 1996, Hiroyama 1974, Kopp & Pneumann 1976) (or CSHKP-model)  filament becomes instabil  it is rising up  a current sheet is establisted  magnetic reconnection takes place

4. Radio Results pairs of forward and reversed drift bursts The starting frequency corresponds to the X-point of magnetic reconnection. fx = 360 ± 58 MHz (16% deviation) (see Fig. 12 in Aschwanden et al. 1995) • remarks: • fx: 272-955 MHz • fx < 532 MHz (F-emission) • fx > 532 MHz (H-emission) • fmax = 532 MHz according to a four-fold Newkirk (1961) model

5. Radio Results II • X-point: • Ne = 1.61 ·109 cm-3 • hx = 60 Mm • B = 20 G • acceleration region: • (by means of TOF measurements, • see Aschwanden 2002) • hacc = 20 Mm • Ne = 2.66 ·109 cm-3 • B = 104 G •  vA = 4400 km/s • wpe/wce = 1.6 • (compare with Sakai‘s PIC code • simulations !!!) • by means of •  4-fold Newkirk (1961) density model • magnetic field model by Dulk & Mc Lean (1978)

6. Budget of Energetic Electrons I  inflowing electron flux  inflowing energy flux  the energy density consists of magnetic thermal kinetic energy energy energy of the inflow with

7. Budget of Energetic Electrons II plasma parameters in the inflow region (at ) special scales: (diameter of the hard X-ray sources) flux equations:

8. Budget of Energetic Electrons III(moderate flares) input: because of: The energetic electrons carry a substantial part of the whole flare energy. (see Lin & Hudson 1971, 1976; Emslie et al. 2004)

9. Budget of Energetic Electrons IV(large flares) input: because of:

10. Discussions summary: moderate flares: large flares: outflow speed: because of: ( : diameter of loop-top-sources) The outflow jet has velocities of 2400 km/s and 15000 km/s for moderate and large flares, resp., i.e., it is almost super-Alfvénic. The transistion of super-Alfvénic flow into a sub-Alfvénic one leads necessarily to a shock formation (see Tsuneta & Naito, 1998).

11. Results •  The acceleration takes place in regions with large Alfven speeds • of about 2200 km/s. •  In the acceleration region, there are typical electron number densities • of about 2.1 · 109cm-3 and magnetic fields of about 46 G leading to a • ratio between the electron plasma and the electron gyro-frequency of 3.2. • Only few percent of the electrons are accelerated up to energies > 30 keV, but they carry a substantial fraction of the incoming energy. • In the case of large flares, only a fast inflow leads to the flux and power of accelerated electrons as requested by RHESSI observations. • A fast inflow also leads to a fast outflow jet with Alfven-Mach numbers of about 4. If all these conclusions are accepted, then: Is there really a „number problem“ ? ATTENTION ! All these values should be regarded as rough estimates, i.e. within an error of  20 %.