The study of the spatial distribution of the synchrotron emission by mildly relativistic electrons (gyrosynchrotron) has a long history. Both loop-top sources and double sources located close to the conjugate magnetic footpoints were reported (Marsh and Hurford, 1982; Kundu et al., 1982; Kawabata et al., 1983). The comparison with theoretical simulations of the gyrosynchrotron brightness distribution along model magnetic loops (see Bastian et al., 1998, for a review) strongly suggests that the distribution of mildly relativistic electrons along an extended flaring loop must be highly inhomogeneous: accelerated electrons are concentrated in the upper part of the loop (Nindos et al., 2000; Melnikov et al., 2002). Some of the centimeter loop-top emissions were observed in the late phase of flares (e.g., Karlický, 2004). They are not related to the main energy release, but possibly to high-energy X-rays detected late in flares (Krucker, personal communication) and possibly the end stage of the spectral hardening observed in non-thermal X-rays (see Section 5.2). The investigation of the acceleration region using gyrosynchrotron emission has greatly profited from combination with hard X-rays. It may result in the measurement of the magnetic field in loop-tops in future work.
Benz et al. (2007) found some coherent radio emission in all flares larger than C5 class, except near the limb where absorption seems to play a role. While there is good association between coherent radio emission and X-rays, correlation in details of the time profile is less frequent. Thus coherent emissions cannot expected to be reliable tracers of the main flare energy release in general. Emissions at higher frequencies, such as decimetric narrowband spikes, pulsations, and stationary type IV events appear to be more directly related to the acceleration process. The association but loose correlation between HXR and coherent radio emission may be interpreted by multiple reconnection sites connected by common field lines, along which accelerated particles may propagate and serve as a trigger for distant accelerations. Thus coherent radio emissions may be interesting diagnostics in special cases.
Correlation of coherent radio emissions with hard X-rays (or gyrosynchrotron emission) has been reported for spikes and pulsations (Slottje, 1978; Benz and Kane, 1986; Aschwanden et al., 1990; Kliem et al., 2000). If these coherent radiations are emitted at the second harmonic of the plasma frequency – the usual assumption – the density of the source region is in the range from 109 cm–3 to a few times 1010 cm–3. This range is a possible indication for the density in the acceleration region. Although initially interpreted as loss-cone emissions of trapped particles near footpoints, they have been found at high altitudes, consistent with loop-tops (Benz et al., 2002; Khan et al., 2002; Kundu et al., 2006). As the emission mechanism of spikes and pulsations is not well understood, the origin of the radiating high-frequency waves cannot be further investigated.
Best candidates for direct emission from the acceleration region are small clusters of narrowband spikes around 300 MHz, reported to correlate in detail with electron beam emission (type III radio bursts). About 10% of all meter wave type III groups are accompanied with spikes near but slightly above the start frequency (Benz et al., 1982). The spikes are concentrated in the spectrogram on the extrapolation of the type III bursts to higher frequency. More precisely, as suggested by Figure 19, metric spikes are located on the extension of type III trajectories, supporting a model of energy release in or close to the spike sources (Benz et al., 1996). If this is the case, radio observations can approximately locate the acceleration region for the type III electrons and measure the electron density of the acceleration region (Section 3).
Type IV emissions occur late relative to the hard X-ray peak and appear to be connected to some late-phase acceleration (Švestka et al., 1982; Klein et al., 1983). They may be related to delayed electron releases of interplanetary electron events in the corona (Klein et al., 2005).
Some radio emissions (like type III and V) are due to electrons escaping from the acceleration region. Hard X-ray flares are associated with meter-wave type III bursts in 33% of all cases, and in 4% of them type III bursts are the exclusive radio emission. Type III emission is caused by electron beams becoming unstable towards growing electrostatic plasma waves at the local plasma frequency. These waves are converted into radio waves slightly above the plasma frequency ,ne is the electron density, e the elementary charge, and me the electron mass. Type III emission thus occurs at a frequency that varies with the local density. Observed at many different frequencies, it can be used to trace the path of the electron beam in the corona. Different beams following different trajectories diverging from the acceleration region have been used to locate the acceleration region (Figure 19). The distance from this region to the start of type III emission depends on the energy spectrum of accelerated electrons (Benz, 2002, p. 32). Future interferometers observing at many frequencies will refine this method.
A major constraint by radio emission on particle acceleration is the fact, that in 15% of larger flares ( C5.0 class) there is no coherent radio emission except some electron beam emitting at very high altitude (Benz et al., 2007). Whether coherent radio emission is necessarily emitted or not, is therefore an observable criterion for the validity of acceleration models. The frequent lack of direct radio emission from the acceleration region suggests that the acceleration is “gentle”, excluding significant deviations from a Maxwellian velocity distribution, such as a monoenergetic beam. The deviations only build up after the non-thermal electrons have traveled some distance and the faster particles have outpaced the slower particles, or after a loss-cone results from magnetic trapping. Gentle acceleration favors acceleration by diffusion in velocity space as predicted by stochastic acceleration (Section 6).
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