5 Model of loop-top hard X-ray emission source

 

Aschwanden et al. (1996b) notice that HXR light curves of many solar flares show two kinds of variability: the smoothly varying and the pulsed fine structure. They argued that the first component was generated either by coronal energy loss during trapping or by chromospheric emission after escaping (trap+precipitation). The pulsed component was produced by electrons precipitated directly without bouncing (direct precipitation).

The smooth and impulsive components were present in HXR light curves of flares investigated in the present paper, however the physical interpretation proposed by Aschwanden et al. (1996b) cannot be adopted. Because of their behind-the-limb location, any radiation of electrons that precipitated into the chromosphere was not seen by the HXT telescope. Therefore, we have to find another explanation of impulses in HXR light curves that are localized in the coronal part of flares.

All loop-top HXR emission sources occupied only a part of the coronal magnetic structures seen in soft X-rays. Following Tsuneta et al. (1997), I have calculated some characteristics of electrons generating the observed hard X-ray radiation. First, the column density, $N_{\rm s}$, needed to stop the non-thermal electrons that radiated within the channels L and M1 was estimated using the formula

$$N_{\rm s}\,=\,8.3~10^{17}\,E^2$$ (3)

where E[keV] is energy of electrons. On the other hand, the actual column density, $N\,=\,n_{\rm e}\,l$, was calculated. As l the longer size of the loop-top HXR emission source was taken from Table 4. The electron density, $n_{\rm e}$, averaged over the whole area of the loop-top HXR source was estimated from the SXT emission measure map. The obtained values of the ratio $N_{\rm s}/N$ are of about 5-100. This means that electrons should undergo this number of bounces within the loop-top area to be effective in HXR emission.

The above consideration shows that for the electrons emitting the observed hard X-rays a confinement mechanism is needed to keep the particles within the loop-top area where enhanced HXR emission was observed. A presence of a magnetic trap at the location of the loop-top HXR source seems to be the most probable explanation. However, a typically assumed explanation employing magnetic mirrors as a consequence of the magnetic field convergence can be used only for the loop-top HXR emission sources of type B. Tsuneta et al. (1997) proposed another scheme of the magnetic trap in which the mirrors are the two slow shocks attached to the reconnection X-point. This scheme can be adopted for some sources of type A in this paper. However, such a scheme needs the special overall magnetic structure which cannot be found in the all investigated events.

The turbulent flare kernel model (Jakimiec 1998; Jakimiec et al. 1998) offers another possibility to confine high-energy electrons in a small volume of the corona. In this model, an MHD turbulence develops by multiple magnetic field reconnections in a volume between three magnetic flux tubes (triple magnetic configuration) in the corona above an active region. The topological property of such a configuration leads to the cascade chaotization of the magnetic field inside the volume of the interaction - each magnetic field line being the result of a reconnection will meet a next field line with which it can reconnect. Finally, many transient current sheets will develop in which the magnetic energy will be dissipated very efficiently.

The magnetic field lines inside the turbulent kernel are tangled while the external magnetic field is laminar. Many reconnections decrease the internal field, since the external magnetic field should be somewhat stronger. Due to this and to the fact that inside the turbulent kernel the non-thermal electrons are transported mainly by turbulent motions, we obtain the very efficient mechanism of the confinement. The turbulence will continuously interact with the surrounding magnetic field. Each reconnection in the boundary layer temporarily opens the kernel. However, as estimated by Jakimiec (1999), thickness of the opening is of the order of 10¹-10² km. Hence the non-thermal electrons can easily escape only from the thin boundary layer of the turbulent kernel.

The energy released in the turbulent flare kernel heats and maintains a large amount of plasma at high temperature and accelerates a part of electrons to higher energies. In the SXR images we recognize such a place as the bright loop-top kernel, in the HXR images - as the loop-top emission source.

It will be shown that the loop-top HXR emission sources of type A can be treated as the turbulent flare kernels and that the application of this model allows to explain their features presented in Sects. 2 and 3. First of all, they were really turbulent, i.e., their SXR spectra obtained by the BCS showed significant non-thermal line broadening (Khan et al. 1995; Mariska et al. 1996; Mariska & McTiernan 1999). This has been verified for each investigated flare, with the exception of event No. 12 for which there is no BCS data. Moreover, the comment of Khan et al. (1995) that the end of the hard X-rays coincided with the time when the non-thermal line broadening stopped decreasing has found the confirmation for events from the present survey.

Since magnetic energy dissipation in the turbulent kernel occurs in many transient current sheets, it allows to expect that the energy release occurs in portions rather than in continuous way. Kliem et al. (1998) have shown that electrons can be very efficiently accelerated by the induced electric field near reconnection X-points. Since the thickness of the acceleration region is very small ($\sim$10¹-10² m), the number of electrons accelerated in a single current sheet is too low to generate the HXR flux that would be resolved as a separate impulse by the HXT telescope. Taking this into consideration we can explain the smooth and impulsive component in HXR light curves of the loop-top emission sources as follows. The smooth component is produced by overlapping spikes radiated by electrons that were accelerated in individual current sheets that occurred almost uniformly in time. Each impulse that has been resolved by the HXT is generated by a temporal accumulation ("cluster'') of current sheets. The presence of impulses shows that the occurrence of the current sheets in the turbulent kernel changes dynamically in time.

Some features of the loop-top HXR emission sources investigated in this paper allow to modify the turbulent flare kernel model. Considering the behind-the-limb location with occulted footpoints of the analyzed events, one can expect that HXR emission of electrons which have escaped from the turbulent kernel is lost, unless the magnetic mirror exists in the upper chromosphere. As was suggested before, it could be the case for the type B sources where an additional acceleration mechanism of electrons should be employed.

Analyzing the SXT temperature maps, Jakimiec et al. (1998) found that the temperature distribution is flat, i.e. $T \simeq {\rm const}$ at the central parts of the flare kernels. They concluded that the energy release is enhanced near the kernel edges where the turbulence interacts with the stronger, external magnetic field. The presence of impulses in HXR light curves for almost the whole duration of the loop-top emission sources proves that some portion of energy is released still inside the kernel, far from the boundary layer.