Astron. Astrophys. 356, 1067-1075 (2000)

4. Discussion

The 1991 March 13 HXR/GR impulsive flare at 08:00 UTC exhibits two successive HXR and microwave bursts referred to as B1 and B2 in Sect. 3. During the whole event, the H emission arises from four kernels (N1, N2, S1 and S2 in Fig. 2). Although the power deposited in the chromosphere by the HXR producing electrons is about thirty times larger during B2 than during B1 (see Table 1), the relationship between the temporal evolutions of the fast H emission and the HXR count rate is found to be the same for each H kernel during both B1 and B2. The intensity time profile of a given H kernel is indeed well represented by a linear combination of two components which evolves on different time scales, i.e. the HXR count rate which varies on 1 s to 10 s time scales and its time integral which smoothly increases with time. This analysis only concerns the H emission observed during both B1 and B2 which appear as two separated HXR bursts above 73 keV. However, observations made by the ULYSSES /GRB instrument indicate that the 25 keV HXR emission shows a plateau between B1 and B2, like H, and a gradual burst which lasts for 7 to 8 minutes after the end of B2 (K. Hurley, private communication). This suggests that the H emission may be also related to the HXR emission between B1 and B2 and after B2. Further analysis is needed to investigate if such a relationship is similar to that described by Eq. 1.

The excellent agreement of the observed H intensity time profile with that modelled with Eq. 1 strongly suggests that H results from energy transport by non-thermal electrons during both B1 and B2. The measurements of tangential linear polarization of the H line during the impulsive part of some HXR bursts support this conclusion (Vogt & Hénoux 1999). However, Vogt & Hénoux (1999) pointed out that low energy protons mirroring in a converging magnetic field could also produce the observed polarization. If this would be the case, our results would imply a close synchronism ( 1 s) between the acceleration of 500 keV protons and 73 keV electrons.

A quantitative interpretation of the present results would need: (i) soft X-ray imaging observations which provide constraints on the model atmosphere of the different loop systems, such as the time evolution of temperature and emission measure; (ii) hard X-ray imaging observations in order to estimate which fraction of the accelerated electrons is injected towards each kernel and (iii) measurements of the H line profile in order to identify the different physical processes which contribute to the formation of H at different chromospheric depths. In the following we thus consider that H is produced by non-thermal electrons and we qualitatively discuss our findings in the framework of the conventional non-thermal thick-target model which has successfully explained various radiative signatures of non-thermal electrons including HXR, microwaves and H (e.g. Canfield & Gayley 1987; Pick et al.1990; Miller et al 1997 and references therein)

4.1. Magnetic field structure

In the non-thermal thick-target model, electrons are accelerated in the corona near the top of loops with sizes ranging typically from a few 10³ km to a few 10⁴ km. The HXR thick-target emission and the H kernels are produced at the feet of the loops into which electrons stream from the coronal acceleration region to the chromosphere. Thus, the H kernels, whose time histories are correlated to the HXR time profile, materialize the feet of loop systems connected to the acceleration region. During the flare under study, the existence of four kernels overlying opposite polarities of the photospheric magnetic field suggests that four loop systems are involved: LS11, LS12, LS21 and LS22 which connect N1 to S1, N1 to S2, N2 to S1 and N2 to S2 respectively. Taking the distance between kernels overlying fields of opposite polarities as typical sizes of the different loop systems we obtain approximately 10⁴ km, 1.7 10⁴ km and 2.5 10⁴ km for LS11, LS12 and LS21 and LS22 respectively. The magnetic structure into which electrons are accelerated and in which they interact to produce the observed HXR, microwave and H emission appears thus to be complex as each kernel is associated to two loop systems. Such a complexity is also revealed by the shape of the microwave spectrum as emphasized in Sect. 3.2. Moreover, it should be remarked that the increase of the number of accelerated electrons from B1 to B2 is associated with an expansion of the different loop systems (Sect. 3.2). This suggests that an increase of the flaring loop size is associated with an increase of the number of accelerated electrons.

4.2. The slow H response

For each of the four kernels, the slow H response is found to be proportional to the time integral of the HXR count rate that is, to the time integral of the power deposited by the non-thermal electrons in the associated thick-target HXR emitting source. The values of the coefficients of proportionality, = /, are given in Tables 3 and 4 for B1 and B2 respectively. Such a contribution to the H time profile has not yet been explicitly incorporated in models (e.g. Canfield & Gayley 1987; Heinzel & Karlický 1992) which simulate the H response to non-thermal electron beams. For most impulsive HXR bursts, it has been shown that the time history of the time integrated HXR count rate closely matches the rising portion of the soft X-ray emission (the so-called Neupert Effect) i.e. of the thermal bremsstrahlung from the hot loop plasma (e.g. Neupert 1968; Dennis & Zarro 1990). The cause of this behavior has been interpreted in various ways which all include heating of the loop plasma by the accelerated electrons (e.g. Brown 1971; Syrovatskii & Shmeleva 1972) or by accelerated electrons and and some other agent such as electric fields which simultaneously accelerate the electrons (e.g. Holman et al.1989) or turbulence (e.g. Lee et al. 1995). Processes leading to density enhancements of the loop plasma such as chromospheric evaporation may also play a role (e.g. Li et al. 1993). This indicates that, for the studied event, the slow H response to non-thermal electrons is partly due to some continuous heat flux from the corona to the chromosphere as was suggested by Gräter (1990) for other flares. Although the H kernels are at the feet of loop systems of different sizes and the energy content in electrons is much higher during B2 than during B1, the coefficients do not vary much from one kernel to the other and from B1 to B2. Such a result is quite surprising because the slow H response of a given kernel is expected to depend both upon which fraction of the non-thermal electrons has been injected in each loop system, and upon the dynamical response of the atmosphere which is probably different from one loop system to the other.

Table 3. The cefficients = / and = / obtained from the application of Eq. 1 to the H observations during B1

Table 4. Same as Table 3 for B2

4.3. The fast H response

The fast H response of a given kernel is found to be proportional to the time profile of the HXR count rate that is, to the time evolution of the power supplied by the accelerated electrons to the thick-target HXR emitting source associated with this kernel. The values of the coefficient of proportionality = / are given in Tables 3 and 4 for B1 and B2 respectively. During B1 the coefficients are about the same for the four H kernels, the response of N1 being slightly, but significantly, stronger than that of the other kernels (see Table 3). The situation is quite different during B2. For both injections of electrons the strongest responses are obtained for N2 and S2 while the response of S1 during the first injection and that of N1 during the second one are weak (see Table 4). Because N1 (resp. S1) are common feet of LS11 and LS12 (resp. LS11 and LS21) it is suggestive that the fast response of the smallest loop system (LS11) is the weakest. Here again, the available data do not allow us to estimate which fraction of the energy transported by the electrons is deposited in each kernel because the model atmosphere associated to that kernel is unknown. The simplest, very crude, assumption is to consider that the atmosphere model is nearly the same for all kernels. Our results would then indicate that:

• during B1 the four kernels receive about the same flux of non-thermal energy. Taking 20 arcsec² for the typical kernel area (see Fig. 2) and the value of P₂₀ given in Table 1 the energy flux deposited by 20 keV electrons in each kernel is 7 x 10¹¹ ergs cm^-2 s^-1.

• during B2 the energy is predominently transported along the larger loop systems and the energy flux deposited by 20 keV electrons in N2 or S2 is 1 x 10¹² ergs cm^-2 s^-1 and 2-3 x 10¹³ ergs cm^-2 s^-1 for the first and second injections respectively.

This latter statement is supported by the fact that during B2 the microwave emission arises predominently from the larger loop systems (see Sect. 3.2). We thus conclude that the differences in the fast H responses of the four kernels from B1 to B2 are due, at least partly, to changes of the relative numbers of electrons which propagate in the different loop systems. It should be noted that energy transport takes place preferentially in the larger loop systems with a larger number of accelerated electrons.

The close similarity between the time profiles of the HXR count rate and of the fast H response of each kernel is qualitatively in agreement with the results of models by e.g. Canfield & Gayley (1987) and Heinzel & Karlický (1992). Indeed, these models indicate that H should be an excellent tracer for the time evolution of the power deposited by accelerated electrons in the chromosphere, that is of the HXR rate for thick-target interactions. Moreover, the initial response to intense beam variations is generally expected to be more rapid than the electron transit time from the acceleration region, so that the shortest time scales of H variations are governed by the shortest time scales of the HXR emission. For the H line center, these short time scales should be associated to the rises of fast HXR variations (Canfield & Gayley 1987). For the present flare, the shortest variations of the HXR rate can only be studied during B1 where the HXR measurements were obtained with a 1 s time resolution ( 200 ms). As an example Fig. 5 displays the time profiles of the fast H emission of N1 (largest ) and of the 73 keV HXR count rate during B1. The H emission tracks the HXR count rate, the coefficient of cross-correlation being 0.84 for a 0 0.5 s lag. The HXR emission exhibits significant pulses with rise times ranging from 0.4 s to 1.5 s as it is generally observed for most impulsive bursts (e.g. Aschwanden et al. 1995; Vilmer et al. 1996). The H emission also shows time structures with similar rise times. Although some of these fast H variations are probably due to remaining seeing effects. there is a clear correspondence between HXR and H pulses. In particular, HXR pulses marked a, b, c and d on Fig. 5, correspond to fast rises of the H emission. This is also the case for the other kernels (see Fig. 4 left panel) except may be for N2 (lowest ). Fig. 5 also shows that H seems sometimes to rise 300 to 500 ms later than the HXR emission. Such a small delay, which is not expected from the models, may not be real and may just reflect that the time profiles of both emissions exhibit successive pulses which partially overlap. Because the H response to a HXR pulse (single electron beam) is generally expected to last longer than the HXR pulse (see Fig. 2 in Canfield & Gayley 1987), the observed onset of a fast H rise will be occasionally detected after that of the corresponding HXR rise. So far, models generally consider a single magnetic loop and a single electron beam which turns on instantaneously and whose energy flux ( 10¹² ergs cm^-2 s^-1) is much smaller than those involved in the present event, with the computed H emission strongly depending on the parameters describing both the loop and the beam. Thus the expectations from these models should not be compared in details to the present findings which have been obtained for a flare where several loop systems are involved and where the electron injection function shows a complex time evolution. Nevertheless our results, in particular the correspondence between HXR and H pulses with 1 s rise times, basically agree with the essential features of the models.

Fig. 5. Time evolution of the fast H intensity response of kern el N1 and of the 73 keV HXR rate during B1. HXR peaks marked a, b, c and d have corresponding ones in H (see text).

© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000
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