3 Estimates of physical parameters

3.1 Plasma parameters

3.1.1 Magnetic field

The general structure of magnetic field before the flare can be seen in Fig. 8. Fujiki (1997) has shown that the pre-flare emission at 17 GHz for the series of flares including the event of November 2, 1992 was optically thin and had free-free origin. The observed averaged degree of polarization ($\simeq\! 5\%$) leads us to an estimate of the line-of-sight component of magnetic field $B_{\rm l} \simeq 150$ G.

At 03:07, a bright SXR kernel was located inside the dome-shaped microwave source. In the bright SXR kernel, plasma density was $n\leq 4\ 10^{11}$ cm^-3, and temperature was $1.4\ 10^7$ K (Feldman et al. 1995). Demand for magnetic pressure to exceed the plasma one leads us to a limitation of $B\geq 200$ G in the SXR kernel in the second stage of the flare.

We assume that the emission of the burst around the peak had gyrosynchrotron origin as it is usual for this spectral range. The power-law spectral index at 02:57:25 obtained from data of 35 and 80 GHz radiometers of Nobeyama Radio Observatory, was 1.5, and the power-law index of the electron spectrum, was 3. Fit of the microwave spectra with the help of Ramaty's code (Ramaty 1969; Ramaty et al. 1994) shows that the magnetic field of 200 G is rather low to fit the turnover frequency of more than 17 GHz. Sufficiently good fit of the total flux data can be achieved with B=300-800 G (Nakajima & Metcalf 1995).

Low degree of polarization of the 17 GHz source (as a rule, less than $10\%$)near the peak of the burst shows that the magnetic field did not exceed a few hundred gauss. Hence we believe that the value of the magnetic field was about the lower boundary of this range (300 G).

3.1.2 Density of background plasma

The observed spectra do not reveal any marks of suppression of emissivity at frequencies down to 3.75 GHz. So we can obtain the upper limit of the background plasma density in the main microwave source assuming that the Razin-Tsytovich frequency $\nu =\frac{\nu _{\rm p}^2}{\nu _B}$ was less than 3.75 GHz. This upper limit equals to $4\ 10^{10}$ cm^-3.

Another estimate of the background plasma density can be obtained from the decay time of the emission at 17 GHz (4.1 min) within the interval 03:12 - 03:22. As we will show below, the bulk of emitting electrons had the energy of about ${\cal E} \sim 2$ MeV in this time interval. We assume that the decay time was equal to the life time of electrons. We can estimate the energy loss time from the expression (Bai & Ramaty 1976)

$T_{\rm loss}=2.6 \ 10^9 \, {\cal E}/n .$

Then the background plasma density was $n\!=\!2.1\, 10^{10}\,{\rm cm}^{-3}$which is in accordance with the estimate from the Razin-Tsytovich effect.

3.1.3 Emitting electrons

To analyse parameters of emitting electrons, we used Ramaty's code (Ramaty et al. 1994) for modelling of gyrosynchrotron emission. Changing the energy boundaries of electron distribution and correlating the calculated spectrum with the observational data, we estimated the energy range of electrons that radiated the bulk of the observed microwave emission.

The turnover frequency during the exponential growth was about 9 GHz, and the flux before the rapid rise (at 02:47) was 450 s.f.u. at 9.4 GHz and 58 s.f.u. at 35 GHz. So the spectral slope was the same as that around the peaks which were considered above, and then the spectral index of electrons was equal to 3. For the size of the upper source of $\simeq 20^{\prime \prime }$ and the magnetic field of 300 G, the Ramaty's code gave the estimate of the distribution of non-thermal electrons as ${\rm d}N/{\rm d}{\cal E}=1.3\ 10^{30}\, {\cal E}^{-3}$ MeV^-1. The main contribution to the observed microwave emission was given by electrons with energy in the range of 0.1-3 MeV.

The modelling of the electron distribution in the main dome-like source in the second stage (source size $37^{\prime \prime }$) showed that the shift of the turnover frequency to a value above 17 GHz was connected with the increase of ${\rm d}N/{\rm d}{\cal E}$ by more than two orders of magnitude in the energy range of 0.5-5 MeV. This source became optically thick for the emission of 5.7 GHz.

The upper source above the dome-like one was observed clearly in 1d-scans at 5.7 GHz during the interval with spikes recorded by SSRT. The turnover frequency in this source was considerably less than 17 GHz, and the number of high-energy electrons in it must be considerably less than that number in the main dome-like source.

In the last stage, the main sources at 5.7 GHz and at 17 GHz differed essentially in time profiles, emission spectrum and height.

The main source at 5.7 GHz was located at a height of about $10\ 10^3$ km. At the frequencies below 9.4 GHz, it manifested itself in a series of sub-bursts with a magnitude of tens s.f.u. occurred till 05:40. The spectra had a turnover frequency of $\leq 3.75$ GHz. This source had a gyrosynchrotron origin. It appeared at 17 GHz during the most powerful sub-burst at 04:12 as a radially elongated source.

The main 17 GHz source was close to the soft X-ray one in the decay phase. The values of the flux increased with frequency, which points to free-free emission mechanism. The brightness temperature was $(3-5)\ 10^6$ K at 17 GHz. Plasma parameters in the emitting SXR region were estimated by Ichimoto et al. (1993) and Feldman et al. (1995) from Yohkoh/SXT data. They have obtained for the bright kernel a temperature of 10⁷ K, a density of 10¹¹ cm^-3, and a size of 10⁹ cm. The corresponding calculated value of the brightness temperature for free-free emission, $T_B=3\ 10^6$ K, agrees with the observed one.

3.2 Sub-second pulses

For the first time, we have found a 17 GHz source of sub-second pulses to be located well above the photosphere. The source size $<7\ 10^3$ km. The time profiles of the observed sub-second pulses show simultaneous onset at the lower frequencies. Assuming that the duration of signal's rise (0.6 s) was equal to the propagation time with Alfvèn velocity ($4.6\ 10^8$ cm s^-1 using the ambient density of $2.1\ 10^{10}$ cm^-3 and the magnetic field of 300 G) across the region of energy release, we obtain that its size was about $2.8\ 10^3$ km. This estimate does not contradict the apparent size of the microwave source.

The microwave spectrum had a maximum in the frequency interval of 5.7-9 GHz. The degree of polarization for the pulses was a few percent. The simultaneous enhancement of the total flux at 5.7-17 GHz can be interpreted in terms of gyrosynchrotron emission of non-thermal electrons. At the peak of the pulse, the power-law index estimated from the ratio of the flux at 9.4 and 17 GHz, was about 2, and the electron spectrum was harder than that one of the background burst.

For the source size of $2.8\ 10^3$ km and the magnetic field of 300 G, the observed microwave flux corresponded to a small density fraction of accelerated electrons with ${\rm d}N/{\rm d}{\cal E}=5\ 10^{28}\,{\cal E}^{-2}$ MeV^-1. To emit the observed flux at 17 GHz, the upper cutoff energy of the electron spectrum must be $\geq 2$ MeV. With the typical energy of radiating electrons of 1-2 MeV, the observed duration of the decay at this frequency was much less than the life time due to Coulomb collisions ($\sim 10^2$ s using the ambient density of $2.1\ 10^{10}$ cm^-3). Since the observations suggest that the electrons were accelerated and confined in a small region high in the corona, these processes were controlled not by Coulomb collisions, but by other mechanisms such as some plasma turbulence. This fine time structure may be indeed a manifestation of a fragmented energy release in a flaring site (see, e.g., Benz 1986).

Another situation was for sub-second pulses at 5.7 GHz occurred in the source above the dome-like one. There was no corresponding brightening at the other frequencies, so the bandwidth of the emission must be rather narrow. A detailed description of these pulses was made by Altyntsev et al. (1995). The size of the source of these pulses appeared to be $\simeq \! 50^{\prime \prime }$. It was found that the apparent size of the source was affected by a significant scattering of the microwave emission at this frequency due to turbulent inhomogeneities of plasma density. (It certainly could affect the observed sources at 5.7 GHz.) From the low degree of the observed polarization and rather high magnetic field needed for electron cyclotron maser mechanism, a conclusion was made that a plasma emission mechanism is favourable. In this case plasma density in the source must exceed 10¹¹ cm^-3.

From the study of similar pulses observed during the flare of September 6, 1992 occurred on the solar disk (Altyntsev et al. 1998), it has been shown that the source was projected onto a loop emitting soft X-rays with sufficiently high density. In the limb flare of November 2, 1992, we see that the dense SXR loop-top was located inside the optically thick dome-like source, and the sub-second impulsive source was much higher. The estimate of plasma density in the dome-like source was $\sim\! 2.1\ 10^{10}$ cm^-3. If the plasma density in the surroundings of the impulsive source was of the same order, then, to realize the density of $\geq 10^{11}$ cm^-3, the background plasma in the impulsive source must be compressed a few times. Such a compression is reasonable for a reconnection site, where the energy release occurred.