3. Second Time Structure of the Solar Flare

[19]  The solar flare on 29 October 2002 began at 2147:02 UT by a sharp increase in the count rate in the energetic channels of the hard X-ray range 15-160 keV and slightly later (at 2148:49 UT) by a more smooth increase in the energetic channels of the soft X-ray range 2.9-14 keV. The flare emission was registered in all 64 channels of these energy ranges of the device. However, for increasing the statistical significance of the results of the data processing, the count rate of 32 channels of the hard X-ray range was reduced to the count rate in five broader energy ranges: 15 -24, 24-42, 42-77, 77-110, and 110-160 keV. The count rate in 32 channels of the soft X-ray range was reduced to the count rates in the ranges: 2.9-3.6, 3.6-5.0, 5.0-7.9, 7.9-11, and 11-14 keV. At the time profiles of the considered flare shown in Figures 3a and 3e for the summed channels of the hard X-ray range and for the summed channels of the soft X-ray range, respectively, complicated structures with pulse duration of 3-5 s are clearly seen. The structures appear on the background of larger pulses with duration of about 10 s. In the 110-160 keV energy range one can see also even larger variations of the X-ray emission flux about 20 s long.

2006GI000139-fig03
Figure 3
[20]  For the detailed analysis of the time structure of the X-ray emission of the flare on 29 October 2002, the modified spectral analysis method (the results of which are presented in detail in Figure 3) was, as in the case of the description of the fine time structure, applied to the series of both soft and hard X-ray emission.

[21]  The CSPs for the count rate in the 15-24 keV channel, as the more informative out of 5 summed channels, and for the filtered out high-frequency components with the values of the parameter TF = 7, 13, 17, 23, 37, and 43 s for the preflare and postflare time intervals are presented in Figures 3b and 3d, respectively. The same pictures for the flare with the values of the parameter TF = 7, 11, 13, 17, 19, and 23 s is shown in Figure 3c. The first CSP shows the normalized spectral density as a function of the "test'' period of the preflare stage 2.2 min long. The resolution of the periodogram is 0.25 s, that is, 4 points fall on one small tick of the scale, so the periods in the periodograms presented are determined with the accuracy of one quarter of a second. At this stage the most powerful component with a period of about 20 s and several weaker components with periods of 4.5, 6.5, 9.5 and 12.5 s should be mentioned. During one minute of the further beginning and development of the flare, the structure of the emission changes: there appear a component with the period of 3.5 s which by his power exceeds almost by a factor of 2 the oscillations with periods of 5, 7, 9 and 13 s, whereas the most powerful component of the preflare stage disappears. At the postflare stage 5 min long, almost all the above mentioned components are left, but the shape and structure of the periodogram changes strongly: almost all components are split to two and more components having peaks much narrower by the half width than at the previous stages of the event. The major part of the emission energy is concentrated in the region of small periods (in the more high-frequency part of the spectrum), that is, the spectrum shape becomes similar to the shape of the spectrum of "purely'' noise signal.

[22]  At the preflare stage, one can reveal periodical components with periods of 6 (the strongest), 12, 18, and 20.5 s (Figure 3f) in the soft X-ray emission 3.6-5.0 keV (Figure 3e). A very strong component with the period of 9.5 s appears during the flare, whereas the periods of other components differ from the preflare ones by 1-1.5 s (Figure 3g).

[23]  Summarizing the results of the performed spectral analysis, one may say that during a flare, unlike during the preflare situation, periodical components with the periods of 10-20 s can appear (in our case it is 3.5 s (Figure 3c) and 9.5 s (Figure 3g)).

[24]  Let us consider the mechanism of MHD wave oscillations, which can explain the observed periodicities. For numerical estimates, let us propose that the loop length L=1.3times 1010 cm, plasma temperature is 10 MK in preflare and postflare time intervals and 25 MK in the flare, typical altitudes of the loop tops is h=L/p = 4times 109 cm, electron density n varies in (1-10)times 109 cm-3 range and magnetic field B=(10-100) G, the average loop width was found to be a=3.5times 108 cm [Aschwanden et al., 2000]. Then the following apply:

3.1. Standing Fast MHD Waves.
[25]  The oscillation period of fast "sausage'' mode may be calculated according to [Edwin and Roberts, 1983]: ts = 2pa/ck approx 6.4(a8(n9)1/2/B1) s, ck is phase speed, a8=atimes 10-8, n9=netimes 10-9 and B1=B/10. For typical parameters of flare loops the calculated period belongs to the range tsapprox (2-70) s. For the fast "kink'' mode the oscillation period depends on the number of nodes j along the loop [Edwin and Roberts, 1983]: tk = 2L/jck approx 205(L10(n9)1/2/B1) s. Thus the period oscillation tk varies from approx 27 to 810 s.

3.2. Standing Slow MHD Waves
[26]  The oscillation period of this mode is t slow = 2L/jcT approx 1300(L10/(T6)1/2) s [Edwin and Roberts, 1983]. For typical parameters t slow approx (320-520) s.

3.3. Propagating MHD Waves
[27]  According to calculations [Roberts et al., 1984] the time period of oscillation is t prop approx 3.8(a8(n9)1/2/B1)approx ts s.

[28]  It is clear that shot time oscillation could be explained by standing fast MHD waves or propagating MHD waves.

[29]  The same oscillations during the solar flares were observed in radio wave range [Melnikov et al., 2002] and in the soft X rays [Asai et al., 2001], explaining by fast sausage MGD oscillations at the fundamental harmonic [Aschwanden et al., 2004].

AGU

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