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| Figure 2 |
[8] Figures 2b, 2c, and 2d present particular fragments of the event with the time resolution of 10 ms and duration of 1 s each. The fragments were chosen in the following way: at the preflare stage of the event (Figure 2b), in the moment of the event (Figure 2c), and at the postflare stage when the flare has already ended in the hard X-ray range (Figure 2d) (24-160 keV); that is, the value of the registered flux of the quanta returned to the preflare level, whereas in the soft X-ray range (2.9-14 keV) the flare still continued.
[9] Figure 2b shows that the structure of the preflare radiation
consists of several pulses with the duration from 10 to 30 ms
determined at half maximum of their amplitude. Profile of each
pulse contains from 3 to 6 points of initial registration of X-ray
flux. If all pulses with the amplitudes exceeding the
s level of
the signal are numerated in Figure 2b from left to right, then,
for example, the width of the first pulse is
DT 
20 ms, the amount
of points is 4, for the third pulse the width is
DT 10 ms, the
amount of points is 3, for the eighth pulse the width is
DT 30 ms,
the amount of points is 6 and so on. The maximal value of the
pulse amplitude is
6 counts for 10 ms, the averaged amplitude is
2 counts for 10 ms. The sequence of pulses most likely is random,
because no regularity in their appearance is seen in Figure 2b.
During the flare parameters of single pulses do not alter (Figure 2c). They
have the same averaged duration, the same character of
appearance. Only their amplitude changes approximately two times
(on an average the maximal value of amplitude comprises 12 counts
for 10 ms above the averaged value of the count rate). At the same
time the averaged value of signal grows 7 times (14 counts in 10
ms). After the flare the count rate returns to its preflare value
(Figure 2d).
[10] While considering the statistics of the value of pulse amplitudes
compared with the standard normal distribution, we see that for
the preflare stage the level of
2s is exceeded only by 3 pulses
(3% compared with 5% for normal distribution), and the level
corresponding to
s
only by 12 pulses (12% compared with 32% for
normal distribution). Quite clear it is not enough to declare that
some determinative component with the characteristic timescale
20-30 ms is present in the initial signal (periodicity and so
on). On the basis of this statistics we may conclude that the
sequence of these elementary pulses is a random process, like
"white'' noise. Similar picture is observed at the postflare
stage of the event (Figure 2d). Here the level of a signal
2s is
exceeded only by 2 pulses from 100 (2%), and the level
corresponding to
s, by 14 pulses from 100 (14%) compared with 5%
and 32% for normal distribution correspondingly. Completely
different situation is observed during the flare (Figure 2c). Here
the level
2s is exceeded by 12 from 100 pulses (12%), which is
more than for the normal distribution. It points out that during
the flare a "nonrandom'' component appears in the measured count
rate which is seen in Figure 2c as a "wave-like'' variation in
the averaged count rate (which is
7 times higher than in the
preflare or postflare periods). The typical timescale of this
wave-like perturbation comprises from 280 ms (if this value is
determined by minimal values of the count speed for the sequence
of pulses presented in Figure 2c) up to 380 ms (for maximal
values).
[11] It is well known that the millisecond pulse structure is observed not only in hard X-ray emission but also in radio emission, where the duration of single pulses comprises from several to several hundred of milliseconds and depends on the frequency of observation [Droge, 1967; Guedel and Benz, 1990; Meszarosova et al., 2003; Magdalenic et al., 2006]. For example, during the investigation of the spikes of the IV type during the solar flare of class C1.1, that took place at 0934 UT on 15 April 2000, there were registered pulses with the duration 10-20 ms, and for the flare at 1437 UT on 15 April 2000 (M1.1) there were registered pulses with the duration 4-30 ms [Magdalenic et al., 2006]. So the duration of spikes registered in hard X-ray radiation on 29 October 2002 are comparable with the minimal duration of spikes registered in the radio frequency range. That is why they can be probably considered as a consequence of the magnetic field annihilation and particle acceleration.
[12] For the detailed analysis of the time structure of X-ray emission of the considered fragments of the given event, we used a modified method of the spectral analysis. The modification of the traditional spectral analysis method was the following. A sampling estimate of the normalized spectral density [Jenkins and Watts, 1972] for the initial time series was calculated depending not on the frequency, but on the test period, this step being due to the formulation of the problem on looking for concealed periodicity in the initial data. Moreover, the initial time series underwent preliminary high-frequency filtration [Alavi and Jenkins, 1965] with the given frequency of the "cut off'' of the filter at the half of the signal power to which the value of the "separating'' period TF corresponds in the time region. The filtration of the initial data was conducted in order to eliminate out of them the trend and more powerful low-frequency components. Then again the estimate of the normalized spectral density as a function of the period was calculated for each high-frequency component (with its particular value of TF ). All these estimates calculated for the initial time series and each high-frequency component with various values of the TF parameter were overlapped upon each other on the same field of a figure forming "combined'' spectral periodogram (CSP).
[13] Such modification of the common method of the spectral analysis makes it possible to study a stability of the position of the revealed period in the periodogram, that is, independence of the detected value of the concealed periodicity of the parameters of the initial time series what are able to influence the processing method applied. The modification makes it also possible to find in the initial signal shorter periods with small values of the amplitudes. The latter happens due to elimination from the initial signal of the trend and more powerful long-period components which provide the main input into the signal dispersion. That is why only weak short-period components contribute to the dispersion of the filtered high-frequency component of the signal. Because of the normalizing of the spectral power, the input of these components into the combined periodogram becomes of the same order as the input of more durable and powerful components of the signal.
[14] The results of the spectral analysis of separated time fragments with a resolution of 10 ms and duration of 10 s each at various stages of the considered event are shown in Figures 2e, 2f, and 2g (where Figure 2e is the spectrum at the preflare stage, Figure 2f is the spectrum for the flare maximum, and Figure 2g is the spectrum for a postflare fragment of the event).
[15] As it follows from spectrograms presented in Figures 2e, 2f, and 2g for the background and for the flare radiation, the spectrum of the signal for the probe period from 30 to 250 ms consists of numerous closely packed peaks in this interval with high porosity and approximately the same intensity. Such shape of the spectral density is similar to the noise signal like white noise. The shape of this part of spectrum confirms the random distribution of elementary pulses presented in Figures 2b, 2c, and 2d. So it is possible to discuss the presence of the quasiperiodic components only in case when the duration of the probe period exceeds 250 ms. For such interval of probe periods the analysis of the spectrogram presented in Figures 2e, 2f, and 2g displays quasiperiodic components with the characteristic periods of the order of several hundred milliseconds. Seven curves of spectral density for each fragment are obtained for seven different values of parameter TF (that describes frequency-time filter), the eighth curve is obtained for the initial signal.
[16] For intervals of the probe periods exceeding 250 ms at all stages
of the event quasi-periods with durations
0.41,
0.54,
and
0.63 s are present. Analyzing these spectrograms, one should consider
not separated peaks corresponding to particular harmonic
components, but their groups separated from each other by larger
intervals than peaks in each of the considered groups. The
obtained results show that such groups in the structure of the
spectral density most probably are due to a "phase
nonstationarity'' of the main harmonic components of the initial
signal (one to each such group) but not by the presence of
multiple stable harmonics close enough to each other in frequency.
At all stages of a flare the values of these quasiperiodic
oscillations remain the same. Only their relative contribution in
energy (dispersion of the signal) is changed. While during the
preflare stage the quasi-harmonic 0.63 s dominates, at the
postflare stage harmonics 0.42 s and 0.54 s are more pronounced.
As these harmonic components are present at all stages of a flare,
probably they relate to the background component of hard X-ray
radiation and do not characterize the flare radiation. From the
other side it follows from Figure 2f that during the flare the
harmonic with the period 0.35s appears, that is present in
spectrograms related to preflare and postflare radiation. Hence
this harmonic component is created during the flare process. This
harmonic is clearly seen as a modulation of elementary pulses in
Figure 2c.
[17] Now we consider briefly the main possibilities of interpretation
of such fine time structure of the hard X-ray emission. Currently,
out of the discussed mechanisms of quick energy release, the
processes related to the "tearing'' mode of magnetic field
reconnection [Kliem, 1994; Somov and Vernetta, 1989; Sturrock,
1966] are the most accepted. The swinging time of the long-wave
tearing mode is determined by the time of diffusion of the
magnetic field into the reconnection region and by the Alfven
velocity. The evaluation of the energy release time as a result of
a tearing instability gives about 0.5 s, if the plasma parameters
in the flare region correspond to the mean values of the
parameters of the coronal plasma: the concentration of particles
is
1010 cm-3, temperature is
2
106 K, induction of the magnetic
field is 200 G, and the characteristic width of the current layer
is
7 103 cm [Kliem, 1994]. On the other hand, the tearing
instability leads to a formation of separate filaments in the
current layer. The filaments being adjacent are able to
"coalesce'' and provide by that a release of the most part of the
energy of the current layer [Pritchett and Wu, 1979]. The
characteristic time of "coalescence'' of current filaments for
the conditions in the solar corona shown above is from 0.2 to 2 s
[Pritchett and Wu, 1979], i.e., is of the same order of magnitude
as the tearing instability. Both these process (filaments
coalescence and tearing instability are mutually related and lead
to "pulse'' reconnection of magnetic fields [Kliem, 1994; Tajima et al., 1987]. The latter determines the modulation of the process
of electron acceleration at subsecond times, the electrons
"emitting'' then in the hard X-ray range.
[18] Now we come to a discussion of the time and spectral characteristics of the flare on 29 October 2002, measured by the IRIS device in the Splash regime with the second time resolution.
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