A search for fast variations in the Fe XXI emission was made for ten flares using the Fourier analysis. Three examples were described. The main results are summarized

Cheng, Chung-Chieh

English

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N87-21811
A SEARCH FOR FAST VARIATIONS
IN THE Fe XXI EMISSION DURING SOLAR FLARES
Chung-Chieh Cheng
E.O. Hulburt Center for Space Research
Naval Research Laboratory
Washington, DC 20375-5000
ABSTRACT. The main results are: I) No periodic oscillation in Fe XXI
emission detected. 2) The shortest timescale of rapid variation persistently
present in the Fe XXI emission is about 20 sec. 3) Statistically significant
isolated bursts of duration 3 to 5 sec are present in some of the flares.
I. INTRODUCTION
Observations have shown that the intensity of soft X-ray bursts from solar
flares varies smoothly with a gradual rise and decay time profile. The
timescales of soft X-ray burst variations range from minutes to hours. On the
other hand, the impulsive hard X-ray bursts typically show fast variations and
spiky time structures, with timescales as short as one tenth of a second
(Hoyng et al., 1976; Kiplinger et al., 1983). Since the soft X-ray burst is
generally regarded as the result of energy transfer from the hard X-ray
electrons, either by direct heating or by the process of chromospheric
evaporation, it is of interest to ask whether the fast variations observed in
the impulsive hard X-ray burst are in any way reflected in soft X-ray bursts.
Studies of the Fe XXV and Ca XIX emissions in solar flares obtained from the
P78-I (Doschek, Kreplin, and Feldman 1979, Doschek et al. 1980; Feldman et al.
1980) have shown that these emissions have a very smooth intensity profile,
when observed with a time resolution of about 30 sec. During the SMM in 1980,
many flares were observed in the UV line of Fe XXI at 1354 _, which o-----riginates
in plasmas with a temperature of about 10 million K. Examinations of
high-time resolution Fe XXI observations generally show gradual rise and fall
profiles, representative of typical soft X-ray bursts. However, these
gradually varied time profiles do show intensity fluctuations. In this paper
we make a quantitative study of the Fe XXI intensity variations_ and assess
whether the observed rapid fluctuations represent intrinsic variations in the
emission or are just due to photon counting statistics.
2. DATA ANALYSIS
The Fe XXI observations were obtained with the Ultraviolet Spectrometer
and Polarimeter (UVSP) on the SMM satellite. In order to study fast
variations, we have chosen flares that were observed with a field of view of
30" x 30" and a slit size of 10" x i0". These 3 x 3 raster element images
263 _ pAGE !_
https://ntrs.nasa.gov/search.jsp?R=19870012378 2020-03-20T11:43:25+00:00Z
were taken every 1.215 seconds for a period of ten minutes. This time
resolution was the highest observed by the UVSP in the Fe XXI mode. Out of 26
flares in the fast Fe XXI mode, 10 were observed from the beginning of the
flare, and showed appreciable Fe XXI emission in the small field of view.
These were chosen for analysis. Figure I (upper panel) shows an example of
the time evolution of the Fe XXI emission in the I November 1980 flare at 1924
UT; the intensity is for the brightest pixel in the field of view (FOV).
Figure I shows there are large fluctuations superimposed on the generally
gradual rise and fall profile. In all figures, the count rate is count per
0.063 sec. As is well known in photon detection and cosmic ray observations,
such fluctuations are most often due to photon counting statistics rather than
due to real signals. How does one determine whether the observed variation is
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statistically significant in the inherently noisy data? If such fluctuation
264
is real, what is its timescale? One technique to answer such questions is the
use of Fourier power spectral analysis. This technique was used by Hoyng et
al. (1976) and Brown, Loran, and MacKinnon (1985) to determine the shortest
tlmescale present in solar impulsive hard X-ray bursts.
We have calculated the power spectra for the I0 flares selected for
analysis, using a standard fast Fourier transform code. Since the analyses
are the same for the flares we studied, we shall present calculations for
three flares to illustrate the results.
In Figure i we have already shown the light curve for the brightest Fe XXI
pixel in the FOV for the I November 1980 flare. The flare occurred in AR 2776
(NOVA designation), and is classified as a IB in HA and M1 in soft X-ray. In
H_ the flare began at 1915 UT, reached maximum at 1922 UT, and ended at 1931
UT. The Fe XXI emission started to increase at 1918 UT and reached peak
intensity at 1924 UT. Figure i also shows the power spectrum. As expected,
the power spectra is dominated by the zero frequency component. The power
decreases sharply towards higher frequencies and levels off at about the
frequency f = 0.2 sec . The high frequency powers are dominated by random
noises. Since the noise in the photon counting experiment generally obeys
Poisson statistics, it is possible to calculate the expected level for the
high frequency powers that are due to noise presented in the data. Hoyng
(1976) has derived such an expression as well as calculated the relative error
in a power spectrum for Polsson distribution. The horizontal llne in the
power spectrum graph is the calculated high frequency power expected from
noise, and the relative error in the power spectrum as a function of frequency
is shown in the lower panel of Figure I. As can be seen, the power does not
rlselabove the noise level until the frequency has decreased to below f = 0.1
sec . At f = 0. I sec, the relative error in the power is about 30%, and the
error approaches unity at high frequencies, again demonstrating the dominance
of noise at high frequencies. Considering the errors involved in the power
spectrum, it is only for f < 0_5 sec - do we see any appreciable power in the
data. If we take f = 0.05 sec , where the error is relatively small, as the
cut off frequency beyond which the power is due to noise, then the
corresponding timescale is about 20 sec. We emphasize that this is the
fluctuation tlmescale that is persistently present in the data that is not
masked by noise. There are no isolated peaks in the power spectrum,
indicating the absence of any periodic variations in the Fe XXI emission.
We also obtained the power spectrum for the total intensity of Fe XXI
summed over the FOV. This is done to increase the count rate to improve its
statistics. Figure 2 shows the total intensity variation, the power spectrum,
and the relative error in the power spectrum. We see that the _wer spectrum
rises above the noise level at the frequency about f = 0.05 sec with
relatively smaller error than that shown in Figure i. This is because of the
increased count rate and comparatively lower noise level. It is clear that
for the i November flare, the shortest timescale persistently present in the
data is about 20 sec. This tlmescale of variability is similar to those found
for Fe XXV emission in some flares observed by the XRP instrument on SMM
(Zarro, Strong, and Saba, 1985).
265
The detection of
persistent variations in the
Fe XXI emission by the Fourier
analysis does not preclude the
existence of isolated bursts
that have timescales much
shorter than those indicted by
the Fourier Power spectrum.
Close examination of the data
shows there are isolated large
changes; see Figures i and 2.
To examine the reality of such
isolated fast variations, we
plotted the difference
(absolute value) between the
observed intensity and a
calculated mean intensity
(Figure 3). The calculated
mean is obtained by a seventh
power polynominal fitting of
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Figure 3
the observed data. Also plotted in the figure is the 3_ level calculated
from Poisson statistics for the observed data. Out of 500 intervals (a total
time period of 10 minutes), there are about 22 intervals in which the observed
intensities are above the 3 _" level. This represents a probability of 4.4% of
occurrence of a signal that is above the mean. From the Poisson distribution,
we know that the probabilty of occurrence of a 30"signal is 0.3% (Bevington,
1969). Therefore, the occurrence of a 34" signal above the mean in the
observed data is 15 times greater than that indicated by the Poisson
statistics. In other words, we would only expect less than 2 intervals in
which the signal rises above the mean, if the 3_" signals are purely random
fluctuations. We can conclude that the observed fast variations, with large
amplitudes, are statistically significant, and, to a reasonable degree of
certainty, real. One particular isolated change with large variation can be
seen in Figure I just before maximum intensity. The intensity jumps about 15%
in about 4 sec. Other isolated bursts show similar timescales of fast
variation. We emphasize that the existence of isolated fast bursts in our data
should only be understood in the statistical sense.
In Figure 4 we present the Fe XXI light curve for the whole raster as well
as its power spectrum for the 6 November 1980 flare. This flare occurred in
AR 2779 which in H_ started at 1228, reached maximum at 1236, and ended at
1258 UT. The H=_ class is unknown but the X-ray class is M3. The Fe XXI
observations started at 1232 UT and continued until 1233 UT. The FOV of the
UVSP covered only part of the flare. The figure shows that the shortest
timescale of fluctuations in the Fe XXI emission is about 20 sec,
corresponding to a cutoff frequency of about 0.05 sec.
Another example of the Fourier analysis of the Fe XXI emission is the 11
November 1980 flare. This flare also occurred in AR 2779. It was a SN flare
in Ho_ , which started at 0625 UT, peaked at 0632 UT, and ended 0645 UT. In
266
X-ray, the flare was a MI. The Fe XXI
observation started at 0628 UT and lasted for
10 minutes. This flare is interesting in
that the FOV of the fast Fe XXI mode covered
an area located at the top of the flaring
loop (Cheng and Pallavicini, 1985). In
Figure 5, we show the total Fe XXI intensity
and its power spectrum. The power rises
-I
above the noise level at about f = 0.I sec ,
which gives a time scale of 1Olsec. The
relative error at f = 011 sec is about 10%
(Figure 5). When the light curve of the
brightest pixel is Fourier analyzed, as shown
in Figure 6, the cutoff frequency that can be
identifie_ in the power spectrum is about f =
0.05 sec , corresponding to a period of
about 20 sec. For this flare there are 3
intervals out of 500 that are 30" above the
mean. This is what is expected from the
Poisson statistics, and therefore, we would
not claim that the isolated large variations
in the data are real.
3. SUMMARY AND DISCUSSIONS
We have made a search for fast variations
in the Fe XXI emission for ten flares using
the Fourier analysis. Examples of three
flares were described in the previous
section. Here we summarize the main results:
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I) We do not detect any periodic
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the flares studied. Figure 4
2) The shortest timescale of rapid variation, persistently present, in the
Fe XXI emission is about 20 sec or longer.
3) Statistically significant isolated bursts of 3 to 5 sec duration are
found in some of the flares. These isolated bursts, superimposed on the
general gradual time profile of the Fe XXI emission, have an intensity
variation from the mean by as much as 15%.
The main purpose of the paper is to find the shortest timescale,
persistently present, in the Fe XXI emitting plasma. A timescale of about 20
sec in the Fe XXI emission is considerably greater than the subsecond
variation found for the impulsive hard X-ray bursts (Kiplinger et al. 1983).
If the heating of the Fe XXI emitting plasma or the soft X-ray emitting plasma
is due to the energy deposition of the energetic electrons responsible for the
impulsive hard X-ray burst, as is commonly assumed, then there might be some
267
is due to the energy deposition of the energetic electrons responsible for the
impulsive hard X-ray burst, as is commonly assumed, then there might be some
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causal relationship between the time variations of the two components. We
note that the chromospheric evaporation, which in the electron deposition
model is the mechanism by which the soft X-ray bursts are powered, begins
within seconds after the electron beam has heated the chromosphere (see, for
example, Fisher et al. 1985; MacNeice et. al. lq84). If a variable electron
beam is responsible for the fast variations in hard X-ray bursts, then we
would also expect the thermal response of the chromosphere in the form of
evaporation to vary accordingly, thereby manifested in the variations of the
soft X-ray emissions. We then might expect to find intensity variation on the
order of seconds in the Fe XXI emission. As we have seen, the shortest time
268
scale of variation we found in our data is about 20 sec. Since the energy
transfer process and the thermal response of the chromosphere are complicated
and are not precisely known, it is difficult, at the present time, to conclude
whether the timescales we found for the Fe XXI emitting plasma are due to
variations in the electron energy depositions. A better understanding of the
timing relationship between the various emission components in the electron
energy deposition model has to wait for more realistic numerical calculations
(see Canfield et al. 1986).
This work is supported in part by NASA under Contract DPR W-15367.
REFERENCES
Bevington, P.R. 1969, Data Reduction and Error Analysis for the Physical
Sciences (New York : McGraw Hill).
Brown, J.C., Loran, J.M., and MacKinnon, A.L. 1985, Astron. Astrophys.
147, LI0.
Canfield, et al. 1986, in Proceedings of the SMM Workshops on Solar Flares.
Cheng, C.-C., and Pallavicini, R. 1985, preprint.
Doschek, G.A., Kreplin, R.W., and Feldman, U. 1979, Ap. J. (Letters), 233,
L157.
Dosheck, G.A. et al. 1980, Ap. J., 239, 725.
Feldman, U., et al. 1980, Ap. J., 241, 1175.
Fisher, G.H., Canfield, R.C., and McClymont, A.N. 1985, Ap. J., 289, 414.
Hoyng, P. 1976, Astron. Astrophys. 147, LIO.
Hoyng, P., Brown, J.C., and Van Beek, H.F. 1976, Sol. Phys., 48, 197.
Kiplinger, A. et al. 1983, Ap. J. (Letters), 265, L99.
MacNeice, P., McWhirter, R.W.P., Spicer, D.S., and Burgess, A. 1984, Sol.
Phys., 90, 357.
Zarro, D., Strong, K., and Saba, J. 1985, preprint.
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A search for fast variations in the Fe XXI emission during solar flares

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