PASJ: Publ. Astron. Soc. Japan 5 1 , 483-496 (1999)
High-Energy Electrons in Double-Loop Flares
Yoichiro HANAOKA
Nobeyama Radio Observatory, National Astronomical Observatory,
Nobeyama, Minamimaki, Minamisaku, Nagano 384-1305
E-mail: [email protected]
(Received 1999 April 26; accepted 1999 June 9)
Abstract
We studied the fast temporal variations in the brightness of the radio and hard X-ray sources of three
double-loop flares. In such flares, the main radio/hard X-ray source is located near to one of the footpoints
of a large overlying loop, where a small, newly emerging loop appears and the two loops interact, and the
remote source is located at another footpoint of the large loop. The following results were obtained from
the analysis: (1) The main source and the remote source basically show a correlated brightness fluctuation,
but the rapid fluctuation of the brightness of the remote source lags behind that of the main source for
about 500 ms. This result is evidence that the electron-acceleration region is close to the main source and,
therefore, it is most presumable that the high-energy electrons in the double-loop flares are accelerated in
the interaction region of the two loops. (2) The brightness of the hard X-rays from the main source and
that of the microwaves from the remote source fluctuate highly, but the microwaves from the main source
fluctuate less. This result means that the microwave-emitting electrons are effectively trapped at the main
source region.
Key words: Sun: emerging flux — Sun: flares — Sun: high-energy electrons — Sun: radio radiation
— Sun: X-rays
1.
Introduction
High temporal resolution is important to study the
characteristics of the high-energy electrons of solar flares
because of their fast temporal variations and large velocities. Fast fluctuations of the hard X-ray counts and
the radio intensities of flares are considered to reflect the
time variation of electron acceleration, and each individual brightening pulse is often supposed to represent an
'elementary burst'. A study of hard X-ray pulse widths
in the range of 0.3-3 s shows a continuous distribution
of pulse widths in this range (Aschwanden et al. 1995).
To resolve such a fine structure of intensity variations, a
temporal resolution of better than 1 s is required.
Recent studies of hard X-ray observations of solar flares
with high temporal resolution gave important information on the location of the electron-acceleration region.
Sakao (1994) shows that the time variations of the two
hard X-ray sources of most double-source flares coincide
very well ( ^ 0 . 1 s). This suggests that the electrons are
accelerated around the top of the loop, which connects
the two sources. Aschwanden et al. (1996a) estimated the
distance between the electron-acceleration region and the
footpoint hard X-ray sources based on an electron timeof-flight analysis, and showed that the acceleration region
of the Masuda-type flares (Masuda et al. 1994) is located
above the loop top. Both of their results are consistent
with the picture that a coronal eruption precedes energy
release by magnetic reconnection above the soft X-ray
flare loop (Shibata 1996). These results indicate that a
timing analysis is very important to define the electronacceleration region.
Besides coronal eruptive events, a collision between an
emerging flux loop and an overlying, pre-existing loop is
also known to be another typical cause of flares. We call
flares occurring under such a loop configuration 'doubleloop flares', and studied the configuration of these two
loops and related active phenomena in the previous papers (Hanaoka 1996, 1997, hereafter Papers I and II). We
revealed the topology of the two loops. Two of the footpoints of the loops, one from the emerging loop and the
other from the overlying loop, are included in a single
magnetic polarity patch. Therefore, the two loops form
a 'three-legged' structure, and the magnetic field has a
'bipolar + remote unipolar' structure. Jets and surges,
namely thermal plasma flows, are also common active
phenomena in such a loop configuration. High-cadence
soft X-ray observations and Ha observations show that
jets and surges flow into the overlying loop from the interaction region of the two loops (e.g., Shibata et al. 1992;
Canfield et al. 1996; also see Paper I). Numerical simulations of the reconnection between an emerging loop and
the overlying magnetic field clearly show the injection
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
Y. Hanaoka
484
of plasma from the reconnection region (e.g., Yokoyama,
Shibata 1995). On the other hand, non-thermal highenergy electrons produced in the double-loop flares probably also originate in the interaction region, as well as the
thermal plasma. However, we do not have any direct evidence that electrons are accelerated in the interaction
region of two loops. Defining the acceleration site is very
important to study the mechanisms of magnetic energy
release and electron acceleration.
Most of the double-loop flares analyzed in Papers I
and II show two microwave sources. An emerging loop
appears near one of the footpoints of a large pre-existing
loop, which corresponds to one of the microwave sources.
This source is also bright in soft and hard X-rays, and we
call this one the main source. The other source is conspicuous only in microwaves, and it is located at another footpoint of the large loop. We call this the remote source.
Since the brightness variations of the two sources in hard
X-rays and microwaves basically coincide well, the brightenings of the two sources are presumed to be caused by
high-energy electrons. Therefore, a detailed analysis of
the time variations of the two sources gives information
about the behavior of the high-energy electrons, and the
electron-acceleration site can be presumed on the basis
of a relative timing analysis of the brightness variations.
However, in Papers I and II, we did not enter into any detailed analysis of the time variations. The purpose of the
analysis in this paper was to study the behavior of highenergy electrons in double-loop flares with high temporal
resolution. We selected three flares from those listed in
Paper II for the analysis, which show rapid fluctuations
in the brightness. All of the selected flares have been
observed in microwaves with the Nobeyama Radioheliograph (NoRH) and in hard X-rays with the Hard X-ray
Telescope (HXT) on board Yohkoh with high-temporal
resolutions. Hard X-ray data obtained with the Burst
And Transient Source Experiment (BATSE) on board
the Compton Gamma-Ray Observatory (CGRO) are also
available for one of the flares.
A detailed description of the data used for the analysis is given in section 2. The results of the analysis are
described in section 3, and a discussion of results is given
in section 4.
2.
Data
In Paper II, thirteen flares, which occur in the doubleloop configuration, are listed. All of them are impulsive flares, and some of them show very rapid fluctuations of the brightness of hard X-rays and microwaves.
We selected three flares, which are suitable to study the
fine structure of the brightness variation; they are listed
in table 1. Figures 1, 4, and 6 show images of these
flares. They were observed with the following instruments, which have high temporal resolutions.
[Vol. 51,
The NoRH is a radio interferometer, which observes
the Sun at 17 GHz (and also at 34 GHz since fall of
1995). Two-dimensional images covering the whole sun
with a spatial resolution of about 12" are obtained with
the NoRH. Standard data of the NoRH have the time resolution of one second, but the raw data (before the onesecond integration) with 50 ms resolution during flares
are cut out from the temporary storage and saved after
daily observation. Therefore, snapshot images of flares
at 17 GHz can be made in every 50 ms, and we can derive the brightness and position of both the main and the
remote sources with 50 ms resolution for our analysis.
The HXT is a hard X-ray imaging instrument, which
provides images of four energy bands with a spatial resolution of 5" and a temporal resolution of 0.5 s in the flare
mode, while only the L-band data are recorded in every
2 s in the quiet mode. Although the temporal resolution
is 0.5 s, it is difficult to make hard X-ray images in every
0.5 s because of the insufficient count rate of the flares
analyzed. However, the hard X-ray images of the flares
analyzed show the main source only. Therefore, the hard
X-ray total counts can be considered as the brightness of
the main source, and its variation can be studied with
0.5 s resolution.
The BATSE provides hard X-ray counts of solar flares
with various temporal and spectral resolutions. The data
recorded in the Discriminator Science Data (DISCSC)
burst trigger mode are the hard X-ray count rates of the
four energy bands with a temporal resolution of 64 ms.
They are most suitable for our study (see Aschwanden
et al. 1995). There is no spatial information, but we
can consider that the hard X-rays observed with BATSE
come from the main source as well as the data obtained
with the HXT. Unfortunately, only the 1993 June 7
event is observed with BATSE.
3.
Results of the Analysis of the Three Selected
Flares
3.1. 1993 June 7 Flare
Images of the 1993 June 7 flare are shown in figure 1.
Because this flare was observed with all of the instruments of the NoRH, HXT, and BATSE, we present the
results of an analysis of this flare first. There are two
microwave bright points shown by white contours in figure la, which are connected by a large soft X-ray loop.
The western footpoint of the large loop shows an intense
brightening in soft X-rays (saturated in figure la), and a
compact hard X-ray source is also located there. This is
the 'main source'. On the other hand, the eastern footpoint of the large loop is remarkable only in microwaves,
and this is the 'remote source'. An Ha image (figure lb)
shows a strong brightening at the main source and a
compact, weak brightening at the remote source. The
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
No. 4]
High-Energy Electrons in Double-Loop Flares
485
Table 1. Selected flares.
Date
1993 F e b r u a r y 0 6 .
1993 April 10 . . . .
1993 J u n e 07
Time (UT)
GOES class
0527
2335
0549
C5.6
C9.1
C4.1
E
7420
7469
7518
S09E67
S08W51
S09W30
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05:43:00-05:43:07
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Fig. 1. Images of a C4.1 flare on 1993 June 7 in NOAA 7518. Each image has a field of view of 3f9 X 3f9, and solar north is
to the top. (a) Soft X-ray image taken with the SXT on board Yohkoh at 05:44:18, overlaid by white contours showing
the 17 GHz image at 05:42:52 taken with the Nobeyama Radioheliograph, and black contours showing the hard X-ray
image of the M l - b a n d (23-33 keV) at 05:43:06 taken with the HXT on board Yohkoh. (b) Ha picture of the flare at
05:44:29 taken with the Domeless Solar Telescope of Hida Observatory. Ha bright points at the footpoints of the large
soft X-ray loop are denoted by arrows, (c) Schematic drawing of the relation between the footpoints of the loops and
the magnetic polarities, presumed on the basis of a magnetogram and the polarization measurement of the radio sources.
(d) Separation between the western radio source (main source) and the eastern radio source (remote source) for the ten
time-periods during the impulsive phase. The size of each cross shows the east-west and the north-south ranges of the
measured positions during each time-period.
remote source is located close to a sunspot. As shown
in figure lc, this flare was probably caused by a collision
between a small emerging loop and a large overlying loop
at the main source (also see Paper II).
Figure 2 shows the total counts of hard X-rays in the
L(14-23 keV)/M 1 (23-33 keV)/M2(33-53 keV)-bands of
the HXT, the total count of the channel 1 (25-50 keV)
of the BATSE DISCSC data, and the radio brightness
of the main and the remote sources at 17 GHz. The
counts of the if-band (53-93 keV) of the HXT and the
higher-energy channels of the BATSE were not used for
the analysis, because their statistics are not sufficient due
to the low count rates. As mentioned in section 2, the
total counts of the hard X-rays are considered to show
the hard X-ray brightness of the main source, because the
hard X-ray emission concentrates at the main source (figure la). The radio and the hard X-ray time variations
show rapid fluctuations within 1-2 s, which are superposed on a slowly varying component. Such a fast and
ragged brightness variation suggests that the electrons
are accelerated within a short time. The 0.5 s resolution
of the HXT barely resolves the rapid fluctuation.
We checked the relative timing differences among
these rapid fluctuations as follows. Sakao (1994) and
Aschwanden et al. (1995) compared the relative timing
for individual peaks in the hard X-ray brightness varia-
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
[Vol. 51,
Y. Hanaoka
t (a)
05:42:50
05:42:00
05:42:20 05:42:40 05:43:00 05:43:20
Start Time (07-Jun-93 05:41:40)
05:43:00
05:43:10 05:43:20 05:43:30
Start Time (07-Jun-93 05:42:45)
05:43:40
05:43:50
05:43:40
Fig. 2. Changes in the hard X-ray and microwave intensities of the 1993 June 7 flare with high temporal resolutions. From top to bottom, the hard Xray counts of the L-band (thick line), the M l - b a n d
(next thick line), the M2-band (thin line) of the
HXT, the hard X-ray counts of the 25-50 keV band
of the BATSE, and the 17 GHz brightness temperature of the main source (thick line) and that of the
remote source (thin line). The time periods used for
the detailed timing analysis are labeled A and B.
tions. However, figure 2 shows that no one-to-one correspondence of the individual pulses between the radio and
the hard X-ray time profiles is very clear, while the major peaks roughly correspond to each other. Therefore,
any one-to-one direct comparison of the individual pulses
is difficult for our case. Then, we compared the rapidly
fluctuating component statistically, after removing any
slowly varying component by Fourier filtering. This is
the same method as that adopted by Aschwanden et al.
(1996a) for an electron time-of-flight analysis.
The rapidly fluctuating component in the time period
labeled B in figure 2, when Yohkoh was in the flare mode
and both the microwave brightness and the hard X-ray
count rates were high, is considered first. The length of
period B is 50 ms (the temporal resolution of the NoRH)
x 1024, which is suitable for Fourier analysis. We extracted the rapidly fluctuating component from the time
variations of this period as follows. Since the method is
based on Fourier filtering, it is assumed that the time
period repeats cyclically, and the end of the time period
adjoins the start of the time period. To remove any discontinuity between the brightness at the end time and
that at the start time, we connected the start and end
points of the time variations with a straight line, and removed the values below the line. Then, the slowly varying component was removed through a high-pass filter.
We show the rapidly fluctuating components of the radio
Fig. 3. (a) Rapidly fluctuating components of the hard
X-ray and microwave intensity variations, of which
the frequencies are higher than the cut-off frequency
of 15, during the period B denoted in figure 2.
The curves correspond to the hard X-rays of the
L / M l / M 2 - b a n d s of the HXT, the hard X-rays of
the 25-50 keV band of the BATSE, and the 17 GHz
brightness of the main and the remote sources, from
top to bottom, (b) Relation between the assumed
delay and the correlation coefficient between two of
the rapidly fluctuating components shown in (a).
The thick dotted/dashed/dash-dotted lines show
the correlation coefficients between the L/M1/M2
bands of the HXT and the 17 GHz remote source,
and the thick gray line shows that between the 2 5 50 keV band of the BATSE and the 17 GHz remote
source. The thick solid line shows the correlation coefficient between the main and the remote sources
at 17 GHz. The thin dotted/dashed/dash-dotted
lines show the correlation coefficients between the
L/M1/M2 bands of the HXT and the 17 GHz main
source, and thin gray line shows that between the
25-50 keV band of the BATSE and the 17 GHz main
and hard X-ray time variations which survive through a
high-pass filter with a cutoff frequency of 15 in figure 3a,
as an example. A cutoff frequency of 15 means that the
wave number included in the 50 ms x 1024 period is 15
and, therefore, the cutoff time scale is 3.4 s. This is similar to a filter scale of 2.5 s optimized for this particular
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
No. 4]
High-Energy Electrons in Double-Loop Flares
flare to divide the B ATSE hard X-ray time variations into
the pulsed and the smooth components by Aschwanden
et al. (1996b).
The upper five curves in figure 3a show a rapidly fluctuating component of the main source in hard X-rays
and microwaves. Simultaneous brightenings can be found
among the five curves, although their coincidences are not
very good. The lowest curve shows the fluctuation of the
remote source at 17 GHz, and it seems to lag behind the
main source at 17 GHz. To check these tendencies quantitatively, we calculated cross-correlation coefficients for
various combinations of these rapidly fluctuating components, shifting the curves step by step to each other. The
results are shown in figure 3b. All of the cross-correlation
coefficients reach 0.3-0.6 at maximum. Therefore, we can
conclude that the hard X-ray and the microwave emission
from the main and remote sources in period B basically
show a similar fluctuation. The position of the peak of
each curve in figure 3b shows the time lag between the
two fluctuating components. The peak positions of the
four thin-line curves show the delay of the fluctuation of
the main source at 17 GHz with respect to the hard Xray fluctuations of the main source. They are located in
the range of 0-200 ms. On the other hand, the correlation coefficient curves between the main source and the
remote source show a much different behavior. The peak
positions of the thick lines in figure 3b show the delay
of the fluctuation of the remote source at 17 GHz with
respect to the hard X-ray and the 17 GHz fluctuations of
the main source. All of them are located in the range of
400-550 ms. This fact means that the rapid brightness
fluctuation of the remote source lags behind the main
source for about 400-550 ms. To check the dependence
on the cutoff frequency of the estimated delays, we calculated the maximum positions of the correlation curves,
while changing the cutoff frequency from 1 through 30.
The results from the BATSE hard X-rays and the microwaves are shown in figure 8b, and the results from the
HXT hard X-rays and the microwaves are shown in figure 8c. Similar results to those in figure 3b were obtained,
except for the cutoff frequencies being far from the optimum value mentioned above. Consequently, the time
difference between the hard X-rays and the microwaves
from the main source is small, but the remote source lags
behind the main source for 400-700 ms. The difference
among the locations of the three instruments may lead to
a difference among the distances of the three instruments
from the sun. This causes an apparent lag between the
radio and the hard X-ray time variations. However, the
difference is less than the diameter of the earth, and the
corresponding time lag is at most only 45 ms. This is
smaller than the scatter of the measured time lags.
In the former half of the impulsive phase, the 17 GHz
intensity of the main source is not so high as that of the
latter half, and there are no high time-resolution data of
487
the HXT, because Yohkoh had not yet entered the flare
mode. However, the BATSE data are available, and the
rapid fluctuation is also seen in this period. We then
cut out a 50 ms x 512 period labeled A in figure 2, and
analyzed the time variations in the same way as described
above. The results are shown in figure 8a. Also, in this
case the fluctuation of the remote source lags for 350600 ms. The scatter of the delay values is larger than
that of time period B, but this is probably due to the
low brightness of the main source at 17 GHz.
Both of the above results show that although the variations in the hard X-ray brightness and the radio brightness of the main source synchronize well, the fluctuation
of the remote source lags behind that of the main source.
Since the distance between the two sources is 6.1 x 104 km
(surface distance) and the time delay is roughly 500 ms,
the velocity of transfer from the main source to the remote one is about 1.2 x 105 km s _ 1 . Such a transfer
should be due to high-energy electrons. Based on these
facts, it is presumed that the electron-acceleration site is
far from the remote source and close to the main source,
and that the accelerated electrons run into both the main
and the remote sources. On the basis of the magnetic
configuration in figure lc, it is most presumable that
the interaction region of the two loops is the acceleration site. Aschwanden et al. (1996b) estimated the distance between the electron-acceleration site and the hard
X-ray source for many flares, including the 1993 June
7 flare, on the basis of electron time-of-flight measurements of hard X-ray data taken with the BATSE. The
estimated distance between the acceleration site and the
hard X-ray source for the 1993 June 7 flare is only about
7.2 ± 3.4 x 103 km and, therefore, the acceleration site
is very close to the main source. This is consistent with
our result, and also supports the presumption that the
acceleration site is the interaction region.
The conspicuous similarity of the hard X-ray time variation observed by BATSE and the brightness variation
of the remote source at 17 GHz is easily recognized in
figure 2. The fact that the correlation coefficient between the BATSE hard X-rays and the microwaves of
the remote source is highest in figure 3b (thick gray line)
confirms this remarkable similarity. This is also clear
evidence that both sources are produced by electrons
accelerated simultaneously. The similarity between the
hard X-ray counts of the HXT and the remote source at
17 GHz is not very clear, but this is probably due to the
limited temporal resolution of the HXT. The similarity
between the BATSE time variation and the remote source
at 17 GHz also means that the magnetic field at the remote source does not change very much during the impulsive phase, because the microwave brightness strongly
depends on the magnetic field strength.
The change in the distance between the two sources
may cause the change of the time delay during the im-
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
[Vol. 51,
Y. Hanaoka
488
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05:24:35-05:24:45
05:24:45-05:24:55
05:24:55-05:25:05
05:25:06-05:25:16
05:25:50-05:26:00
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05:26:20-05:26:31
05:26:31-05:26:41
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-65
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E-W distance (104 km)
Fig. 4. Images of a C5.6 flare on 1993 February 6 in NOAA 7420. Each image has a field of view of 3.'9 x 3'9, and solar north
is to the top. (a) Soft X-ray image taken with the SXT at 05:24:38, overlaid by white contours showing the 17 GHz image
at 05:24:26 taken with the Nobeyama Radioheliograph, and black contours showing the hard X-ray image of the M l - b a n d
(23-33 keV) at 05:24:37 taken with the HXT. (b) Soft X-ray image taken with the SXT after the flare at 06:11:53. The
loop structure connecting the two radio sources is not clear in (a), but it is seen in this picture of the post-flare phase.
(c) Schematic drawing of the relation between the footpoints of the loops and the magnetic polarities, presumed on the
basis of the polarization measurement of the radio sources, (d) Distance of the two radio sources measured from the disk
center for the ten time-periods during the impulsive phase. The size of each cross shows the east-west and the north-south
ranges of the measured positions during each time-period. The crosses for the time periods 1-5 and those for 6-10 are
drawn in black and gray, respectively.
pulsive phase. During the observation of this flare, the
atmospheric condition at Nobeyama was not very good,
and it is difficult to measure the positions of the two microwave sources within a precision of about 5". However,
we can measure the change in the separation between the
two microwave sources. Figure Id shows the separation
between the sources measured on the 17 GHz images. A
systematic motion along the north-west direction can be
found. However, the variation in the separation throughout the flare (~ 2000 km) is much smaller (~ 3%) than
the distance between the two sources, 6.1 x 104 km, and,
therefore, this motion does not affect the time delay.
Figures 9a, 9b, and 9c show the amplitude of the
rapidly fluctuating components. We calculated the ratio
of the RMS amplitude of the rapidly fluctuating components to the average intensity for various cutoff frequencies. It is clear that the brightness of the main source at
17 GHz fluctuates less, and that the hard X-ray brightness of the main source and the 17 GHz brightness of the
remote source fluctuate much.
3.2. 1993 February 6 Flare
Figure 4 shows the images of the 1993 February 6 flare.
This flare also shows two major microwave bright points,
and an intense soft X-ray and hard X-ray bright point is
located at one of them. The large loop connecting the
main and remote sources is not clear in figure 4a, but it
can be seen in figure 4b, which was taken after the flare.
We have no Ha observation of this flare. The variations of
the brightness of the main source of the L/Ml/M2-bands
of the HXT and 17 GHz, and that of the remote source
at 17 GHz, are shown in figure 5. The time variations
show fast fluctuations, and some of the peaks in the radio
brightness variation cannot be resolved in the hard X-ray
profiles. Since two major-brightenings occurred in this
flare, we cut out two 50 ms x 1024 periods labeled A
and B in figure 5. A timing difference analysis, which is
similar to that for the 1993 June 7 flare, was carried out,
and we obtained the results shown in figures 8d and 8e.
The coincidence of the hard X-ray and 17 GHz brightness
variations of the main source, and the delay of the remote
source are clearly seen, even though the scatter of the
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
High-Energy Electrons in Double-Loop Flares
05:24:00
05:24:30
05:25:00
05:25:30
05:26:00
Start Time (06-Feb-93 05:23:50)
05:26:30
05:27:00
Fig. 5. Changes of the hard X-ray and microwave intensities of the 1993 February 6 flare with high temporal resolutions. From top to bottom, the hard
X-ray counts of the L-band (thick line), the M l band (next thick line), the M2-band (thin line) of
the HXT, and the 17 GHz brightness temperature
of the main source (thick line) and that of the remote source (thin line). The time periods used for
the detailed timing analysis are labeled A and B.
results for period A is large. This large scatter is due to
the low count rate of the HXT during period A.
Figure 4d shows the movements of the main and the
remote sources in microwaves. Since the atmospheric
condition at Nobeyama was good during this flare, we
could measure the precise positions of both sources on the
17 GHz images. The distance between the two sources at
the second brightening is obviously larger than that of the
first one. The delay of the remote source in period B (figure 8e) is larger than that in period A (figure 8d), which
is consistent with the increase of the distance. The hard
X-ray brightness and the microwave brightness of the remote source of the second brightening are larger than
those of the first one, but the brightness of the main
source at 17 GHz shows an opposite behavior. This is
probably due to the difference in the magnetic field between the first and the second brightenings caused by
movement of the sources.
Figures 9d and 9e show the amplitude of the rapidly
fluctuating component of periods A and B, respectively.
The remote source fluctuates more than the main source
at 17 GHz in period A, and the M l - and M2-band
counts of the HXT fluctuate more than the main source
at 17 GHz in both the periods.
489
3.3. 1993 April 10 Flare
Figure 6 shows images of the 1993 April 10 flare. This
flare also shows two major microwave bright points, and
an intense soft X-ray and hard X-ray bright point is located at one of them. The main and remote sources are
connected with a large soft X-ray loop. This flare was
observed in Ha, and a faint brightening in Ha was found
at the remote source, while no hard X-ray emission was
observed from the remote source. The remote source was
close to a sunspot, though it is not clear in figure 6b. The
variations of 17 GHz and hard X-ray brightness are shown
in figure 7. The time variations show rapid fluctuations,
and some of the peaks in radio brightness variation cannot be resolved in the hard X-ray profiles. We cut out
a 50 ms x 1024 period labeled A in figure 7, which covers the entire impulsive phase. A similar relative timing
analysis to the 1993 June 7 flare was carried out, and
we got results shown in figure 8f. Coincidence of the
hard X-ray and the 17 GHz brightness variations of the
main source, and the delay of the remote source is clearly
seen. The measured delay is 350-700 ms. The positions
of the main and the remote sources at 17 GHz shown in
figure 6d show no large movement during the impulsive
phase.
Figure 9f shows that the amplitude of the rapidly fluctuating component. The remote source at 17 GHz and
the M2-band counts of the HXT fluctuate more than the
main source at 17 GHz.
4.
Discussion
Jf..l.
Time Delay and Electron-Acceleration Region
Based on a timing-difference analysis of the three
double-loop flares, we obtained the following common results. The rapidly fluctuating components of the brightness variation of the main and remote sources show a
definite correlation. The similarity in the brightness variation between the microwave emission from the remote
source and the hard X-ray emission from the main source
observed with the BATSE in the 1993 June 7 flare is particularly remarkable. Furthermore, the rapidly fluctuating component in microwaves of the remote source lags
behind that of the main source, while there is no substantial timing difference between the microwaves and the
hard X-rays from the main source. The time delays of
the microwaves from the main source with respect to the
hard X-rays and the time delays of the microwaves from
the remote source with respect to the microwaves and the
hard X-rays from the main source are given in table 2.
The surface distances between the two radio sources are
also listed. As mentioned in subsection 3.2, the positions
of the main and remote sources in period A of the 1993
February 6 flare are substantially different from those in
period B. Then, the values for periods A and B of this
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
[Vol. 51,
Y. Hanaoka
490
11111111111111111111111111111111111
i
i
i i i i | i i n i i i i i |
(d)
-9EE
*°
-10 E-
1 23:32:52-23:32:56
2 23:32:56-23: 33:00
3 23:33:01-23:33:05
4 23:33:05-23: 33:09
5 23:33:10-23: 33:14
6 23:33:14-23: 33:18
7 23:33:19-23: 33:23
8 23:33:23-23:33:27
9 23:33:28-23:33:32
10 23:33:32-23: 33:36
§
-Htco
• 1 2 E-
remote source
(-)
main source
-13
*
50
'
'
'
'
51
52
53
54
E-W distance (104 km)
* •*
55
Fig. 6. Images of a C9.1 flare on 1993 April 10 in NOAA 7469. Each image has a field of view of 3'9 x 3'9, and solar north is
to the top. (a) Soft X-ray image taken with the SXT at 23:33:00, overlaid by white contours showing the 17 GHz image
at 23:33:22 taken with the Nobeyama Radioheliograph, and black contours showing the hard X-ray image of the M l - b a n d
(23-33 keV) at 23:33:15 taken with the HXT. (b) Ha picture of the flare at 23:33:39 taken with the Flare Telescope of
the National Astronomical Observatory. Ha bright points at the footpoints of the large soft X-ray loop are denoted by
arrows, (c) Schematic drawing of the relation between the footpoints of the loops and the magnetic polarities, presumed
on the basis of a magnetogram and the polarization measurement of the radio sources, (d) Distance of the two radio
sources measured from the disk center for the ten time-periods during the impulsive phase. The size of each cross shows
the east-west and the north-south ranges of the measured positions during each time-period. The movement of the sources
are small, and the crosses labeled 1-10 overlap with each other.
Table 2. D i s t a n c e a n d t i m e delay b e t w e e n t h e m a i n a n d t h e r e m o t e sources a n d t h e a p p a r e n t velocity of electrons.
F l a r e / T i m e period
1993 F e b r u a r y 6 A . . . .
1993 F e b r u a r y 6 B . . . .
1993 April 10 A
1993 J u n e 7 A / B
average
T i m e delay
( m a i n source)
100±71
22±43
90±72
55±69
69 ms
T i m e delay
( r e m o t e source)
ms
ms
ms
ms
N a k a j i m a et al. (1985).
L a n g , Willson ( 1 9 8 9 ) . .
Willson et al. (1993) ..
flare are given separately in table 2. The listed time delays and their errors are the averages and the standard
deviations calculated from the values plotted in figure 8,
except the data points of too low and too high cutoff frequencies. The delay of the remote source with respect to
the main source is obvious, and the average delay of the
377±97
493±51
442±62
518±74
465 ms
1.7-25 s
3-6 s
<1.7s
ms
ms
ms
ms
Surface d i s t a n c e
A p p a r e n t velocity
6.1 xlO 4 km
7.8
6.9
6.1
16.2 xlO 4 k r n s " 1
15.8
15.6
11.8
14.5
15-89
26
20
3-11
<10
>12
three flares is 465 ms. The microwave fluctuation of the
main source also shows a delay with respect to the hard
X-ray fluctuation in all the cases. However, note that the
delays are not necessarily larger than the error.
The time delay of microwaves with respect to hard Xrays has been widely discussed by various authors (see
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
No. 4]
High-Energy Electrons in Double-Loop Flares
Start Time (10-Apr-93 23:32:35)
Fig. 7. Changes of the hard X-ray and microwave intensities of the 1993 April 10 flare with high temporal resolutions. From top to bottom, the hard
X-ray counts of the L-band (thick line), the M l band (next thick line), the M2-band (thin line) of
the HXT, and the 17 GHz brightness temperature
of the main source (thick line) and that of the remote source (thin line). T h e time period used for
the detailed timing analysis is labeled A.
Bastian et al. 1998, and references therein). In many
cases, the peak time of a simple impulsive spike in hard
X-rays and that in microwaves were compared, and a
time lag of the peak in microwaves was often found. A
relative timing study for the fluctuating component after
removing the slowly varying component, which is similar to our study, was also carried out by Cornell et al.
(1984); they have shown that the microwaves lag behind
the hard X-rays for about 0.2 s. Such a time delay is often accounted for by spectral hardening of non-thermal
electrons due to the longevity of higher energy electrons,
the delayed acceleration of higher energy electrons, etc.
However, it is not easy to apply such mechanisms to the
flares analyzed here, because the remote source shows a
definite delay with respect not only to the hard X-rays,
but also to the microwaves from the main source. As
mentioned above, the microwaves from the main source
do not show any substantial delay with respect to the
hard X-rays. Furthermore, as shown in section 3, the microwave brightness of the remote source fluctuates more
than that of the main source. Since such mechanisms as
electron trappings make the brightness variation smooth,
it appears that the trapped electrons do not play a dominant role in the microwave brightening at the remote
source.
Consequently, it is most plausible that the delay in the
remote source is due to the longer flight time of the highenergy electrons traveling from the acceleration region to
491
the remote source than that to the main source. Therefore, the electron-acceleration region is close to the main
source, and is probably located at the interaction region
of the two loops. The electrons in the double-loop flares
are accelerated simultaneously within the time-scale of
the fluctuation, namely less than a few seconds, at the
interaction region of the two loops, and the accelerated
electrons run into both the main and the remote sources.
Electrons of a wide energy range are accelerated simultaneously, because the hard X-ray emitting electrons have
the energy lower than about 100 keV (roughly twice of
the energy of the observed hard X-rays), and the energy of the microwave emitting electrons with the gyrosynchrotron mechanism are generally much higher (see
Dulk 1985; the energy of electrons is discussed in subsection 4.2). As described in section 1, thermal plasma flows
(jets and surges) are known to originate in the interaction
region. Therefore, the interaction region is the source of
both the thermal plasma flows and the non-thermal highenergy electrons. The interacting loop model is appropriate to both the non-thermal and the thermal phenomena.
Figure 10 shows the schematic view of the interacting
loops and the active phenomena caused by them.
Remote radio sources are an important feature of the
flares analyzed in section 3. Such a remote radio source
distant from the main radio source of a flare has been
already reported by various authors, and some of them
pointed out a short delay in the brightness variation of
the remote source with respect to that of the main source
(Nakajima et al. 1985; Lang, Willson 1989; Willson et
al. 1993). The time delay and the surface distance between the sources of the flares analyzed by them are also
listed in table 2. The flares reported by Lang and Willson
(1989), and Willson et al. (1993), and some of the flares
reported by Nakajima et al. (1985) show quite large surface distance. In these flares, the remote source is located
in a different active region from the region including the
main source, while the three flares analyzed in this paper
occur in a single active region. As shown in table 2, the
inferred velocity of energy transfer from the main source
to the remote source is about 105 km s _ 1 . Therefore, they
concluded that high-energy electrons run from the main
source to the remote source and make the remote source
bright. Gary and Hurford (1990) also reported a flare
with a radio remote source. They estimated the delay of
the remote source to be 10-20 s, but their temporal resolution is 10 s, and therefore, the precise estimation of the
velocity is difficult. However, they concluded that both
the main and the remote sources are brightened by the
gyrosynchrotron emission on the basis of the radio spectral analysis. Therefore, the observation by Gary and
Hurford (1990) also indicates the travelling high-energy
electrons from the main source to the remote source. Because of the lack of soft X-ray data, the loop configuration
of these flares is not clear, but it is natural to consider
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
[Vol. 51,
Y. Hanaoka
492
(b) 1993 June 7 B
(a) 1993 June 7 A
800
600
Delay
SLU)
400
200
0
800
'*--—-
H
• ^ — ^~
V^-^. 1
:
r x
;
f\\\
600
-co 400
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S
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Cutoff Frequency
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.
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- • " • ' "
H
-200
14
10
15
20
Cutoff Frequency
(c) 1993 June 7 B
800
.
800
1
I
K
6001
'
25
1
30
(d) 1993 February 6 A
''
•
T
'
^, %
X
—
•
T-«
- - - - ^.
| J
1 -|
--
, N
•- " **»"-".
-
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•"'!
• -
-•
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1 «j
-200
10
15
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Cutoff Frequency
25
30
10
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Cutoff Frequency
1
[
600 I
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pm t r *
,-r
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25
(f) 1993 April 10 A
(e) 1993 February 6 B
800
-J-J
. i
10
15
20
Cutoff Frequency
J_L_L
25
•*
id
0h
li
»i
30
-200
10
15
20
Cutoff Frequency
Fig. 8.
Measured delays between two of the rapidly fluctuating components of the hard X-ray and microwave intensity
variations for various cutoff frequencies for the five time periods of the three flares denoted in figures 2, 5, and 7. The plot
for period B of the 1993 June 7 flare is split into two panels. The thick and thin gray lines in panels (a) and (b) show the
delay of the 17 GHz brightness of the remote source and that of the main source to the 25-50 keV hard X-ray counts of the
BATSE. The thick and thin, dashed/dotted/dash-dotted lines in panels (c)-(f) show the delay of the 17 GHz brightness
of the remote source and that of the main source to the hard X-ray counts of the L / M l / M 2 - b a n d s of the HXT. The thick
solid lines in all the panels show the delay of the 17 GHz brightness of the remote source to that of the main source.
that these flares also occur under the double-loop configuration. Nakajima et al. (1985) and Gary and Hurford
(1990) reported that the remote source is strongly polarized and associated with no or weak Ha source. Such
features are common with the flares analyzed in Papers I
and II, including the three flares analyzed here.
4-2. Energy of Electrons
Based on the time delay and the surface distance between the main and the remote sources listed in ta-
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
High-Energy Electrons in Double-Loop Flares
No. 4]
493
(a) 1993 June 7 A
0.40
0.30 h
= 0.20 P
E
<
0.10
o.oo
4
6
8
10
Cutoff Frequency
12
10
15
20
Cutoff Frequency
(c) 1993 June 7 B
(d) 1993 February 6 A
0.40
0.40
0.30K
0.30
= 0.20
E
0.20
<
0.10F
0.10
0.00
0.00
5
10
15
20
Cutoff Frequency
25
30
(e) 1993 February 6 B
0.40
1
• '
i
•
• '
'
5
10
15
20
Cutoff Frequency
25
30
(f) 1993 April 10 A
i
0.30 F-
= 0.20
E
<
0.10F-
0.00
10
15
20
Cutoff Frequency
10
15
20
Cutoff Frequency
Fig. 9. Amplitudes of the rapidly fluctuating components of the hard X-ray and microwave intensity variations for various
cutoff frequencies for the five time periods of the three flares denoted in figures 2, 5, and 7. The plot for period B of the
1993 June 7 flare is split into two panels. The gray lines in panels (a) and (b) show the amplitude of the 25-50 keV hard
X-ray counts of the BATSE. The dashed/dotted/dash-dotted lines in panels (c)-(f) show the amplitude of the hard X-ray
counts of the L / M l / M 2 - b a n d s of the HXT. The thick and thin solid lines in all the panels show the amplitude of the
17 GHz brightness of the main source and that of the remote source, respectively.
ble 2, we estimated the apparent velocity of the electrons,
which travel from the electron-acceleration region toward
the remote source. Although we do not know the exact
position of the electron-acceleration region, we assumed
that the distance between the acceleration region and the
remote source is the same as that between the main and
the remote sources for simplicity. The results are also
given in table 2. The estimated velocity gives the energy
of the electrons. The three flares analyzed here gave similar velocities, roughly half the speed of light, and the
average is 14.5 x 104 km s _ 1 . The apparent velocities
estimated by Nakajima et al. (1985), Lang and Willson
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
Y. Hanaoka
494
electron acceleration site
overlying
loop
Fig. 10. Schematic drawing of a double-loop flare and
behavior of high-energy electrons. The interaction
region of the two loops is the origin of high-energy
electrons and thermal plasma flows, such as jets and
surges.
(1989), and Willson et al. (1993) are also listed in table 2.
The velocities are up to half the speed of light, and are
not much different from our estimation. Although these
velocities were calculated on the basis of the surface distance, the actual length of the large loop connecting the
main and remote sources should be longer. The assumption of a semi-circular loop gives TT/2 times the surface
distance for the actual loop length; based on this assumption, the average velocity becomes 22.8 x 104 km s _ 1 . The
corresponding electron energy is 275 keV.
Furthermore, the electrons, of which the pitch angle is
not generally zero, gyrate around the magnetic field line
and their flight length is longer than the geometrical loop
length. Therefore, the electron energy of 275 keV is the
lower limit. If the remote source has the same magnetic
field strength as the electron-acceleration region, the electrons, of which the pitch angle ranges from 0 to n/2 at
the acceleration region, converge at the magnetically conjugate point at the remote source. In the case that the
pitch angle has such a wide distribution, the actual flight
length of the electrons is also widely distributed. The
average of the actual flight length is 1.23-times the geometrical length when the magnetic field at the footpoints
is strong enough (see the Appendix). This flight length
gives the electron velocity and corresponding energy of
28.1 x 104 km s - 1 and 955 keV, respectively. However,
based on the following reason, these values are considered to be an upper limit. The widely distributed flight
lengths of electrons make the time variation of the microwaves at the remote source smooth. On the other
hand, as shown in section 3, the microwaves from the re-
[Vol. 51,
mote source show fluctuation as high as the hard X-rays
from the main source. Therefore, the pitch angle of the
electrons contributing the microwave emission from the
remote source is distributed only in a small range close to
0. In such a case, the average flight length is smaller than
that in the case of the isotropic pitch-angle distribution
ranging from 0 to 7r/2, and the typical electron energy
is smaller than the above value, 955 keV. The limitation
of the pitch angle is probably caused by the asymmetry of the magnetic field. As shown in section 3, the remote source is located in the vicinity of the sunspots and,
therefore, the magnetic field at the acceleration region is
presumed to be weaker than that at the remote source.
In this case, only electrons with small pitch angles reach
the remote footpoint, while electrons with large pitch angles are reflected high above the remote footpoint. Since
the magnetic field is strongest at the remote footpoint,
only those electrons with small pitch angles effectively
emit microwaves.
Consequently, we can say as a conclusion that the
typical energy of electrons, which contribute to the microwave emission at the remote source, are several hundred keV (up to ~ 1 MeV). Since the apparent velocities
estimated by Nakajima et al. (1985), Lang and Willson
(1989), and Willson et al. (1993) listed in table 2 are not
much different from our estimation, similar velocities and
energy values to our results are obtained from their estimation, if we take the effects of the loop geometry and
the electron gyration into account. The above results
represent a direct measurement of the velocity and the
energy of the microwave-emitting electrons, which travel
toward the remote source from the electron-acceleration
region.
4-3.
Rapid Fluctuation and Behavior of Electrons
All of the flares analyzed here show rapid fluctuations
of the brightness. The amplitude of the fluctuations are
shown in figure 9. As mentioned in section 3, the following features are revealed from this figure:
(1) The fluctuation of the remote source at 17 GHz is
larger than that of the main source at 17 GHz, except for only one case, namely the former half of the
1993 February 6 flare.
(2) The fluctuation of the main source in the BATSE
hard X-rays (25-50 keV) and in the HXT M2-band
(33-53 keV) is larger than that of the main source at
17 GHz in all of the analyzed cases. The fluctuation
in the HXT Ml-band (23-33 keV) is also larger than
that of the main source at 17 GHz, except for the
case of the 1993 April 10 flare.
(3) Relatively low fluctuation is found in the brightness
variations of the main source at 17 GHz and the
HXT L-band.
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
No. 4]
High-Energy Electrons in Double-Loop Flares
The lower fluctuation of the HXT L-band (14-23 keV)
counts compared to the M l - and the M2-band counts
is probably due to radiation from the thermal plasma
included in the counts of the L-band. On the other
hand, the relatively low fluctuation of the main source
at 17 GHz is presumed to be caused by trapping effect, because, as mentioned before, generally the energy of electrons which emit gyrosynchrotron radiation
in microwaves is higher than those emitting hard X-rays
observed by the BATSE/HXT, and the higher-energy
electrons undergo the trapping effect more severely.
Aschwanden et al. (1997) have shown that the higher
energy hard X-rays of the 1993 June 7 flare observed
with the BATSE show a delay due to the trapping effect with respect to the lower energy ones in the energy
range of 20-200 keV. Since the energy of the microwaveemitting electrons is higher than this range, this result
confirms that the smoothness of the microwave time variation at the main source is caused by the trapping effect.
The electrons are probably trapped locally at the main
source, because the fluctuation of the remote source at
17 GHz is high.
As described in subsection 4.2, the high fluctuation
of the remote source is probably related to the stronger
magnetic field at the remote source than at the main
source. On the other hand, the radio brightness of the
remote source is comparable to the main source. These
facts indicate that much fewer electrons contribute to the
brightening at the remote source than the main source,
because the radio brightness strongly depends on the
magnetic field strength. Most of the electrons running
into the remote source are probably effectively reflected
before they precipitate into the remote source because of
the stronger magnetic field of the remote source. This
is also suggested by the hard X-ray and the Ha observations. As shown in section 3, the remote sources cannot be found in hard X-rays, and are faint in Ha. The
brightness of hard X-rays and Ha depends on the number
of precipitated electrons, while the radio emission comes
from both the precipitated and reflected electrons. As
described in subsection 4.2, Nakajima et al. (1985) and
Gary and Hurford (1990) also pointed out that the remote source shows strong polarization and weak or no
Ha brightening. They also concluded that the remote
source is brightened by the small number of electrons
in the strong magnetic field. The relation between the
asymmetry of the magnetic field strength in a loop and
the hard X-ray emission was discussed by Sakao (1994),
and the ratios of precipitating/trapped electrons for various magnetically asymmetric cases were calculated by
Aschwanden et al. (1999).
Prom the above discussion, the behavior of the highenergy electrons in the analyzed flares are summarized
as follows. The electrons of a wide energy range are simultaneously accelerated at the interaction region of the
495
two loops near to the main source within a few seconds.
Although most of the electrons precipitate or are trapped
in the main source region, a part of electrons escape the
main-source region and run into the remote source. If
the magnetic field at the remote source is strong enough,
the remote source shows intense radio radiation, while
the hard X-ray and the Ha emission are weak. Such a
behavior of the electrons are schematically shown in figure 10.
The BATSE data used in this paper were obtained
through the CGRO BATSE Solar Flare Data Archive
maintained by the Solar Data Analysis Center at NASAGoddard Space Flight Center and provided by the
BATSE team headed by Dr. Gerald Fishman. Hida Observatory of Kyoto University and the solar physics division of the National Astronomical Observatory kindly
provided us with the Ha pictures. The author is grateful to Dr. H. Nakajima and the referee for their helpful
comments.
Appendix. Electron Pitch Angle Effect
To estimate the actual flight length of electrons from
the acceleration region to the remote source, we need to
calculate the increase in the flight length due to electron
gyration around the magnetic field line. Aschwanden et
al. (1996a) assumed a uniform distribution of the pitch
angle at the loop top, and calculated the average electron
flight length to the mirror point near to the footpoints
of the loop, because they analyzed the flares of which
the electron-acceleration region is presumed to be located
above the loop top. They estimated that the flight length
is 56% larger than the length of the geometrical loop
length. In our case, the acceleration region is located
near to the foot point of the large loop, and we need to
calculate the flight length from the footpoint to the top
of the loop.
Assume an electron of which pitch angle is af at the
footpoint, where the magnetic field strength is Bf, move
to the loop top, where the magnetic field strength is Bo,
and its pitch angle becomes ao- The position along the
loop, 5, is measured from the loop top, and the geometrical length from the loop top to the foot point is Sf. Based
on the conservation of the magnetic moment, their relation is written as
sin 2 ao
~Bo~
=
sin 2 af
sin 2 a(s)
=
~BT
B(S) '
.
(
}
We adopt the same parabolic expression of the magnetic
field B(s) as that of Aschwanden et al. (1996a),
B{s) = B0 (l + r^j,
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
(A2)
496
Y. Hanaoka
where r — (Bf/Bo) — 1. T h e actual flight length of electron, -Sgyi-o is given by
Sf
f
( \
J0
ds
cos a(s)
ds
f
J0
/
i
(A3)
l
sin' a{s)
Using equations ( A l ) and (A2), we obtain t h e ratio of
t h e actual flight length to t h e geometrical length, Q ( a f ) ,
as
J
QipLf)
g y r o (<*f)
Si
r-fl
sinaf
• sin
r s i n af
sin 2 af
r-fl
(A4)
If we assume t h e isotropic pitch angle distribution at the
acceleration region at the footpoint, t h e average ratio is
given by
Qa
-f-
Q(oc{) • 27rsinafrfo:f.
(A5)
T h e magnetic field strength at t h e loop t o p is expected
to be weaker t h a n t h a t at t h e footpoint. If Bf ^> BQ,
Qave simply becomes
Qa
7T^
1.23.
(A6)
In this case, t h e actual flight length is 2 3 % longer t h a n
the geometrical length on the average.
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