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Improvement of Yohkoh HXT imaging and an analysis of the 1997 November 6, X9 flare
Adv. Space Res. Vol.26. No. 3, pp.Sol-504,200O Q 2000 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain
Pergamon
0273-1177100$20.00+ 0.00
www.elsevier.nl/locate/asr
IMPROVEMENT AN ANALYSIS J. Satol,
S. Masuda’,
PII: SO273-1177(99)01102-3
OF YOHKOH HXT IMAGING AND OF THE 199’7 NOVEMBER 6, X9 FLARE T. Kosugi3,
and T. Sakao’
‘National Radio Observatory, Nobeyama, Minamisaku, 384-l 305, Japan 2Solar Terrestrial Environment Laboratory, Nagoya Univ., Toyokawa, 442-8507, 31nstitute of S p ace and Astronautical Science, Sagamihara, 229-8510, Japan
Japan
ABSTRACT The imaging capability of the Hard X-ray Telescope (HXT) on board Yohkoh has been drastically improved by (1) adopting new instrumental response functions (modulation patterns) derived from a self-calibration procedure that makes use of solar flares themselves as calibration sources, (2) revising and (3) the Maximum Entropy (MEM) image synthesis procedure for better total flux estimation, One of the most intense flares so far incorporating in MEM properly estimated observation errors. observed with HXT, the 1997 November 6, X9 flare, has been analyzed with the new HXT imaging program. Two footpoint sources are clearly seen and show systematic motions during the impulsive phase. This may provide a new clue to understand the coronal magnetic field structure involved in 0 2000 COSPAR. Published by Elsevier Science Ltd. the energy release process of flares. INTRODUCTION teleThe Hard X-ray Telescope (HXT; Kosugi et al. 1991) on board Yohkoh is a Fourier-synthesis scope. It measures a set of spatially modulated incident photon counts with 64 hi-grid modulation collimators and an image is synthesized with the Maximum Entropy Method (MEM) or other image The HXT has so far observed more than 1300 flares since launch in 1991 synthesis procedures. August. Most of them have been successfully synthesized into images and have revealed several important characteristics of solar flare hard X-ray sou.rces (e.g., Sakao 1994; Masuda 1994). Image quality, however, has not always been satisfactory; the synthesized images sometimes showed scattered patches with size being smaller than the HXT spatial resolution and/or spurious structures sporadically appearing/disappearing with time. Such a degradation of image quality also tended to occur when we pursued higher image quality, i.e., higher signal-to-noise ratio, by accumulating photon counts. This was strange and implied that something was wrong or inappropriate in the HXT image synthesis. We have analyzed this problem and found how to solve it. This paper briefly discusses the essence of the improved HXT MEM imaging, and then applies it to the analysis of an X-class flare of 1997 November 6. IMPROVEMENT
OF
HXT
IMAGING
The causes of the HXT image degradation were threefold: (1) th e mismatch of the a.ctual modulation patterns with those used in the image synthesis, (2) an inaccurate estimate of the total flux, and (3) the incorporation of underestimated noise/observation error terms in the MEM imaging program. Correspondingly we have made the following improvements for achieving the full imaging capability of HXT: (1) Modulation patterns of the 64 collimators, accurately estimated with a self-calibration procedure in which solar flares are used as calibration sources, are incorporated. (2) The MEM formulation is revised to include an accurate total flux estimate. (3) Noise/observation error terms, estimated in the self-calibration as a byproduct, are properly incorporated in the MEM imaging
502
J. Sat0 et al.
program. Details of these improvements, together with examples of improved HXT images, are fully discussed in Sato (1997) and Sato et al. (1998). Th e essence is briefly summarized below.
Self-Calibration of HXT
Modulation Patterns How can we calibrate the instrumental response function whose original images we have no prior knowledge?
(modulation
patterns)
using solar flares, of
Suppose first for simplicity that only one of the 64 modulation patterns is incorrect, i.e., the pattern used for image synthesis slightly differs from the actual one. In this case, we may expect that the synthesized image is mostly determined by photon counts from the other (correct) 63 collimators, so that it well represents the original. Then, the photon counts estimated from the synthesized image are almost the same as the observed for the 63 modulation collimators but not so for the incorrect one. Hence we have a possibility to know what modulation pattern is incorrect. The situation is basically the same even when all the 64 modulation patterns have minor incorrectness. Since errors in individual modulation patterns tend to be independent of each other, the errors may cancel out and the synthesized image may still well resemble the original. Thus we have possibility to find modulation patterns whose error level is much higher than the “average” error level. Even if we know that a certain modulation pattern is incorrect, it does not necessarily mean that we know the direction of correction for a better pattern. Since one modulation pattern basically contains two important free parameters, i.e., amplitude and phase, we need to obtain a unique correction vector in the two-dimensional space. It is obvious that a unique determination is impossible so long as we use only one flare data; photon count may be overestimated as a result from either an overestimate of the amplitude or a lateral shift of the peak position of the modulation pattern toward the source position due to the phase error. This ambiguity, however, can be removed if we simultaneously make use of many flares taken with the same set of modulation patterns. Based upon the concept given above, we have constructed a self-calibration scheme in which the 64 modulation patterns are iteratively improved to converge finally into the most plausible patterns. The patterns thus obtained are, in general, consistent in phase with those obtained from prelaunch measurements and used so far for the HXT imaging, but differ in amplitude to a significant degree. We have confirmed that adoption of the newly obtained modulation patterns is essential in improving the HXT imaging capability.
Revised MEM Formulation and Error Estimate The Maximum Entropy Method (MEM) so f ar used in HXT imaging is one of the standard or classical ones (e.g., Frieden 1972, Gull and Daniel1 1978), in which the total flux is given a priori as a constant. This is not appropriate for HXT since the total flux estimated from any linear combination of the 64 modulation patterns is dependent on the source location and not necessarily accurate enough (e.g., Alexander and Metcalf 1997). H ence, we have developed a new formulation of MEM in which the total flux is a free parameter to be determined in accordance with the MEM principle. In addition, noise/observation error terms need be properly incorporated as functions of observed This has been achieved by analyzing photon counts for any MEM to provide a plausible solution. the uncertainty of the modulation patterns still remaining after the self-calibration discussed above.
Improved HXT Images With the above improvements combined together, we have achieved high-quality imaging of HXT. Figure 1 compares HXT L-band (14-23 keV) images synthesized with the new imaging program of photon (bottom) with th ose synthesized with the old program (top), for different accumulations counts. It is clear from the new images shown in figure 1 that hard X-ray images (L: 14-23 keV) show similar source structures’over a wide range of photon counts, with an improvement of image quality In contrast, the old HXT image tends to become unrealistically with increasing photon counts. patchy, beyond the instrumental resolution, with increasing photon counts. Other weak points of the HXT imaging, not mentioned in this paper, are also alleviated drastically. Now we can say that, with the new HXT imaging program, flares, from weak to intense as well as from small- to large-sized, are satisfactorily synthesized into images from the impulsive phase to the decay phase.
Improvement
of Yohkoh HXT Imaging
92/Ol/13 HXTCL) FOV 158x158 arcsa
Figure photon with
1 : Examples count
the old (top
peak brightness,
row) and
X-CLASS
L-band
i.e.,
(14-23
keV)
w 300 cts/SC
(left
new (bottom
with contours
l/2 step is adopted) of each map is 158 AN
of HXT
accumulation,
denoting
OF
synthesized
column)
row) imaging
and
programs.
70.7 ~ 12.5% (l/&’
of the peak supplemented x 158 arcsec.
FLARE
images
from
two different
step except
for the top right map where
by gray scale below the 12.5% level.
1997 NOVEMBER
sets of
w 3000 cts/SC (right column), Each image is normalized by the The field of view
6
The new HXT imaging program enables us to analyze a very intense flare from its initial rise, through the peak, to the decay without being bothered by a large photon counts around the peak. This advantage is quite important, because such an intense flare is detected with high signal-to-noise ratios at full time resolution of 0.5 s even in the highest energy band, and thus provides a chance to investigate the rapid variations of purely nonthermal hard X-ray sources in the impulsive phase. An intense flare, X9 in GOES class, occurred in AR 8100 at S16W62 on 1997 November 6. This yielded larger photon counts (in higher energy bands) than any other so far observed with HXT. The intense hard X-rays only lasted for a few minutes; this flare is a typical impulsive flare. We have synthesized images of this flare at the time resolution of 0.5 s over the four HXT energy bands (14-23-33-53-94 keV). The hard X-ray images, as a whole, reveal the presence of two intense sources, 10 to 20 arcsec apart from each other in the north-south direction, and in addition two relatively weak sources to the west of the intense ones, apparently seen in limited time intervals. The two intense sources, hereafter called Fl (northern source) and F2 ( southern source) respectively, seem to be footpoint sources located at the conjugate footpoints of a flaring loop (e.g., Hoyng et al. 1981; ’ f comparison Sakao 1994). A b rie of the HXT images with a SOHO MD1 magnetogram suggests that Fl and F2 are located in opposite magnetic polarities. It has been known that double footpoints are not necessarily stationary; they frequently show systematic motions, with either increasing or decreasing footpoint separation (Sakao et al. 1998). Since the footpoints are believed to represent the regions where energetic electrons stream down along magnetic field lines, the motions reflect shifts of electron injection site or energy release site in a solar flare, and hence may provide a crucial hint to understanding the coronal magnetic field structure and its change during a flare. A result of our preliminary analysis is summarized in Figure 2. As expected, Fl and F2 show similar time variations in flux to each other. The centroid positions of Fl and F2 at representative times, marked in the time profiles by vertical bars with numbers, are shown in the inset of Figure 2, which vividly reveals that both sources rapidly move at projected velocities of order 100 km/s. The motions of the two footpoint sources are complex; Fl first moves to the south-east direction, slightly approaching the magnetic neutral line, but turns around toward the north-west direction nea.r the
J. Sato et al.
504
Figure measured dashed
2:
Intensity with
time
profiles
HXT
in the H band
lines denoting
the systematic
and
positions
(53-94
keV).
of sources Only
Fl
and
representative
F2 (F2 intensity: data
points
l/2
are plotted,
scaled) with
motions
intensity peak, while F2 shows a more complicated motion, moving back and forth in the east-west direction, eventually separating from the neutral line. It is interesting, however, that the two motions are in some sense synchronous to each other. During the rising stage in hard X-ray intensity, the two sources move in the vicinity of the neutral line (from point 1 to point 5), and the separation between them does not increase so much. On the contrary, the two sources move systematically during the declining stage (from point 7 to point lo), and the separation increases monotonically. Superposed upon such systematic motions, we see abrupt shifts or jumps of source position; a most typical example is seen in the locus of F2 from point 3 to point 4. This jump is much larger than the measurement error, which is less than 1 arcsec judging from the r.m.s. scatter of 0.5-s data points (not shown in Figure 2). As clearly seen from this example, the hard X-ray footpoint motion can be measured with HXT with an accuracy of better than 1 arcsec, given enough hard X-ray photon counts. In the case of the 1997 November 6 flare, the double footpoint sources show complex but systematic motions. It suggest that the flaring magnetic field structure is complex, and that the energy release or particle acceleration is directly related to the number of site shifts in a systematic way. Since hard X-ray intensity we anticipate that some quantitative energetic electrons that precipitate towards the footpoints, analysis of energy release will be made available in conjunction wit,h the coronal magnetic field structure. Towards this goal, the study is in progress. The authors would like to thank the SOHO MD1 team for allowing D. M. Zarro, N. Gopalswamy, and H. S. Hudson are acknowledged MD1 data with HXT data as well as valuable discussions.
us to make use of the MDT data. for their help in coaligning the
REFERENCES Alexander, D., and Metcalf, T. It. 1997, Astrophys. J., 489, 442. Hoyng, P. et al., 1981, Astrophys. J. Lett., 244, L153 Kosugi, T. et al., Solar Phys., 136, 17 (1991). Sakao, T., PhD Thesis, The University of Tokyo (1994). Five years of Yohkoh Sakao, T. et al., in Observational Plasma Astrophysics: Watanabe, T., Kosugi, T., and Sterling, A.C., Kluwer, pp. 273 (1998). Sato, J., PhD Thesis, The Graduate University for Advanced Studies (1997). Sato, J. et al., Submitted to Publ. Astron. Sot. Japan (1998).
and
Beyond,
Eds:
Pergamon
0273-1177100$20.00+ 0.00
www.elsevier.nl/locate/asr
IMPROVEMENT AN ANALYSIS J. Satol,
S. Masuda’,
PII: SO273-1177(99)01102-3
OF YOHKOH HXT IMAGING AND OF THE 199’7 NOVEMBER 6, X9 FLARE T. Kosugi3,
and T. Sakao’
‘National Radio Observatory, Nobeyama, Minamisaku, 384-l 305, Japan 2Solar Terrestrial Environment Laboratory, Nagoya Univ., Toyokawa, 442-8507, 31nstitute of S p ace and Astronautical Science, Sagamihara, 229-8510, Japan
Japan
ABSTRACT The imaging capability of the Hard X-ray Telescope (HXT) on board Yohkoh has been drastically improved by (1) adopting new instrumental response functions (modulation patterns) derived from a self-calibration procedure that makes use of solar flares themselves as calibration sources, (2) revising and (3) the Maximum Entropy (MEM) image synthesis procedure for better total flux estimation, One of the most intense flares so far incorporating in MEM properly estimated observation errors. observed with HXT, the 1997 November 6, X9 flare, has been analyzed with the new HXT imaging program. Two footpoint sources are clearly seen and show systematic motions during the impulsive phase. This may provide a new clue to understand the coronal magnetic field structure involved in 0 2000 COSPAR. Published by Elsevier Science Ltd. the energy release process of flares. INTRODUCTION teleThe Hard X-ray Telescope (HXT; Kosugi et al. 1991) on board Yohkoh is a Fourier-synthesis scope. It measures a set of spatially modulated incident photon counts with 64 hi-grid modulation collimators and an image is synthesized with the Maximum Entropy Method (MEM) or other image The HXT has so far observed more than 1300 flares since launch in 1991 synthesis procedures. August. Most of them have been successfully synthesized into images and have revealed several important characteristics of solar flare hard X-ray sou.rces (e.g., Sakao 1994; Masuda 1994). Image quality, however, has not always been satisfactory; the synthesized images sometimes showed scattered patches with size being smaller than the HXT spatial resolution and/or spurious structures sporadically appearing/disappearing with time. Such a degradation of image quality also tended to occur when we pursued higher image quality, i.e., higher signal-to-noise ratio, by accumulating photon counts. This was strange and implied that something was wrong or inappropriate in the HXT image synthesis. We have analyzed this problem and found how to solve it. This paper briefly discusses the essence of the improved HXT MEM imaging, and then applies it to the analysis of an X-class flare of 1997 November 6. IMPROVEMENT
OF
HXT
IMAGING
The causes of the HXT image degradation were threefold: (1) th e mismatch of the a.ctual modulation patterns with those used in the image synthesis, (2) an inaccurate estimate of the total flux, and (3) the incorporation of underestimated noise/observation error terms in the MEM imaging program. Correspondingly we have made the following improvements for achieving the full imaging capability of HXT: (1) Modulation patterns of the 64 collimators, accurately estimated with a self-calibration procedure in which solar flares are used as calibration sources, are incorporated. (2) The MEM formulation is revised to include an accurate total flux estimate. (3) Noise/observation error terms, estimated in the self-calibration as a byproduct, are properly incorporated in the MEM imaging
502
J. Sat0 et al.
program. Details of these improvements, together with examples of improved HXT images, are fully discussed in Sato (1997) and Sato et al. (1998). Th e essence is briefly summarized below.
Self-Calibration of HXT
Modulation Patterns How can we calibrate the instrumental response function whose original images we have no prior knowledge?
(modulation
patterns)
using solar flares, of
Suppose first for simplicity that only one of the 64 modulation patterns is incorrect, i.e., the pattern used for image synthesis slightly differs from the actual one. In this case, we may expect that the synthesized image is mostly determined by photon counts from the other (correct) 63 collimators, so that it well represents the original. Then, the photon counts estimated from the synthesized image are almost the same as the observed for the 63 modulation collimators but not so for the incorrect one. Hence we have a possibility to know what modulation pattern is incorrect. The situation is basically the same even when all the 64 modulation patterns have minor incorrectness. Since errors in individual modulation patterns tend to be independent of each other, the errors may cancel out and the synthesized image may still well resemble the original. Thus we have possibility to find modulation patterns whose error level is much higher than the “average” error level. Even if we know that a certain modulation pattern is incorrect, it does not necessarily mean that we know the direction of correction for a better pattern. Since one modulation pattern basically contains two important free parameters, i.e., amplitude and phase, we need to obtain a unique correction vector in the two-dimensional space. It is obvious that a unique determination is impossible so long as we use only one flare data; photon count may be overestimated as a result from either an overestimate of the amplitude or a lateral shift of the peak position of the modulation pattern toward the source position due to the phase error. This ambiguity, however, can be removed if we simultaneously make use of many flares taken with the same set of modulation patterns. Based upon the concept given above, we have constructed a self-calibration scheme in which the 64 modulation patterns are iteratively improved to converge finally into the most plausible patterns. The patterns thus obtained are, in general, consistent in phase with those obtained from prelaunch measurements and used so far for the HXT imaging, but differ in amplitude to a significant degree. We have confirmed that adoption of the newly obtained modulation patterns is essential in improving the HXT imaging capability.
Revised MEM Formulation and Error Estimate The Maximum Entropy Method (MEM) so f ar used in HXT imaging is one of the standard or classical ones (e.g., Frieden 1972, Gull and Daniel1 1978), in which the total flux is given a priori as a constant. This is not appropriate for HXT since the total flux estimated from any linear combination of the 64 modulation patterns is dependent on the source location and not necessarily accurate enough (e.g., Alexander and Metcalf 1997). H ence, we have developed a new formulation of MEM in which the total flux is a free parameter to be determined in accordance with the MEM principle. In addition, noise/observation error terms need be properly incorporated as functions of observed This has been achieved by analyzing photon counts for any MEM to provide a plausible solution. the uncertainty of the modulation patterns still remaining after the self-calibration discussed above.
Improved HXT Images With the above improvements combined together, we have achieved high-quality imaging of HXT. Figure 1 compares HXT L-band (14-23 keV) images synthesized with the new imaging program of photon (bottom) with th ose synthesized with the old program (top), for different accumulations counts. It is clear from the new images shown in figure 1 that hard X-ray images (L: 14-23 keV) show similar source structures’over a wide range of photon counts, with an improvement of image quality In contrast, the old HXT image tends to become unrealistically with increasing photon counts. patchy, beyond the instrumental resolution, with increasing photon counts. Other weak points of the HXT imaging, not mentioned in this paper, are also alleviated drastically. Now we can say that, with the new HXT imaging program, flares, from weak to intense as well as from small- to large-sized, are satisfactorily synthesized into images from the impulsive phase to the decay phase.
Improvement
of Yohkoh HXT Imaging
92/Ol/13 HXTCL) FOV 158x158 arcsa
Figure photon with
1 : Examples count
the old (top
peak brightness,
row) and
X-CLASS
L-band
i.e.,
(14-23
keV)
w 300 cts/SC
(left
new (bottom
with contours
l/2 step is adopted) of each map is 158 AN
of HXT
accumulation,
denoting
OF
synthesized
column)
row) imaging
and
programs.
70.7 ~ 12.5% (l/&’
of the peak supplemented x 158 arcsec.
FLARE
images
from
two different
step except
for the top right map where
by gray scale below the 12.5% level.
1997 NOVEMBER
sets of
w 3000 cts/SC (right column), Each image is normalized by the The field of view
6
The new HXT imaging program enables us to analyze a very intense flare from its initial rise, through the peak, to the decay without being bothered by a large photon counts around the peak. This advantage is quite important, because such an intense flare is detected with high signal-to-noise ratios at full time resolution of 0.5 s even in the highest energy band, and thus provides a chance to investigate the rapid variations of purely nonthermal hard X-ray sources in the impulsive phase. An intense flare, X9 in GOES class, occurred in AR 8100 at S16W62 on 1997 November 6. This yielded larger photon counts (in higher energy bands) than any other so far observed with HXT. The intense hard X-rays only lasted for a few minutes; this flare is a typical impulsive flare. We have synthesized images of this flare at the time resolution of 0.5 s over the four HXT energy bands (14-23-33-53-94 keV). The hard X-ray images, as a whole, reveal the presence of two intense sources, 10 to 20 arcsec apart from each other in the north-south direction, and in addition two relatively weak sources to the west of the intense ones, apparently seen in limited time intervals. The two intense sources, hereafter called Fl (northern source) and F2 ( southern source) respectively, seem to be footpoint sources located at the conjugate footpoints of a flaring loop (e.g., Hoyng et al. 1981; ’ f comparison Sakao 1994). A b rie of the HXT images with a SOHO MD1 magnetogram suggests that Fl and F2 are located in opposite magnetic polarities. It has been known that double footpoints are not necessarily stationary; they frequently show systematic motions, with either increasing or decreasing footpoint separation (Sakao et al. 1998). Since the footpoints are believed to represent the regions where energetic electrons stream down along magnetic field lines, the motions reflect shifts of electron injection site or energy release site in a solar flare, and hence may provide a crucial hint to understanding the coronal magnetic field structure and its change during a flare. A result of our preliminary analysis is summarized in Figure 2. As expected, Fl and F2 show similar time variations in flux to each other. The centroid positions of Fl and F2 at representative times, marked in the time profiles by vertical bars with numbers, are shown in the inset of Figure 2, which vividly reveals that both sources rapidly move at projected velocities of order 100 km/s. The motions of the two footpoint sources are complex; Fl first moves to the south-east direction, slightly approaching the magnetic neutral line, but turns around toward the north-west direction nea.r the
J. Sato et al.
504
Figure measured dashed
2:
Intensity with
time
profiles
HXT
in the H band
lines denoting
the systematic
and
positions
(53-94
keV).
of sources Only
Fl
and
representative
F2 (F2 intensity: data
points
l/2
are plotted,
scaled) with
motions
intensity peak, while F2 shows a more complicated motion, moving back and forth in the east-west direction, eventually separating from the neutral line. It is interesting, however, that the two motions are in some sense synchronous to each other. During the rising stage in hard X-ray intensity, the two sources move in the vicinity of the neutral line (from point 1 to point 5), and the separation between them does not increase so much. On the contrary, the two sources move systematically during the declining stage (from point 7 to point lo), and the separation increases monotonically. Superposed upon such systematic motions, we see abrupt shifts or jumps of source position; a most typical example is seen in the locus of F2 from point 3 to point 4. This jump is much larger than the measurement error, which is less than 1 arcsec judging from the r.m.s. scatter of 0.5-s data points (not shown in Figure 2). As clearly seen from this example, the hard X-ray footpoint motion can be measured with HXT with an accuracy of better than 1 arcsec, given enough hard X-ray photon counts. In the case of the 1997 November 6 flare, the double footpoint sources show complex but systematic motions. It suggest that the flaring magnetic field structure is complex, and that the energy release or particle acceleration is directly related to the number of site shifts in a systematic way. Since hard X-ray intensity we anticipate that some quantitative energetic electrons that precipitate towards the footpoints, analysis of energy release will be made available in conjunction wit,h the coronal magnetic field structure. Towards this goal, the study is in progress. The authors would like to thank the SOHO MD1 team for allowing D. M. Zarro, N. Gopalswamy, and H. S. Hudson are acknowledged MD1 data with HXT data as well as valuable discussions.
us to make use of the MDT data. for their help in coaligning the
REFERENCES Alexander, D., and Metcalf, T. It. 1997, Astrophys. J., 489, 442. Hoyng, P. et al., 1981, Astrophys. J. Lett., 244, L153 Kosugi, T. et al., Solar Phys., 136, 17 (1991). Sakao, T., PhD Thesis, The University of Tokyo (1994). Five years of Yohkoh Sakao, T. et al., in Observational Plasma Astrophysics: Watanabe, T., Kosugi, T., and Sterling, A.C., Kluwer, pp. 273 (1998). Sato, J., PhD Thesis, The Graduate University for Advanced Studies (1997). Sato, J. et al., Submitted to Publ. Astron. Sot. Japan (1998).
and
Beyond,
Eds: