A H A R D X - R A Y O B S E R V A T I O N OF A S O L A R

F L A R E W I T H 1 0 0 MS T I M E R E S O L U T I O N

K. HURLEY and G. DUPRAT

Centre d'Etude Spatiale des Rayonnements, 9, avenue de Colonel Roche, 31400 Toulouse, France

(Received 7 April; in revised form 10 September, 1976)

Abstract. A solar flare which occurred on 4 July 1974 was observed in hard X-rays with a balloon-borne detector. When analyzed with a time resolution of 100 ms, four 2 s long spikes are observed, which are correlated with decimetric emission. Spectral analysis shows that the hardest X-rays were produced during the decay phase of the burst, when the microwave emission reached its peak. It is argued that the fine time structure could either be a bounce time effect, or that it could be due to the electron acceleration mechanism.

1. Introduction

It is generally agreed that the time structure of a solar X-ray burst can be

interpreted in terms of electron acceleration processes. Some X-ray bursts display

a characteristic two component structure, consisting of an impulsive event

superimposed on a slowly varying one (Kane, 1969), which may indicate the

presence of two acceleration processes during a single burst. The nature of the

impulsive component (thick vs thin target, continuous vs impulsive acceleration)

has been the subject of much controversy. It is suspected that fluctuations on time

scales of less than one second are present during the impulsive phase; X-ray

observations made to date, with time resolutions of - 1 s or more (e.g., Kane and

Anderson, 1970; Datlowe et al., 1974; Hoyng et al., 1975) suggest, but do not reveal,

such fluctuations. In this paper, we present high time resolution (100ms)

data which give clear evidence for the existence of variations on time scales of ~< 1 s.

These data were associated with an H a flare of importance 1 B located in the McMath plage region 13043 (15 ~ S, 04 ~ W), which reached its maximum intensity

around 0650 UT on 4 July, 1974.

2. Experiment

The data described in this paper were recorded in the course of a balloon borne

cosmic X-ray experiment. The gondola was launched from Gap, France, and was

floating at 1 . 9 g c m -2 at the time of the observation. Figure 1 shows the

geometry of the observation; a similar, although smaller, detector has been described elsewhere (Hurley, 1972), and we give here only the principal charac-

teristics. The central detector (1) consists of a 0.64 cm thick by 12.7 cm diameter

NaI(T1) scintillator, optically coupled to a 5.08 cm thick by 12.7 cm diameter CsI(Na) scintillator; both are viewed by a single photomultiplier, and pulse shape discrimination is employed in order to accept only those pulses due to energy

Solar Physics 52 (1977) 107-116. All Rights Reserved Copyright �9 1977 by D. Reidel Publishing Company, Dordrecht-Holland

108 K. HURLEY AND G. DUPRAT

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Fig. t . Geomet ry of the observation. The detector, consisting of a central phoswich (1), an anticoincidence annulus (2), and a collimator (3), is at 1.9 g c m -2. The 9.6 ~ FWFM viewing cone is

pointed at 13.7 ~ from the zenith.

losses in the NaI(T1). This 'phoswich' arrangement reduces the background and gives more precise energy loss spectra, since it helps eliminate photons which Compton scatter in the NaI(T1). This central detector is surrounded by an optically separate annulus of CsI(Na) (2), viewed by 6 photomultipliers; above the main detector and the annulus is a drilled CsI(Na) collimator (3), 20.3 cm. in diameter by 5.1cm thick, optically separate and viewed by 4 photomultipliers. An array of 293 holes leading to the main detector defines a viewing angle of 4.8 ~ full width at half maximum, and an active area of 60 cm 2. The central detector is operated in anticoincidence with the annulus and collimator.

The detector was pointed at the Perseus cluster of galaxies, which was at 13.7 ~ from the zenith, while the Sun was at a zenith angle of 62.3~ the Sun, Perseus, the zenith, and the detector all lay in the same plane during the observation, to within ~<1 ~

Solar photons may reach the upper surface of the collimator (324 cm 2) directly (that is, without scattering in the atmosphere); in order to reach the central detector, however, they must scatter at least once in the overlying atmosphere (Figure 1). Only the integral count rate of the collimator >~30 keV is monitored, while the events in the central detector are pulse height analyzed in 128 channels before transmission to the ground. We will discuss the collimator data first.

3. Time Structure of the Event -Col l imator Data

The collimator counting rate, after conversion to an analog voltage, is transmitted to the ground continuously; thus the limiting time resolution is either that

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imposed by the telemetry ( - 1 ms) or that imposed by count rate statistics. For most parts of the X-ray event, the excess count rate in the collimator is well above 1000 counts s -a, and we have chosen to average the count rates over 100 ms for

the analysis which follows. Using this same time resolution, we have analyzed a background portion of the data, and we verified that the count rate profiles thus

obtained obeyed Gaussian statistics. We also note that, even during the most intense part of the event, the dead time in the collimator did not increase above 50% ; thus saturation and pulse pile up effects are not important for these data.

The collimator count rate began to increase above background at 6:46:54.0 UT, and continued to rise slowly until 6:47:33.0, when an impulsive increase began. A t 6:47:43.0, the impulsive phase ended, and a slow decrease started; a broad maximum in this decrease occurred around 6:47:50.0. At 6:48:31.6, the count rate was down to the background level. The part of the event displaying the finest time structure is shown in Figure 2. This event, whose total duration is 100 s, displays the characteristic features noted by Kane (1969): a slow rise, sharp spikes, a broad maximum, and a decay somewhat longer than the rise.

As indicated in Figure 2, we have subdivided the event into three regions, which we will refer to hereafter as rise, impulsive, and decay.

We have performed a power spectrum analysis of the entire event as seen by the collimator. A large peak appears at 3.5 seconds; however, when either the rise or decay portion alone is analyzed, there are no peaks. This, along with the fact that power spectrum analyses tend to respond very strongly to two or more peaks superimposed on otherwise featureless data, leads us to believe that the 3.5 s response is due simply to the 4 peaks in the impulsive portion, and that it would not be correct to call this event periodic. More information can be gained by considering the structure of the individual peaks; e.g., referring to Figure 2, it can be seen that the first spike rises approximately linearly to a maximum in about 0.8 seconds, and that the fourth falls approximately linearly from a maximum in

about 2.8s. Despite the quasi-linearity of the spikes, it is perhaps more convenient to think in terms of e-folding rise and fall times: these are - 1 . 8 s and - 5 . 8 s, respectively.

4. Energy Structure ot the Event - Central Detector Data

To reach the central detector, a solar photon must scatter either in the overlying atmosphere, or in the collimator. In order to correct for atmospheric effects, we

began by using a Monte-Carlo program which evaluated the degradation of a photon beam in the atmosphere due to Compton scattering, Rayleigh scattering, and photoelectric absorption (St. Marc, 1973). Photons incident on the top of the atmosphere were followed until they were either backscattered out of the atmos- phere, photoelectrically absorbed, or until they reached the detector. The surpris- ing result of this program was that the shape of the spectrum observed in the central detector was hardly different from the shape which would have been

A HARD X-RAY OBSERVATION OF A SOLAR FLARE 11 t

observed if the detector had been pointed directly at the sun; the intensity observed, however, was reduced considerably. For example, at 50 keV, only - 1 photon cm -2 is detected for - 7 0 0 0 photons cm -2 at 0 g cm -2.

This suggested that the central detector was responding primarily to photons which had scattered only once, through approximately the same angle (62.3 ~ 13.7 ~ or 48.6~ and which had therefore lost only a small fraction of their original energy. To verify this idea, we calculated, by direct integration, the probability that a photon penetrate the atmosphere and reach the conical space viewed by the

detector without interacting, then Compton scatter in this space towards the detector, and then reach the detector with no further interactions. As the results of this calculation were in agreement with the Monte-Carlo results, we are confident that the central detector was indeed counting singly scattered photons, and furthermore, due to the small range of angles subtended by the central

detector at any part of the cone, photons which had all scattered through approxi- mately equal angles. We later verified, in the laboratory, that the effect of scattering in the walls of the collimator was negligible compared to atmospheric

scattering. The effect of atmospheric scattering was thus calculated for a series of trial

spectra of the form k E -~ photons cm -2 s -1 keV -1 incident at the top of the

atmosphere, where E is the photon energy in keV, and where the exponent 3' was allowed to vary from 3.6 to 6.5. The deformed spectra were then used as input to a program which simulated the detector response (But-Van et al., 1973). Finally, these calculated spectra were compared to the observed spectra, and the X 2 test was applied to estimate the goodness of fit. The results are given in Figure 3. The best fits to the rise, impulsive, and decay portions of the event are 8.7 x 108 E -46, 7.9 x 108 E -4A, and 1.1 x 101~ E -5"1, respectively, with X 2 per degree of freedom

of 0.12, 0.78, and 0.73, respectively. Evidence for spectral change, however, must not rest on the best fit values alone, but also on the confidence regions around the best fit values. The assignment of such confidence regions becomes a complex problem when the calculated spectra depend nonlinearly on one or more of the parameters (in our case, 3/). Different authors have treated the problem differently (Cline and Lesser, 1970; Margon et al., 1975; Kellogg et al., 1975); we have adopted the t reatment of Margon et al. (1975) which is to define a region of P % confidence about the best fit values of m parameters by

2 2 2 X p = X m i n ~- Xp(m),

where )Cp 2 is the chisquare value corresponding to P % confidence, 2 Xmin is the chisquare corresponding to the best fit values of the parameters, and x~(rn) is the chisquare corresponding to P% probability for m degrees of freedom. In our case, m = 2, and we have taken P = 90%. We have displayed the results in an inset in Figure 3. The actual values of k and ~/for the rise, impulsive, and decay portions of the event have a 90% probability of lying anywhere within the contours indicated. We note, finally, that this technique may not always give the

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Fig. 3. Detected spectra (left-hand scale) and spectra incident at the top of the atmosphere after correction for atmospheric scattering and detector effects (right-hand scale) for the rise, impulsive, and decay portions of the event. Inset: Chisquare contours in the k;. 3' plane. The best fit values of k and ~, are indicated by a + for the rise, impulsive, and decay portions. The contours around the best fit values represent 90% probability values. Thus the actual values of k and 3' have a 90% probability of lying

anywhere within these contours.

A H A R D X - R A Y O B S E R V A T I O N O F A S O L A R F L A R E 113

correct confidence intervals if the fit is extremely nonlinear (Kellogg et al . , 1975), and it is essential to verify that the regions thus defined actually correspond to the probability P. We have done this by generating a series of random spectra based on our observed spectra; that is, spectra whose m e a n values correspond to the observed spectra shown in Figure 3, but whose actual values are normally distributed about this mean with the standard deviations shown in the figure. By comparing the best fit values of k and 3' for these random spectra to the calculated contours, we verified that a fraction very close to 0.90 of the k, 3' thus

found lay in the contours.

5. Discussion

Although small optically, this solar event was quite intense in X-rays; during the impulsive part, the energy between 27 and 50keV reached 4.3• 10 -4 ergs cm -2 s -1 at the Earth. The radio emission was also intense; in Figure 4, we have plotted the radio fluxes at 500 MHz (Yamashita, 1975), and at 1000, 2000, 3750, and 9400 MHz (Tanaka, 1975). An interesting feature is evident from these curves: the maximum of the X-ray event (the impulsive part) does not correspond to the maximum of the microwave event, i.e., the fluxes at 3750 and 9400MHz. Instead, the X-ray maximum is coincident with a spike in the decimetric flux, at 500, 1000, and 2000MHz. We have examined high time resolution data (2 sweeps s -a) from the Culgoora Solar Observatory (Stewart, 1975), and find that the 4 X-ray peaks are indeed correlated with 4 features in the radio spectrograph record at 1000 MHz. At higher and lower frequencies, these features tend to blend into the continuum, although there is some evidence that they continue to lower frequencies.

Turning now to the decay portion of the X-ray event, we note that, although the rather large chisquare contours do not permit us to draw any definite conclusions concerning changes in the exponent y, it is nevertheless clear that higher energy X-rays (up to 100 keV) are present during this part of the event. It is interesting to note that the microwave flux reaches a peak during this period.

Recently, Takakura (1972) has shown that it is possible to give a self consistent interpretation to the microwave and hard X-ray emission accompanying a solar flare, when synchrotron self-absorption in a dipole field is taken into account properly. In this model, the X-ray emission is from a thin target, and the microwave emission spectrum (frequencies ~>2 GHz) is determined mainly by the electron spectrum at energies above 100 keV. The model thus depends upon a comparison between the microwave spectrum at frequencies above 2 GHz, and the X-ray spectrum at energies above about 100keV. In principle, this then allows a determintion of both the thermal and nonthermal electron densities in the source, as well as of the source volume. For example, Anderson and Mahoney (1974) applied this model to an X-ray observation made under conditions quite similar to the ones described here. In our case, the application of Takakura's

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A HARD X-RAY OBSERVATION OF A SOLAR FLARE 1 ~ 5

calculations is not straightforward, because we have only an upper limit to the X-ray fluxes above 100keV. In is nevertheless interesting to determine the

constraints which can be imposed on the source parameters with the data

available f rom the decay phase, when the hardest X-rays were observed, and the

microwave flux was the most intense. Using our upper limit to the X-ray flux above 100keV, and Takakura ' s

Equat ion (A-31), we obtain

n rn(>0 .2 ) V ~ < 1.7 • 10 45 cm 3,

where nr is the number density of thermal electrons in cm -3, n ( > 0 . 2 ) is the number density of nonthermal electrons with energies (hv/mc2)>0.2, also in

c m -3 , and V is the volume of the source in c m 3.

Next, using the microwave data up to 9.4 GHz, we find that the flux increases as

fl , where f is the frequency. From Takakura ' s Figure 2, this allows us to

determine two parameters of the radio source. First, X, a measure of the upper boundary of the radio source, must be about__ ~; second, ~, a measure of the optical thickness of the source, must be about x/10. Assuming Takakura ' s standard value of 2500 G for the magnetic field in the photosphere, we obtain a source volume V = 5.4 • 1027 cm 3, and a nonthermal electron density n(>0.2) = 1.6 • 107 c m 3.

Finally, using the X-ray data, we obtain, for the thermal electron density, n-r<~2 • 10 l~ cm -3, which places the source in the lower corona, and is consistent with the thin target interpretation. Using Takakura ' s configuration for the source

region, the volume V can be used to determine the characteristic dimension d of

the source: in this case, d ~ 7 0 0 0 kin. The upper boundary of the radio source in

this model occurs at about 5 d, or 35 000 km, and the time taken by a 50 keV electron to traverse this distance would be at least 0.3 s.

We are thus lead to two possible interpretations of the time structure of the

impulsive portion. First, that it is simply due to the bounce of a group of electrons in a magnetic bottle; the spacing between the peaks (1-2 s) is not inconsistent

with this idea, especially considering the uncertainties in the numbers derived

f rom Takakura ' s model. Second, that the time structure is due to the acceleration

mechanism; some support for this idea can be found in the radio spectrograph data, in which the radio emission correlated with the four peaks appears to drift to lower frequencies and to blend into a large series of Type I I I bursts. This suggests that these electrons are escaping, and not trapped. In this case, the acceleration

mechanism would have to have a characteristic time constant corresponding to the rise time of the X-radiation, or 1.8 s.

We conclude that this X-ray event, due to the fact that the hardest X-rays were produced after the impulsive phase (cf. Kane, 1969) must be considered as a ra ther unusual one. However , the fine time structure of the impulsive phase might well turn out to be common to many events, when analyzed with sufficiently high t ime resolution. An interesting point which could be studied with high time

116 K. HURLEY AND G. DUPRAT

resolution measurements is the relation between spectrograph records of decimet- ric emission, and X-ray emission.

Acknowledgements

We are grateful to Kinsey Anderson for loaning us the detector used in this experiment. We acknowledge helpful discussions with R. Bouigue, G. Vedrenne, and R. Talon, and thank F. Cambou for his support and encouragement. This work was supported by CNES Convention Number 75-212

References

Anderson, K. A. and Mahoney, W. A.: 1974, Solar Phys. 35, 419. Bui-Van, A., Giordano, G., Hurley, K., and Mandrou, P.: 1973, A Monte-Carlo Program for

Scintillation Counter Response, CESR Report 73-382. Cline, D. and Lesser, P. M. S.: 1970, Nucl. Instr. Meth. 82, 291. Datlowe, D. W., Elcan, M. J., and Hudson, H. S.: 1974, Solar Phys. 39, 155. Hoyng, P., Brown, J. C., Stevens, G., and Van Beek, H. F.: 1975, in S. R. Kane (ed.), 'Solar

Gamma-, X-, and EUV Radiation', IAU Syrup. 68, 233. Hurley, K.: 1972, J. Geophys. Res. 77, 46. Kane, S. R.: 1969, Astrophys. J. 157, L139. Kane, S. R. and Anderson, K. A.: 1970, Astrophys. J. 162, 1003. Kellogg, E., Baldwin, J. R., and Koch, D.: 1975, Astrophys. J. 199, 299. Margon, B., Lampton, M., Bowyer, S., and Cruddace, R.: 1975, Astrophys. J. 197, 25. St. Marc, A.: 1973, l~tude de la Propagation des Photons X ~ travers l'Atmosphrre, Application h la

Spectromrtrie du Rayonnement X Auroral, Thesis, Patti Sabatier University, Toulouse, France. Stewart, R. T.: 1975, Private Communication. Takakura, T.: 1972, Solar Phys. 26, 151. Tanaka, H.: 1975, Private Communication. Yamashita, F.: 1975, Private Communication.