D E T E R M I N A T I O N OF T H E S O L A R X - R A Y S P E C T R U M

BY U S I N G T H E A T M O S P H E R I C E X T I N C T I O N

M. LANDINI Arcetri Observatory

(Received 22 February, 1967)

Abstract. Indications about the spectral distribution of the solar radiation below 20 Zk are obtained by comparing the atmospheric extinction of the solar radiation measured by three ion chambers in the satellites SOLRAD 7 and 8.

The data refer to July 5, 6 and 8, 1965 and July 23, 1966 when the satellites passed from light to darkness into or out of the earth's shadow.

The spectral intensity distribution is shown for the four days, and a comparison is made between active and quiet days.

The aim of this paper is to investigate the spectral distribution of the solar radiation in the region from 2 to 20 A, and its variation with the solar activity, using the atmos- pheric extinction.

The measurements have been performed by means of the satellites SOLRAD 7 and 8, instrumented by the Naval Research Laboratory. Telemetry data were received at Arcetri when the satellites passed into or out of the earth's shadow.

The satellites have been instrumented with ion chambers for monitoring the solar radiation in the bands 1-8 A, 8-16 A, and 44-60 A (KREFLIN, 1965a, b). Three cham- bers sensitive to these wavelengths have been used, but the 44-60 A chamber is sensitive also from 3 to 20 A.

The telemetered signal is the current measured by the ion chambers. This quantity depends on the spectral distribution E(2) according to

I (N) = 1.609 10 -19 e)A f 8(2) T(2, N) E(2) d2

A2

(1)

where I is the current in Amp6res, o) is the ion pair production per erg for the gas in the chamber, A the window area in cm 2, 5(2) the chamber efficiency, T(2, N) the transparency function of the atmosphere, and N = S~ n(s) ds is the total number of particles in a column with area 1 cm 2 by s cm long, s being the distance from the sun to the satellite. Due to the variation of the transparency with N the problem is equi- valent to that of having as many counters with efficiency e(2)T(2, N) as there are points where I (N) is known. By reducing the integral to a sum, and solving the linear system in E(2) the spectral distribution may be obtained (MANDELSTAM, 1965a).

It is necessary to remember that the measured signal I is not known as a function of N, but as a function of the time when the telemetry is performed. Therefore, to use Equation (1) the function N(t) should be known. It would be possible to compute N(t) assuming an atmospheric model and using the orbital data of the satellite, but

Solar Physics 2 (1967) 106-111 ; �9 D. Reidel Publishing Company, Dordreeht - Holland

DETERMINATION OF THE SOLAR X-RAY SPECTRUM 107

this method introduces some arbitrariness and errors since the orbital data are not sufficiently accurately known. Below, a way is shown to obtain N(t) from a comparison of the signal from the three chambers.

The integral in Equation (1) is performed over that region A2 where the 'effective' efficiency e(2) T(2, N) differs from 0. The transparency function is assumed to have the form

T(L N) = e -k~N,

where k(2) is the mean air cross-section. In order to write the transparency in this form it is necessary to assume that k(2) does not vary along the ray path s. This is not true because of the changes of composition of the atmosphere, but the variation is less than 5~o in the region where the absorption takes place.

It is possible to solve the problem in a much simpler way considering instead of I(N):

I(O)I(N) f_ e(;) - r ( z N)

A2 A)~

where I(0) is the current measured outside of the atmosphere, and to compute the function I(N)/I(O) for different assumed shapes of the spectrum, taking into account the efficiency of the chambers.

The assumed spectra were those computed by Mandelstam and Prokudina et al. (MANDELSTAM, 1965a, b), in the region between 1 and 100 A for electron temperatures T e o f l , 2 a n d 3 106~

The functions I(U)/I(O) for the chambers 1-S A, 8-16 A and 44-60 A are shown in Figure 1 for Te = 1, 2 and 3 106 ~ for the case when the current of the 44-60 A

t I(N) 1 .0

,B

.6

.4

.2

O i0 ~0 10 ~9

8 - 1 6 A CounPer

1_~ ~ Co~n~ ~ ~ J

~/ Counter

_ N

lO~,e,

Fig. 1. Absorption curves for the 1-8 A, 8-16 A and 44-60 A chambers computed according to the theoretical spectra given by Mandelstam for Te = 1, 2 and 3 106~ The figure shows the expected telemetry signal in percents of the maximum value versus the total number of absorbing particles

in a column 1 cmz wide.

108 M. LANDINI

Fig. 2.

1(~'

"7,=i: i~ 4

~a

~E (D

16 5

- 6 I0

I 0 7

1-8 1

I ~ l p 6VII 65

6 VII 65

I- I ! 5Vl165 i

__•. 6 VII 65

6 VII 65 5VII65

�9 1 Flare {maximum phase) Ariel I](1962) =~ quiet Sun conditlon Ariel n(1962) A N. R.L [1963)

I 8 - 1 6 I

4,_6o 44_60 ~(.~)

i I r J i I :> 0 10 20 30 40 50 60

SpectFa! distributions obtained f rom the atmospheric extinction measurements of July 5, 6 and 8, ]965, taken by the SOLRA~) 7 satellite.

chamber which is due to the 3-20 ~ band is ~ of that due to the 44-60 A band (low activity conditions).

A comparison of the measured signal I(t)/Imu X of the 8-16 A chamber, with the three curves I(N)/I(O) for the 8-16 ]~ chamber in Figure 1, yields three functions N(t). These are used to transform I(t)/Imax for the 44-60 A chamber into I(N)/I(O) for the 44-60/~ chamber. As is clear from Figure 1 the variations of the 8-16 ]t signal with

DETERMINATION OF THE SOLAR X-RAY SPECTRUM 109

Te are larger than the variations of the 44-60/~ signal. Therefore only one of the three I(N)/I(O) curves fits to the corresponding curve in Figure 1 for the 44-60 • signal. It gives the right spectral shape and the right N(t). The situation in Figure 1 applies to the case when the contribution of the 3-20 A band to the 44-60 A signal is ~ of the contribution of the 44-60 N band. Of course, for each assumed spectral shape, the true contribution is computed, and a comparison is made with the corresponding curve.

The same type of argument can be applied to the 1-8 A chamber for the days when the signal was above the threshold.

From the spectral shape obtained in this way, the actual spectral values can be computed using the measured Ima x.

The measurements were performed for 4 days: July 5, 6 and 8 1965 (1965-16-d satellite) and July 23, 1966 (1965-93-a satellite). July 5 and 8 were days with a low solar activity; July 6 and 23 showed a higher activity.

The computation was performed taking A2-bands 2 N wide. The spectral reso- lution of the method is 2-3 ~ and is due to the variation of the air cross-section with wavelength and to the fact that a full solar disk is observed.

The derived spectral shapes may be characterized by Te-values ranging from 2 to 3 106 ~ for the 8-16 N band, but the spectrum is extremely variable for the 1-8 ~t band. The results are shown in Figures 2 and 3, where the intensity outside the earth's atmosphere, in erg cm -2 sec-~ ~ - i is plotted against the wavelength. No indication of the error is given because it changes from wavelength to wavelength for different spectral shapes. An average error can be evaluated by computing the variations produced by arbitrarily changing Te from 2106 OK to 3 106 +K and by examining the consequent change in the spectral shape: it gives a factor __+ 3.

It is assumed that the function I(t) is determined only by atmospheric absorption and that no variation of the solar flux occurred during the measurements. This as- sumption looks reasonable since a complete extinction lasted about one minute. During quiet sun conditions it is sure that no flux variation can occur in such a short interval of time, but this might not be true in the presence of solar activity. However, no appreciable variation was measured during one minute immediately after the end of the eclipse, when the signal was unaffected by absorption.

For July 5 and 8 the flux below 8 A was under the threshold of the 1-8 ~ counter; the spectrum indicated in Figures 2 and 3 for those days can be considered to be an upper limit in this spectral range. In Figures 2 and 3 a comparison is made with measurements performed by Ariel II in 1962 (POUNDS, 1965) and by the Naval Re- search Laboratory in 1963 (BLAKE et al., 1965). The two measurements of July 6 and 23 coincide with optical flares of importance 1 and 1 -, both in their beginning phase. The flux between 44 and 60 A increased by a factor of 1.7 from low activity (July 5 and 8) to high activity (July 6) in 1965; between 11 and 19 2t it increased by a factor of 10 to 20 and this factor goes up to 400 below 5 A.

It is interesting to compare the fluxes of the two active days of July 6, 1965 and July 23, 1966.

l 10 M. LANDINI

Fig. 3.

23 VII 66

i f : 3

x

"Y~ 1~ 4 X 2 ~Ftare (.sl-art.ing phase) Ar ie t ~ ( 1 9 ~ 2 )

~E o

t ~ L- ea

x

m

I_B~,G) I0 6 I 414.60(B) 44-60(8)

I I I I

B_ 16(K)

I I ] P I I

o 20 3 o 4o so so

Spectral distribution obtained from the atmospheric extinction measurements of July 23, 1966, taken by the SOLRAD 8 satellite.

On July 23 one obtains in the 9-19 A band about the same values as on July 6,

the intensity is a little lower for the region below 9 A, and 1.8 times higher in the 44-60 A band.

This indicates that below 19 A the flux is almost entirely due to the activity present at the moment of the measurements; the excess of 1.8 times in the 44-60 A band can be attributed to the background. Indeed, also the increase showed by the decimetric radionoise emission is of the same order: the ratio of the 10.7 cm mean flux (Ottawa) between July 23, 1966 and July 6, 1965 is 1.5 (CRPL, 1965-66).

This is in agreement with the fact that the radiation in the band 44-60 A comes from large regions around active centers, just like the decimetric radiation. This is not true for the radiation below 20 A, which appears to be due to the very active regions on the sun as shown by the few X-ray pictures present in literature.

DETERMINATION OF THE SOLAR X-RAY SPECTRUM 111

References

BLAKE, R., CHUBB, T. A., FRIEDMAN, H., and UNZICKER, A. E. : 1965, Ann. Astroph. 28, 583. CRPL: U.S. Department of Commerce N.B.S. Bulletin (1965-66) Solar Geophysical Data, Part

B. Boulder, Colo. KREPLIN, R. W.: 1965a, 'Final Data and Calibrations for the Fall 1964 N.R.L. Satellite Experiment

(1965-16-D)'. U.S. Naval Research Laboratory. KREPLIN, R. W. : 1965b, 'Final Data and Calibrations for the Explorer XXX NRL SOLRAD 8 X-ray

monitoring satellite (1965-93-A)'. U.S. Naval Research Laboratory. MANDELSTAM, S. L. : 1965a, Space Sci. Rev. 4, 587. MANDELSTAM, S. L." 1965b, Ann. Astroph. 28, 614. POUNDS, K. A.: 1965, Ann. Astroph. 28, 132.