. 

Semi-Annual Status Report 

Hydrogen Emission from Jupiter: 

Hydrogen Emission from Sunlit Atmosphere of Saturn 

NASA Grant NAG-5-560 

Submitted to 

National Aeronautics and Space Administration 

bY 

D. E. Shemansky and J. B. Holberg 

April, 1987 

(hAS1-CP-180245) HYCECGEL i!Ll$E1Cbl FBGB 

JEPIPEB: HPDBCGLL EfilSSICB FECE SUNLIT 

N87-19325 

AIBOSPHEBE CP SAID68 Semiansual Status 

BeFort (Arizcoa Driiv-, 'Incsc~.) 25 p Unclas 

CSCL 03B 63/91 43764 
2 

ABSTRACT 

Successful IUE observations of the equatorial sunlit atmosphere of Jupiter and Saturn have been 

obtained. Spectra containing atomic and molecular hydrogen and solar reflection continuum emissions have been analyzed, with the purpose of determining the long term temporal behavior of the 

electroglow process. Quantitative estimates have been established for the first time using a model 

analysis of the short wavelength region of the spectrum. Both systems show varying degrees of long 

term variability in hydrogen emission rate, but the time scale is too short to determine whether there 

is a dependence on solar cycle activity. As part of the emission modeling program, a preliminary 

point source spreading function for the WE SWP instrument has been established, suggesting a 

wavelength dependence in spectral line width different from previous analyses. Further IUE observations are planned for both Jupiter and Saturn. 

INTRODUCTION: OBJECTIVES 

JUPITER 

A question of recognized importance to the understanding of the source and flow of energy in 

Jupiter’s atmosphere, is the long term behavior of the EUV emissions. The initial epoch for usable 

observations relevant to this question is -1970. The principle reference points are rocket observations in 1968-72, Pioneer 10 (PIO) and Voyager (V) spacecraft encounters in 1973 and 1979 near the 

times of solar minimum and maximum activity respectively, and IUE measurements beginning in 

1978. Recent reanalysis of rocket observations obtained originally by Giles et al. (1976), together 

with the P10, Voyager, and IUE data indicate that the H, band emissions have remained relatively 

constant, while the H Lya emission has varied in intensity by an order of magnitude (Shemansky 

and Judge 1986; Appendix A). The more recent IUE measurements in this series (1985-1986) which 

have now provided a measure of both H Lya and H, emissions, with the application of spectral 

models, suggest that the H, bands may have increased in brightness at solar minimum whereas the H 
3 

Lya values decreased. This result contrasts with H Lya measurements of Uranus over the 

1982-1985 period in which there is no long term variation (Clarke et al. 1986). Table 1 shows a 

summary of results. On this basis Jupiter exhibits a substantially larger variation at the H Lya 

emission rate than the solar source between minimum and maximum activity. The H Lya bulge 

phenomenon showing longitudinal variation in emission rate is unique to Jupiter. The proposed 

bulge mechanism (Shemansky 1985) requires particle energy deposition in the exosphere, a symptom 

of which is the observed equatorial H, Rydberg bands. The apparent strong variability of the H 

Lycr emission both in absolute terms and in relation to the H, Rydberg systems, is basically not 

understood, but it appears to imply a changing abundance of H forced primarily by variations in 

loss rate rather than production rate. 

The April 1985 and November 1986 IUE results obtained in this program show a reduced absolute H Lya intensity, but not to the extent obtained from the equivalent results near solar minimum 

in 1974. The analysis of the 1985, 1986 measurements also have obtained a measure of H, Rydberg 

brightness which may have increased relative to 1979. The reason for an apparent decreased abundance of atomic hydrogen in the face of an increase in the major dissociation source is an interesting mystery. Further investigation is required to determine the extent of the dependence on the 

solar cycle. 

It should be emphasized that although the brightness of the strong Jovian H Lya line has been 

monitored since shortly after the launch of IUE, little of this data can be used to establish the corresponding intensities of the H, band emissions. These emissions are complementary to the H Lya 

intensity, providing a spectroscopic diagnostic of the dissociation and energy deposition rates. 

Understanding the role played by solar EUV radiation in catalyzing this emission will require 

knowledge of the behavior of the Lya and H, band components throughout the solar cycle. 

SATURN 

We propose to obtain further observations of Saturn’s sunlit atmospheric emissions, on the basis 

of preliminary analysis of very recent measurements obtained in the 9th year IUE program on 1986 
4 

DOY 252 and 254. These results show a mean H Lya brightness a factor of 5 below the value 

measured by Voyager 1 in November 1980. The details of the analysis indicate that the IUE and 

Voyager results can be directly compared as discussed below, and we conclude that the apparent 

change in emission brightness is real. The present result is remarkable because the disk averaged 

brightness of Saturn in H Lya (0.88 2 0.2 kR) is less than the mean value obtained for Uranus by 

Clarke et al. (1986). The Saturn disk averaged brightness in H Lya radiation has not been monitored on a frequent basis so that the time scale of the variation is not well defined. Since the 

launch of the IUE observatory and the Voyager encounters with the outer planets it has become 

apparent that, contrary to our expectations, the solar UV flux contributes only a small fraction of 

the energy deposited in the upper atmospheres of Saturn and Jupiter (Broadfoot, et al, 1981a, Broadfoot et al., 1981b; Shemansky, 1985; Yelle, et al., 1986. Evidence for this is the high exospheric 

temperatures (1000 K for Jupiter, 420 K for Saturn and 800 K for Uranus), the intense, non- auroral, H, band emissions (3 kR from Jupiter and 1 kR from Saturn) and the H Lya to H, band 

brightness ratio which indicates a high altitude, collisional source for both emissions. These developments imply that the measured solar UV flux can no longer be used as the sole input for calculations of the physical state of Saturnian and Jovian upper atmospheres. Rather, we must rely on the 

H, band brightness to measure the energy deposition and infer the exospheric temperature, ionization rate and atomic H mixing ratio in the upper atmospheres (Table 2 shows estimates of dissociation rates based on Voyager data). Fortunately our understanding of the properties of the H, 

molecule, and consequently synthetic spectra, have advanced sufficiently to allow the accurate determination of total emission brightness, energy deposition and electron temperature (given a sufficient 

signal to noise ratio) from the measured H, band spectrum (Shemansky et al., 1985; Shemansky, 

1985). Similarly, the H Lya line is produced predominantly by collisional excitation rather than 

resonant scattering of solar Lya. The resonant scattered contribution is less than 50% on both 

Saturn and Jupiter [Shemansky, 1985; Yelle et al., 19861. For this reason the H Lya to H, band 

brightness ratio directly reflects the atomic H mixing ratio and hence the altitude of the excitation 

source. The H Lya to H, band brightness ratio provides an important clue to the nature of the 
5 

underlying energy source and the physical state of the upper atmosphere. 

The relative instability of Jupiter and Saturn in apparent abundance of atomic hydrogen must 

carry clues to the source process if the nature of the variability can be identified. It is not clear 

what the relationship to solar cycle is, because all three outer planets, Jupiter, Saturn, and Uranus 

according to available data show different behaviors in relation to solar activity. 

RESULTS; DISCUSSION 

JUPITER 

We now have an IUE point of reference in August 1984, April 1985, and November 1986. The 

analysis of this data (Table 1, Figure 1) shows a moderately reduced H Lya intensity, but a relative 

bulge amplitude roughly the same as that observed by Voyager. This appears to imply that the H 

Lya is excited at about the same atmospheric and ionospheric density levels as in 1979. The solar 

reflection continuum is at the same level as that obtained by both Voyager and IUE observations in 

1979 with the exception of the 1986 result which shows a value 16% larger (Table 1). H, band intensities obtained from model calculations compared to the April 1985 IUE data indicate values that 

are basically the same as an analysis of the Clarke, Moos and Feldman (1982) results, Is (H, 

L~+WR) = 4.4+ - 1.6 kR. This value is -45% larger than the Voyager measurement in 1979. Analysis of the November 1986 spectrum (Figure 2) gives a value 5.4 ~1.7 kR, moderately higher, than 

the 1985 and earlier value, but about a factor of- 2 larger than the Voyager value of Is (H, 

L~+WR) = 3.0 kR. We have proposed further IUE observations of Jupiter to extend the data base 

further into the solar minimum period. The additional data we are proposing to obtain here would 

be composed of a series of bracketed SWP exposures designed to measure H Lya as well as the 

fainter H, features. These data would characterize the Jovian equatorial emission under solar minimum conditions. The importance of obtaining an equatorial H, emission spectrum lies in the fact 

that the emission is clearly unaffected by hydrocarbon absorption, and provides a direct measure of 

energy deposition rates. 

-- 
6 

SATURN 

We have obtained measurements of the Saturn electroglow spectrum on 1986 DOY 252 and 254 

in this program. Observing conditions were remarkably good. Analysis of the data requires relatively more model analysis than is the case for Jupiter, in order to account for extinction effects, 

geocorona, and non uniformity of the source in the field of view. 

Table 3 shows a comparison of earlier results. The corrections for foreground and background 

LISM contributions and foreground geocorona require model calculations that have not yet been 

made for the Clarke et aL(1981) observations. Moreover at the time of these observations, Saturn 

was not in a favorable position in respect to extinction effects in the intervening LISM. Crudely 

estimated extinction coefficients are given in Table 3. The measured H Lya brightness from IUE is 

substantially lower than the V1 result, which we attribute mostly to extinction, by the interplanetary 

medium (ISM/IPM) partly to the analysis method, and possibly partly to variability in the source. 

The 1980 IUE observations are close enough to solar maximum to constitute a solar maximum reference. Observations in 1986 and 1987 will provide measurements near solar minimum, under much 

more favorable conditions (see Table 3 for extinction estimate in 1986). 

It should be emphasized that although the brightness of the H Lya line on Saturn has been 

monitored over much of the lifetime of IUE, little of this data can be used to establish the corresponding intensities of the H, band emissions. As we have pointed out H, emissions are complementary to the intensity of the H Lya line, providing a spectroscopic diagnostic of the excitation 

process. Understanding the role played by solar EUV radiation in stimulating this Saturnian EUV 

emission will require knowledge of the behavior of both components at conditions of solar maximum and minimum. Unfortunately the observations designed to provide H, band intensities in this 

program have not been reduced to this extent for lack of available time (1986 DOY 252, 254) for 

analysis. We therefore do not have a measure of how accurately the band emissions can be measured. 

The observational sequence in the last program (1986 DOY 252, 254) is shown in Table 4. The 

I 

Table includes the reduction of the H Lya brightness. We regard this as the best combination of 
exposures required to obtain both H, band H Lya and solar reflection continuum. 

continuum albedo is low enough that moderate changes in eddy diffusion coefficient 

able. 

7 

The reflection 

may be detectWe require models of the LISM as well as the geocorona in order to properly reduce the data. 

We have developed a model of the geocorona for this purpose, and we have used the recent Ajello, 

et al. (1987) model of the LISM to take complete account of the extraneous H Lya! signal in the 

data. The result of the application of the models is shown in Table 4. This is the only IUE observational data from Saturn that has been analyzed in this way, and it will be necessary for comparative purposes to reanalyze the earlier data obtained by Clarke et al. (1981). Table 4 shows the 

sequence of observations with the measured H Lya intensity in Col. 4. Interspersed with the Saturn 

observations are background data obtained 60" north of the planet. The background is composed of 

geocoronal and LISM components as estimated in Col. 5 and 6 of Table 4. The component of the 

LISM in the foreground to the planet is estimated to be 0.463 kR as given in Table 3, using the 

Ajello, et al. (1987) LISM model. The total LISM intensity in the look direction was 0.622 kR. 

Although the observed emission brightness varied from -3.1 kR to -1.8 kR during the sequence, 

most of the variation appears to be caused by the geocoronal component, and the derived Saturn 

emission brightness is basically constant during the sequence with an estimated mean value of IHLya 

= 0.88+ - .2 kR. The geometry for the 1986 DOY 252, 254 observations is ideal in the sense that the 

planet is essentially directly upstream from the earth relative to the bulk inflow of the LISM, so that 

extinction of the planetary signal is at a minimum. However, the observing geometry at the time of 

the Clarke et al. (1981) observations indicates a substantially larger extinction factor (Table 3). If 

these estimates are correct the evidence indicates that the Saturn emission brightness in H Lya has 

varied by a factor of 5. The inference is that the abundance of atomic hydrogen on the planet must 

have changed significantly. 

The analysis of the 1986 DOY 252, 254 data is incomplete, because there has been insufficient 

time to reduce line by line data to obtain estimates of the H, equatorial emission. We therefore do 

not have a good assessment of the uncertainties in determining H, band intensities. In contrast to 
8 

the H Lya analysis described above, auroral and ring reflection components must be removed from 

the data in order to analyse the H, band electroglow emissions. 

DEVELOPMENT OF EMISSION MODELS 

We use an H, emission model that has been employed extensively in the analysis of both Voyager observations of H, emission from Jupiter and Saturn (Shemansky and Ajello, 1983; Shemansky 

1985) as well as interpretation of electron excited H, emissions in the laboratory (Ajello -- et al., 1984, 

Shemansky -- et al. 1985). We have developed and applied an accurate model of the IUE instrument 

transmission function for use with our calculations of the emission structure of the H, Rydberg systems (see accompanying report). It is composed of a convolution of a gaussian (point source) and a 

trapezoidal function. The FWHM of the trapezoidal function is constant as a function of wavelength. However on the basis of our analysis of a point source H Lya line, and results reported by 

Cassatella et al. (1983), we apply a gaussian function with a linear FWHM dependence on wavelength, ranging from 3.44A at 1216A to 6.40 A at 1900 A. This analysis differs from that of Cassatella et al. at short wavelengths (see accompanying report). The instrument transmission function is 

clearly an important factor in the analysis of discrete structure, and the variation of the gaussian 

point source function measurably affects results. We use an H, emission model that has been employed extensively in the analysis of both Voyager observations of H, emission from Jupiter and 

Saturn (Shemansky and Ajello, 1983; Shemansky 1985) as well as the interpretation of eIectron 

excited H, emissions in the laboratory (Shemansky -- et al., 1985). As far as we are aware it is the 

most comprehensive model of H, emission employed so far. 

Figure 2 shows the analysis of the November 1986 spectrum. All of the spectral components 

are modeled, including solar reflection continuum. 
9 

REFERENCES 

Ajello, J. M., D. E. Shemansky, T. L. Kwok, and Y. L. Yung, Phys. Rev. A., 29, 636, 1984. 

Ajello, J. M., A. I. Stewart, G. E. Thomas, A. Graps, Astrophys. J., June 15, 1987 (in press). 

Broadfoot, et al., J. Geophys. Res., - 212, 206, 1981. 

Broadfoot, et al., J. Geophys. Res., 86, 8259, 1981. 

Cassatella, A., J. Barbero, P. Benvenuti. IUE ESA Newsletter #18, Dec. 1983. 

Clarke, J. T., H. W. Moos, and P. D. Feldman, -- Ap.J. Letters, 245, L127, 1981a. 

Clarke, J. T. H. W. Moos, and P. D. Feldman, Ap. J., 255, 806, 1982. 

Clarke, et a., J. Geophys. Res., 91, 8771, 1986. 

Giles, J. W., H. W. Moos, and W. R. McKinney, J. Geophys. Res. 81, 7597, 1976. 

Shemansky, D. E., and J. M. Ajello, J. Geophys. Res., 88, 459, 1983. 

Shemansky, D. E., J. Geophys. Res., - 90, 2673, 1985. 

Shemansky, D. E.., J. M. Ajello, and D. T. Hall, -- Ap.J., 296, 765, 1985. 

Shemansky, D. E. and D. L. Judge, submitted, 1986. 

Yelle, R. V., B. R. Sandel, D. E. Shemansky, and S. Kumar, J. Geophys. Res., 91, 8756, 1985. 
10 

TABLE 1 

Jupiter sub-solar brightness with no correction for 

ISM/IPM extinction 

Obs. Date I(HZLy+WR) I HL a) I(H Lya) (1600A) 111 Remarks 

tw [my I(H:,Ly+m) R/A CML 

Rocket a 1972/ 144 2.4 1. 0.4 50. 100 Disk Average 

Rocket 1978/335 

1978/335 

3.1 1.5 0.5 74. 100 

13 

19 

106 

106 

Calculated 

Sub-solar Point 

Disk Average 

Sub-Solar Point 

IUE c 1979/158 74. Sub-Solar Point 

v2 d 1979/187 3.0 16 5.3 76. 240-330 

v2 d 1979/187 3.0 22. 7.2 65. 60- 150 

Sub-solar Point 

Sub-solar Point 

1UE e 1979/ 120 

-150 

IUE e 1980/120 

-180 

15 

12 

100 Sub-solar Point 

100 Sub-solar Point 

4.4+ 1.6 8 .O 1.8 7656 100 Sub-solar Point 

IUE 1985/99 4.451.6 5.8 1.3 7656 280 Sub-solar Point 

IUE 1986/304 8.2 1.6 100 Sub-solar Point 

IUE 1985/99 - 

IUE 1986/304 5.2~1.5 6.0 1.1 8556 280 Sub-solar Point 

a) Judge and Shemansky (1985) analysis of Giles et al. (1976) rocket experiment, 

E-W H bands distribution shows no limb darkening (Shemansky, 1985) 

b) Clarke et al. (1980) rocket experiment 

c) Present work, estimate from SWP 5448 

d) Shemansky (1985) analysis of V2 data 

note: l(1600A) - 0.43; Table 3 should read "Atmospheric Reflection 1660A; Solar" 

I( 1660A) 

to IUE aperture size. 

e) Clarke et al. (1981a) corrected upward by a factor of 1.16 on 1983 correction 

f> Present work Holberg and Shemansky (1985). 
11 

TABLE 2 

Exobase Production Rates and Escape of Atomic 

Hydrogen from the Outer Planetsa 

Jupiter Saturn Uranus 

1.6 x 1030 3 x 1029 2 x 1028 

5.1 x 109 

19. 

0 

5-7.3 

3.0 x 109 

1.7 x 109 

6. 2.3 

-10 -80 

1.6 x 109 

3 x 1028 1.6 x 1028 

1011 

5 x 108 

8 x IOs 

2 x 104 

2.8-5.3 - 

2 x 104 

> 2. 

1.0 x 109 4.0 x 108 

aThese estimates exclude auroral activity (see text). 

(1) Dissociation production rate (s-1); 

(2) (cm2 s-1) 

(3) HI escape energy (ev); 

(4) Escape yield (O/O) 

(5) Loss rate (kg yr-1); 

(6) (atoms/s) 

(7) 

(8) Exosbase ion density (cm-3); 

Loss lifetime for 200 km am H, (yr) 

(9) YIS (Eq. 1) 

(IO) Ionization Rates (ions cm-2 s-1) 
12 

TABLE 3 

Rough estimate of extinction by the 

ISM/IPM for observations of H Lya 

Date I(H Lya) 

(kR) 

a b C 

T 

Jupiter 

Rocket 1972/144 1.5 0.236 1.9 0.6 I 100 

Rocket 1978/355 19. 0.30 26 100 

v2 1979/ 187 22. 0.0 22. 

IUE 1980/ 120 15. 0.30 20. 100 

IUE 1980/120 12. 0.30 16. 100 

IUE 1985/99 8. 0.236 10. 2.3 100 

7.2 60- 150 

/I50 

/I50 

Saturn 

IUE~ 1980/19 0.9 .85 2.2 

IUE~ 1980/125 0.7 .85 1.5 

v2 198 1 /236 3.0 0.0 3.0 2.8 

v1 1980/3 16 4.9 0.0 4.9 5.3 

a) Brightness before correction for extinction 

b) Calculated optical thickness (see text) 

c) Brightness after correction for extinction 

d) Clarke et al. (1981b) corrected upward by factor of 1.16 on basis 

of 1983 correction to IUE aperture size. Saturn is known to 

have no limb darkening effect in H Lya and therefore no limb 

darkening corrections are applied to the measured data. 
TABLE 4 

1986 DOY 252 and 254 SATURN IUE OBSERVATIONS OF H LYa 

SWP Exposure Scattering ILy-a ILy-a ILy-a ILY-O? 

Duration Background Observed Geocorona ISM Saturn Emission 

(Min) (FN/S) (kR) (kR) (kR) (kR) 

29 1 70a 30 

29 172 80 

29173 30 

29 174" 15 

29 175 15 

29 176 25 

29 177 25 

29 189" 30 

29190 30 

29191 30 

29 192 15 

WEIGHTED MEAN 

--- 

2.83 

2.65 

2.25 

2.83 

2.50 

--- 

2.39 

2.27 

2.37 

0.9 17 

2.862 

3.137 

2.276 

2.295 

1.979 

1.747 

2.166 

2.220 

1.903 

1.819 

0.295 

1.65 1 

2.019 

1.593 

1.220 

0.920 

0.686 

1.604 

1.124 

0.803 

0.625 

0.622 

0.508 

0.508 

0.622 

0.508 

0.508 

0.508 

0.622 

0.508 

0.508 

0.508 

--- 

0.976 

0.849 

0.788 

0.765 

0.768 

0.8 17 

0.822 

0.953 

0.8 850.2 

--- 

--- 
- 

U 

- Y 

I 

r 

a 1 

I 

z 

n 

3 

- 2 

a 

0 

1: 

Figure 1 

14 

Fig. 1 H Lya brightness Jupiter 

center, calculated from 

IUE measurements in 1984- 

1986, as a function of CML. 

Geocoronal and LISM 

components have been removed ,using model calculations referenced to 

interspersed IUE background 

measurements. 

August 1984 

0 April 1985 

a November 1986 

1250 1350 1450 1550 1650 

Wavelength (A) 

Fig. 2 Reduced composite spectrum 

of Jupiter obtained November 

1986. The data is a combination of SWP29576 (15 min.) 

SWP29576 (80 min.) and 

SWP29577 (90 min.) such that 

the entire spectrum contains 

unsaturated signal. The 

heavy overplotted line is a 

model calculation of electron 

excited '-;2 , combined with 

an H Lya line and a model 

of the solar reflection 

continuum. 

Figure 2 
4 APPENDIX A 

Evidence for Change in Particle Excitation 

of Jupiter's Atmosphere 1968-1979 

D. E. Shemansky 

Lunar and Planetary Laboratory 

University of Arizona 

Tucson, AZ 85721 

and 

D. L. Judge 

Center for Space Sciences 

University of Southern California 

Los Angeles, CA 90089-1341 

January 5, 1987 

Submitted to: Journal Geophysical Research 
. -. cc 

Abstract 

Analysis of the Pioneer 10 and rock t ob se ma tion of disk av K ged 

emission from the sunlit atmosphere of Jupiter indicates that the spectrally 

integrated EUV brightness was reduced by at least a factor of 2 relative to 

Voyager spacecraft observations in 1979. Most of the variation is caused by 

the H Ly a component in the spectrum, which was reduced - 1 order of 

magnitude near the tine of solar minimum in 1972-1973. Although the analysis 

of the data does not produce entirely consistent results, the weight of 

evidence points to a factor of order - 2 lower abundance of HI in Jupiter's 

atmosphere in 1972-1973 relative to 1979. The low emission rate in H Ly a 

near the tine of solar minimum in this proposed scenario is caused by an 

electroglow energy deposition rate reduced by a factor of - 3. The apparent 

reduced abundance of HI implies a reduced thermospheric temperature, even 

under the assumption of a constant electroglow deposition rate. 
NE SWP Point Source and Filled Field 

Spectral Transmission Function 

D. E. Shenansky, J. B. Holberg, and D. T. Hall 

Lunar and Planetary Laboratory 

University of Arizona, Tucson, AZ 85721 

In the analysis of discrete emission spectra obtained with IUE, we have found 

that it is important to apply an accurate spectral transmission function. In the 

course of applying model calculations to emission spectra of the outer planets 

using the SWP camera we have established what we believe to be a more accurate 

function particularly at the shortest wavelengths. Cassatella et al. (1985) have 

provided a valuable analysis of the system in both the dispersive and non 

dispersive coordinates. Figure 6 of the Cassatella et al. (1985) paper shows a 

plot of the FWHM for the SWP based on point source observations in the large and 

small aperatures, showing variation in the FWHM width of emission lines as a 

function of wavelength, using extracted spectra as given by the IUESIPS. 

Cassatella et al. suggested that resolution was at a peak in the 1300-1400 A 

region, although uncertainty in the measured widths increased at the shorter 

wavelengths due to the poor quality of the available sources. Many of the 

features of major interest in outer planet atmospheric observations occur in the 

vicinity of the H Lya line. In order to produce a better measure of the point 

source spreading function, we obtained a measurement of the H Lya line in emission 

from the geocoronal background, using the small aperture. This spectrum in flux 

numbers is shown in Figure 1. Although the source fills the field of the small 

aperture, the line is assumed to be equivalent to a point source function, because 
2 

the ultimate instrumental resolution is the limiting factor at the solid angle 

defined by the aperture. A model calculation using a Gaussian function with FWHM 

= 3.44 A provides an optimum fit to the line. Figure 1 shows the Gaussian curve 

integrated over the mean channel interval of the instrument in comparison to the 

observed line. The fit clearly appears to be exceptionally good. If one applies 

the data plotted by Cassatella et al. a value FWHM - 5.3 A would be obtained, 

approximately 50% larger than the present result. On this basis with the trend 

shown in the Cassatella et al. data we recommend that a linear function be 

applied to the calculation of the FWHM values of the Gaussian shape as a function 

of wavelength, 

0 

0 

FWHM = a A + b, ' (& 

1150 1 LA 2000 

(1) 

where 

-t 

a = 4.444 x 10 . b = -1.984. 

0 0 0 0 

The quantity FWHM varies from 3.44 A (@1216A) to 6.9 A (@2OOOA). Figure 2 

shows a plot of the proposed linear FWHM function against the data provided by 

Cassatella et al.. and the present result at 1216 A. In model calculations for 

spectra of sources filling the SWP large aperture, we have applied a convolution 

of the point source function given above with a constant trapezoidal shape 

function having a full width at the peak of 

0 

FWP = 7.24 (& , (2) 

FWHM = 9.96 (h (3) 

with a value 

The parameters for the trapezoidal function have been designed to provide a best 

fit to the H Lya line of uniform intensity filling the large aperture. Figure 3 
3 

0 0 

shows a direct comparison of 1216 A and 1800 A monochromatic lines modeled for a 

uniform spatially diffuse source, illustrating the effect of the variational point 

source function. The spectra in this case are given in absolute units, using the 

IUE photometric calibration curve as it would be applied to real data. Each line 

is fixed at a brightness of 1R. The Figure 3 plot of differential (R/& brightness 

indicates differences in peak value of the order of 105, the 12161 line being 

significantly narrower. Another effect that should be noted in Figure 3 is that 

the 1216A line shows a noticeable asymmetry in its shape. This is caused by the 

fact that the IIJE calibration curve is not flat in the 1150-1300 1 region of the 

spectrum; the application of the calibration curve to the instrumental 

transmission function distorts the shape of the resultant calibrated spectrum. At 

12161 this causes very little error in the integrated line intensity (< 151, but 

model analysis should follow the procedure described here in order to accurately 

describe the calibrated spectrum at and below 1216 A The FWHM value of the 1216 

1 feature in this calculation is 10.5 A Note that the calibration curve distorts 

the shape of the 1216 1 line in Figure 3 sufficiently to cause the peak in the line 

profile to occur - 1 1 shortward of the position of the source line. Attempts to 

adjust the wavelength scale using calibrated spectra may therefore introduce 

errors; such adjustments should be made to the flux number spectra prior to 

application of the calibration curve. From this point of view spectral analysis 

with or without the use of models should be done using flux number spectra, with 

a subsequent conversion to absolute quantities; in effect, the calibration process 

applies conversion factors to photons that do not match the wavelength of the 

conversion factor, causing distortion of the true instrumental transmission 

fane t ion. 

0 

0 

0 
4 

We recommend that model calculations be carried out in a two stage process 

in which point source gaussian lines are first placed in a buffer with integration 

channel widths of The buffered data is then treated as a monochronatic 

line source for the trapezoidal transmission function. The resultant convoluted 

spectrum can then be integrated to match the mean channel width of the IUESIPS 

data. A code for a normalized trapezoidal function integrated over user selected 

channel widths is given below. 

>cl 0.1 8. 

Ref e r enc e 

Cassatella, A., J. Barbero, D. Benvenuti, On the international ultraviolet explorer 

(IUE) point spread function at low resolution, ISJE Newsletter #24, June 1984, p. 

84. 
0002 

0003 C 

0004 C 

0005 C 

0006 C 

0007 C 

0008 c 

0009 c 

0010 c 

0011 c 

0012 c 

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0014 c 

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0020 c 

0021 c 

0022 c 

0023 C 

0024 

0025 

0026 

0027 C 

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0029 C 

003 0 

0031 

0032 

0033 

0034 

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003 6 

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003 8 

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0041 

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0059 

0060 

0061 

0062 

10 

50 

60 

65 

70 

SUBROUTINE TFUN2 (W, WZ, SN1, SN2,WRES ,ERR) 

TRAPEZOIDAL TRXNSHISSION FON(XION 

W= WAVELENGTH OF DELTA FUNCTION LNE 

WZ=WAVELENGTH OF SHORT WAVELEh'GLcH EDGE OF 1 ST C"EL 

SNl=FiPHW/WRES , WHERE EPHY IS E7HH OF TBXUSHISSION FUNTION 

SX=HIpP/WRES , WBESE HWP IS THE HALF WIDTH OF THE WEZOID PEAK 

WRES KIDTH OF DATA C"EL p1 UNITS OF I 

IERB.I-1 NDICATES OKWWE OF TBCLUS DIXNSION M COIIXON 

DES 1/4/83 

OF THE TIMNSFORH DATA FILE 

THE DATA DEPOSRED IN THE T&LYSFORMED FILE IS I-NS 

TRxNS(25) ON ESIT COKTruNS LINE TRXIVSMISSION FUNCTION 

MCI(CH=FIRST LOCATION I24 DATA FILE FOR SUMMATION OF THE 

WCH=LAST LOCATION IN DATA FILE FOR SUMMATION OF THE 

WHEXJi I IS THE LINE mNSm 

IN LOCATIONS nUrJS(1) TERU ncXuS(N3tAX) 

TRANSFORMED LINE: SUM IVRANS(1) INTO MINCH 

TRXXSFORYED LEE; SUX IIZ?UNS(N3lXS) NO HXCH 

FIRST CBANNEL IN DATA FlLE IS NUJIBEXED +I 

WAVELENGTHS DU'CRUSE WlcrH INCREASN CHX\%EL NUMBEB 

THE TRXNSMISSION FUNCITON IS WRJULIZED TO 1.00 

SN2=0.0 DEGENERATES THE FUNCTION TO A TBMNGLE 

DIMENSION UF(4) ,BF(4) 

COMMON TRANS(25) ,N~HAX,UD\ICH, .WAXCH,NCH 

DATA RF/ 1.0 ,-I. 0, -1.0 , I. 0 / 

ERR=O 

SNCH=(W-WZ) /IRES 

NCH=IFIX( SNCHI 

PCX=SNl-SN2+NCH- SNCH 

Np-IFIX(PcH) +1 

DGPCH-NP 

NM=IFIX(2.0 *( SNl-SNZ)-DEL) 

NMAX=NM+l 

IF(NMAX.GT.25) GO TO 70 

MINCH= NCH+ I-NP 

MAXCH=WCH+NM 

DO 10 I=1,25 

rnS(I)=O.O 

UF(I)=O.O 

UF(2)=SN1-2.0*SN2 

UF (3 1 =SNl 

UF(4) t2.0 *( SM-SN2) 

TN=SNl*UF(2) 

TN=O .5/TN 

DO 60 I=l,NMBI 

&I-1 

DO 50 K=1,4 

&PH=N+DEL-UF(K) 

IF(ALPH .GI!. 0.0) sG2.0*ALpE+1,0 

IF(ALPH .LT, 0.0 .AND. ALPE .GT. -1.0) SL4ALPE+l.0).*2 

IF(ALPH .LE, -1.0) SIr.O.0 

TBANS(I)=TaANS(I)+BP(K) *SL 

TRANS( n =TN*TBANs (n 

c0"UE 

REruRN 

IERR=-1 

GO TO 65 

END 
Figures 

Fig. 1 X comparison of the observed and nodeled profile of the Ly a line in 

the SWP small aperture. The observed profile represents the net 

flux number spectrum from a 335 m exposure (SWP25630) of the 

geocoronal Lya background. 

Observed data; 0000. 

Idode 1 c a 1 cnl a t ion;-------. 

An optimal fit to the observed data is shown calculated using a 

Gaussian profile with FWHM = 3.44 A integrated over channel widths 

corresponding to the IUE data interval. 

Fig. 2 Point Source Gaussian FWHbI as a function of wavelength, recommended 

for use in the analysis of IUE SWP data. The formula for the linear 

function is given in the text. 

fJ - FWHM determined from Figure 1. 

0- Small aperture data from Cassatella et al.; 2-3 measurements 

a- Small aperture data from Cassatella et al.; 4-9 measurements 

Fig. 3 Model calculations of IUE SWP monochromatic lines at 1216A and 

1800A, from a spatially diffuse source. The data is calibrated (WA) 

using the IUE SIPS calibration function. Each line has an integrated 

brightness of 1 B. The line shapes are calculated using the 

convolution of Gaussian point source and Trapezoidal aperture 

function with parameters given by Eqs. (1) - (3). Distortion and 

shifting of the peak position of the 1216A line is caused by the 

strong wavelength dependence of the calibration curve in that region 

of the spectrum. 
e 

1 1 I I 1 1 I 

t 

\I 0 

4 

1 

U 

u 

rl 

3 

N 

N 

ri 

0 

cu 

Ti 

4 

UT) 

0 

Figure 1 
e 

I 1 I I I I I I 1 

I\ u3 UT) T m 00 

Figure 2 
3 

N 

0 

\I 

I 

0 

I 

Ti 

0 

Figure 3