Library, »•"• Bld6

JUL 1 1964

^ecUnlcal vtote 92o. 3/4

ABSOLUTE PHOTOMETRY OF THE LIGHT OF THE NIGHT SKY

The Zenith Intensity of Haleakala (latitude N 20.7°)

and at Fritz Peak (latitude N 39.9°]

F. E. ROACH AND L. L. SMITH

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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technical ^Gte 214

Issued June 29, 1964

ABSOLUTE PHOTOMETRY OF THE LIGHT OF THE NIGHT SKY

The Zenith Intensity of Haleakala (latitude N 20.7°)

and at Fritz Peak (latitude N 39.9°)

F. E. Roach and L. L. Smith

Central Radio Propagation Laboratory

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U. S. Government Printing Office Washington, D.C. 20402

Price: 35 cents

CONTENTS

PAGE

ABSTRACT iv

1. INTRODUCTION 1

2. THE OBSERVATIONAL MATERIAL -— 1

3. THE SEPARATION OF STARLIGHT, ZODIACAL LIGHT, AND AIRGLOW- k

k. THE INTEGRATED STARLIGHT 13

5- DISCUSSION OF THE OBSERVATIONAL RESULTS 18

6. THE GALACTIC LIGHT 23

7- THE ZODIACAL LIGHT 29

8. SUMMARY AND CONCLUSIONS 36

ACKNOWLEDGMENTS 37

APPENDIX A. ABSOLUTE UNITS IN NIGHT SKY PHOTOMETRY kl

APPENDIX B. THE ABSOLUTE CALIBRATION 1+5

REFERENCES 51

ill
ABSOLUTE PHOTOMETRY OF THE LIGHT OF THE NIGHT SKY

The Zenith Intensity at Haleakala (latitude N 20.7°)

and at Fritz Peak (latitude N 39-9°)

F. E. Roach and L. L. Smith

Central Radio Propagation Laboratory

National Bureau of Standards, Boulder, Colorado

and

Institute of Geophysics

University of Hawaii, Honolulu, Hawaii

A study is presented of one year of systematic zenith observations

made with similar photometers at two observing stations: Haleakala

(latitude N 20.7°) and Fritz Peak (latitude N 39-9°). It is shown that,

for an effective wavelength of 5300 A, there is a change of intensity

with sidereal time (and therefore right ascension) due to three components: (l) integrated starlight, (2) zodiacal light, and (3) airglow

continuum. Quantitative separation of the components is made. A critical comparison is made with some earlier investigations with particular

reference to the problem of the galactic light.

*This paper was prepared while the authors were guests at the

Institute of Geophysics of the University of Hawaii. F. E. Roach was

the recipient of a Senior Specialist Award from the East-West Center of

the University of Hawaii for the academic year 1963-6^-.

IV
1 . INTRODUCTION

The light of the night sky includes three primary sources:

(1) An astronomical component due to the light from stars and nebulae,

(2) a solar system component (zodiacal light) due to sunlight scattered

chiefly by dust in interplanetary regions, and (3) a terrestrial component (airglow) originating in the Earth's upper atmosphere.

If a filter is employed which excludes strong airglow emissions,

the airglow component cannot be identified with a specific resolved

emission, and it has become customary to refer to it as a "continuum"

even though the possibility exists that it may actually be the summa- tion of many discrete emission features, each of which is too faint to

be recorded even on long-exposure spectrograms

The earth-bound observer not only has to attempt the resolution

of the three components but also must contend with the effects of the

extinction and scattering of the lower atmosphere. The problem of

making the extinction and scattering corrections becomes progressively

more difficult as the horizon is approached but, fortunately, zenith

observations are not seriously affected.

A random zenith observation includes the starlight, zodiacal light

and airglow components in unknown proportions. To effect an initial

separation, we have taken advantage of the fact that, in the first

approximation, the starlight and zodiacal light vary with sidereal time,

whereas the airglow does not . The separation of the starlight and

zodiacal light is accomplished in a series of approximations utilizing

the systematic changes of galactic and ecliptic coordinates of the

zenith (Figure 1 and Table l) as a function of sidereal time.

2. THE OBSERVATIONAL MATERIAL

The observations utilized are a portion of the material obtained

at the two stations with standardized zenith photometers as described by

Purdy, Megill and Roach [1961]. The full program includes records of
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zenith intensities using interference filters centered on 5300 A, 5577 A,

5893 A, and 63OO A, the last three for specific airglow emissions and

the first as a general control for the estimation of background xadiations and their elimination from the emission filter data. The present

study is concerned with the 5300 A observations only.

The totality of data includes 153 nights of observations at

Haleakala (from July 12, 1961, to July 25, 1962) and 108 nights at Fritz

Peak (from December 3L, 19^1^ to January 1, 1963). Zenith intensities

relative to a built-in standard light are recorded at 5 -minute intervals

corresponding to changes of ~L-l/K° in sidereal tine. Considerable overlap thus occurs, each sidereal time having many independent observations,

making it possible to average out sporadic changes.

The principal results of this study are given in Tables 2 and 3

I

in Table 2 the total light and the integrated starlight for each degree

of sidereal time and in Table 3 the mean zodiacal light intensities as a

.y..y. function of ecliptic latitude. The resolution of the three components

was accomplished in a series of approximations which will be outlined in

the next section. In Table k we summarize the over-all averages of the

components for the two stations. All intensities are given in units of

S-,q (visual) units (see Appendix A) referred to "6utside the atmosphere."

3- THE SEPARATION OF STARLIGHT, ZODIACAL LIGHT AND AIRGLOW

In Figure 2 we show the grand-average curves of the observed

intensities for the two stations as a function of sidereal time. A

casual inspection of Figure 2 shows Immediately the intensification of

the two arms of the Milky Way as they traverse the zenith near sidereal

times 80° and 300°. A*more than casual inspection brings out what wae

known decades ago by the classical astronomers, namely that the contrast

between the Milky Way and the sky in the vicinity of the galactic pole

Each degree of sidereal time included between 15 and 30

individual readings

.

**Since a given sidereal time corresponds to a given zenith value

of the ecliptic latitude (Table l) the zodiacal light component assumed

by us for a given sidereal time (Table 2) may be found by reference to

Table 3.
Table 2

OBSERVED TOTAL INTENSITY (OMITTING BRIGHT STARS) AND

DEDUCED INTEGRATED STARLIGHT IN THE ZENITH OF HALEAKALA

AND FRITZ PEAK AS A FUNCTION OF SIDEREAL TIME

Intensities In S^q (vis) Units

HALEAKALA FRITZ PEAK HALEAKALA FRITZ PEAK

Sidereal Integrated Integrated Sidereal Integrated Integrated

Time Total Starlight Total Starlight Time Total Starlight Total Starlight

1* 263 68 298 111 46° 306 84 364 152

2 263 68 299 110 47 308 86 366 154

3 264 69 300 111 48 308 86 368 154

4 265 68 301 112 49 310 86 370 156

5 265 68 302 112 50 310 86 371 157

6 265 66 303 113 51 311 87 373 159

7 266 67 304 114 52 311 87 375 159

8 266 67 305 113 53 312 88 377 161 9 267 67 306 114 54 312 86 381 165

10 267 67 307 113 55 313 87 403 187

11 268 68 309 115 56 313 87 385 169

12 268 68 310 116 57 313 87 . 384 168

13 269 67 311 115 58 314 88 392 174

14 27P 68 312 1.16 59 315 87 390 172

15 271 67 313 117. 60 316 88 393 175

16 272 68 314 116 61 317 89 359 141 17 272 68 316 118 62 319 91 353 135

18 273 67 317 119 63 321 95 360 142

19 274 68 318 118 64 322 96 358 138

20 275 67 319 119 65 32A 98 366 146

21 277 69 320 120 66 326 100 367 147

22 279 71 322 120 67 327 101 373 153

23 281 71 323 121 68 329 103 391 171 24 282 72 325 123 69 331 105 390 170

25 282 72 326 122 70 335 109 397 177

26 284 73 327 123 71 337 113 417 197

27 284 73 328 124 72 341 117 435 213

28 285 74 330 126 73 345 121 454 232

29 286 73 331 126 74 348 124 470 248

30 286 73 333 128 75 352 128 469 247

31 287 74 335 130 76 354 130 473 251

32 288 73 337 130 77 359 135 447 225

33 289 74 339 132 78 365 141 438 216

34 290 75 341 134 79 381 159 433 211

35 291 74 342 135 80 402 180 428 206

' 36 293 76 344 135 81 406 184 415 193

37 294 77 347 138 82 411 189 407 185

38 296 77 350 141 83 414 192 420 198

39 298 79 352 141 84 419 197 418 196

40 299 80 354 143 85 420 198 416 194

41 300 81 356 145 86 421 199 411 189

42 301 81 357 146 87 422 200 418 196

43 303 83 359 147 88 423 201 422 200

44 304 84 361 149 89 424 202 394 172

45 305 85 362 150 90 438 216 376 154
Table 2

C0NTINUE(2)

HALEAKALA FRITZ PEAK HALEAKALA FRITZ PEAK

Sidereal Integrated Integrated Sidereal Integrated Integrated

Time Total Starlight Total Starlight Time Total Starlight Total Starlight

91° 442 220 369 147 136° 269 49 260 48

92 440 218 365 143 137 268 48 259 47

93 438 216 361 139 138 267 47 257 46

94 434 212 359 137 139 266 47 256 45

95 ^ _ 430

"~426 ~ 208 356 134 140 265 46 255 44

" "204 353 131 141 263 44 253 42

97 423 201 351 129 142 263 44 252 43

98 416 192 348 126 143 262 45 I 250 41 99 412 188 346 124 144 261 44 249 40

100 408 184 343 121 145 259 42 247 40

101 405 181 340 118 146 258 43 246 39

102 401 177 337 115 147 259 44 245 38

103 396 172 335 113 148 256 41 244 37

104 392 168 332 110 149 254 41 243 38

105 388 164 330 108 150 252 39 242 37

106 376 154 32? 10$ 151 251 38 241 36

107 373 149 324 102 152 249 38 240 36

108 367 143 320 98 153 247 36 240 36

109 360 136 318 98 154 246 35 239 35

110 355 131 315 95 155 244 34 238 34

111 347 121 311 91 156 242 32 238 36

112 338 112 308 88 157 242 32 238 36

113 331 105 304 84 158 241 33 237 35

114 328 102 300 80 159 240 32 237 37

115 325 99 296 76 160 239 31 236 36

116 321 95 293 73 161 239 33 235 35

117 317 89 290 72 162 238 32 235 37

118 314 86 289 71 163 237 31 234 36

119 308 80 287 69 164 236 32 233 35

120 306 78 284 66 165 236 32 232 36

121 301 73 282 64 166 235 33 231 35

122 298 70 280 62 167 234 32 230 34

123 296 70 279 63 168 234 32 230 36

124 294 68 278 62 169 234 34 229 35

125 291 65 276 60 170 233 33 228 34

126 288 62 274 58 171 232 32 227 33

127 286 60 273 57 172 232 33 226 34

128 283 59 271 55 173 231 32 225 35

129 280 56 270 56 174 230 33 225 35

130 278 54 269 55 175 229 32 224 34

131 276 52 267 53 176 228 31 222 33

132 273 51 266 52 177 227 32 222 33

133 272 50 265 53 178 226 31 221 34

134 271 49 263 51 179 225 30 221 34

135 270 48 262 50 180 225 32 220 33
Table 2

CONTINUE (3)

HALEAKALA FRITZ PEAK HALEAKALA FRITZ PEAK

Sidereal Integrated Integrated Sidereal Integrated Integrated

Time Total Starlight Total Starlight Time Total Starlight Total Starlight

181° 224 31 219 32 226° 217 55 202 47

182 223 32 218 33 227 217 57 202 47

183 223 32 218 33 228 217 57 203 50

184 222 31 217 33 229 217 57 203 50

185 222 33 216 32 230 218 59 204 51 1$6 222 33 216 32 231 218 59 204 52

187 221 34 215 33 232 219 60 204 52

188 220 33 214 32 233 220 61 205 54

189 220 34 214 34 234 221 64 205 55

190 220 34 213 33 235 222 65 206 56

191 219 33 212 32 236 223 55" "266' W

192 218 34 211 33 237 224 67 207 59

193 218 34 211 33 238 226 71 207 59

194 218 34 210 34 239 227 72 208 60

195 217 35 209 33 240 228 73 208 62

196 217 35 208 32 241 229 76 209 63

197 217 37 208 34 242 230 77 209 63

198 216 36 207 33 243 231 78 210 64

199 216 36 206 33 244 232 79 211 67

200 216 37 206 33 245 232 79 211 67

* 201 216 37 205 32 246 233 82 212 68

202 216 39 204 33 247 234 83 212 68

203 216 39 203 32 248 234 83 213 71 204 217 40 202 32 249 235 84 214 72

205 217 42 201 31 250 236 85 214 72

206 217 42 201 31 251 238 89 214 72

207 217 44 200 32 252 239 90 215 75

208 216 43 199 31 253 240 91 216 76

209 217 44 199 33 254 242 93 216 76

210 217 46 198 32 255 244 95 217 77

211 218 47 198 32 256 246 97 218 78

212 218 47 198 34 257 248 99 218 78

213 218 49 198 34 258 253 105 219 81 214 218 49 199 35 259 256 108 220 82

215 218 49 199 37 260 260 112 221 83

216 218 51 200 38 261 265 117 222 84

217 218 51 200 40 262 269 121 223 85

218 218 53 200 40 263 276 128 230 92

219 218 53 200 40 264 283 135 232 94

220 218 53 200 41 265 289 141 236 98

221 217 53 201 42 266 296 148 242 114

222 217 53 201 44 267 301 153 246 108

223 217 53 201 44 268 307 159 250 112

224 217 55 202 45 269 322 174 254 116

225 217 55 202 47

—,-,., i 270 330 182 ( 259 121
Table 2

CONTINUE (4)

1 HALEAKALA FRITZ PEAK HALEAKALA FRITZ PEAK

Sidereal Integrated

- Integrated Sidereal Integrated Integrated

Time Total Starlight Total Starlight Time Total Starlight Total Starlight

271° 334 186 262 124 316° 296 134 438 281

272 338 190 269 131 317 295 131 448 291

273 340 192 275 137 318 294 130 428 261

274 340 192 280 142 319 292 128 416 257

275 344 196 284 146 320 290 125 400 241

"" 2?6 351 203 288 150 321 288 123 386 226

277 365 217 292 154 322 287 122 383 223

278 379 231 298 160 323 285 118 371 211 279 394 246 302 164 324 283 116 369 207

280 398 250 306 168 325 282 115 347 185

281 389 241 312 174 326 280 111 340 176

282 398 250 316 178 327 279 110 330 166

283 391 242 319 179 328 277 106 322 158

284 392 243 340 200 329 276 105 323 157

285 377 228 360 220 330 274 103 319 153

"~~286 374 225 355 215 331 273 100 318 152

287 375 226 373 233 332 272 99 315 147

288 384 235 374 234 333 270 97 313 145

289 387 238 388 246 334 268 93 311 141 290 391 240 381 239 335 26? 92 309 139

291 405 254 336 244 336 266 89 306 136

292 425 284 401 259 337 264 87 304 133

293 461 310 422 278 338 263 86 302 131 294 515 364 451 307 339 262 83 300 127

295 539 386 471 317 340 262 83 298 125

296 545 392 485 341 341 261 81 29? 124

297 531 378 491 345 342 260 80 295 121 298 498 345 486 340 343 260 80 293 119

299 477 324 487 341 344 260 78 291 115

, 300 457 302 495 349 345 259 77 290 114

301 440 285 525 377 346 259 75 288 112

302 428 273 530 382 347 258 74 287 109

303 416 259 520 372 348 258 74 285 107

304 411 264 499 349 349 257 71 283 103

305 404 247 476 326 350 257 71 282 102

306 396 239 451 301 351 256 69 280 100

307 380 221 394 243 352 255 68 278 96

308 354 195 370 219 353 255 68 278 96

309 340 181 366 215 354 255 66 278 94

310 327 168 372 219 355 255 66 280 96

311 320 160 381 228 356 255 66 282 98

312 315 155 397 244 357 256 65 284 99

313 307 147 407 254 358 256 65 236 101 314 300 138 421 266 359 257 64 290 105

315 298 136 444 289 360 259 66

1 —.- —.. ... 296 109
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Table 4.

Summary of Grand Averages

in S-jQ (vis) units.

Contributor Haleakala Fritz Peak

Total light

(including bright stars)

Starlight

(including bright stars)

316

126

318

134

Starlight

(excluding bright stars)

Zodiacal Light

Airglow

103

147

43

116

116

68

Sum

(excluding bright stars) 293 300

10
is much less than it would be if starlight were the exclusive source

of the light of the night sky. This is sufficiently important to

justify a little expansion.

The ratio of intensity in the Milky Way to that at the galactic

pole, according to Roach and Megill [1961], is 372/31 =12. In con- trast, Figure 2 illustrates that the observed ratio in our two cases is

about 2. The conclusion is inescapable that there must be a very significant source of light in addition to starlight which dilutes the

observed ratio compared to its value for starlight alone. The argument

is almost trivial, but it illustrates in principle our analytical procedure. About ll/l2 (approximately 200 S-j_q (vis) units) of the intensity of the light near the galactic pole is predicted as due to non- stellar sources which is in rough agreement with a more sophisticated

interpretation to be presented below.

A similar conclusion is reached by an even more general argument.

According to Seares, et al. [1925], the total light from all the stars

is equivalent to that from 1092 stars of the first visual magnitude.

The mean light per square degree is thus

r-. pto = O.O265- first magnitude (visual) stars

' per square degree

or

O.O265 x 398O = 105 10th magnitude (visual) stars

per square degree*.

We note that the average total zenith intensity at both stations is

about 300 S10 (vis ) (Table k) . Thus again some 200 S10 (vis) must be

due to the combined zodiacal light and airglow.

We proceed in our discrimination of the components in the following steps: (l) determine the average observed intensity as a function

of sidereal time, (2) for each degree of sidereal time, subtract from

For convenience we use the "number of tenth magnitude (visual)

stars per square degree" as our unit of intensity and designate it as S10 (vis )' See Appendix A for a discussion of units.

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SIDEREAL TIME IN DEGREES

Figure 2. Observed zenith intensities at Fritz Peak

and Haleakala as a function of sidereal time.

The smooth curves underdrawing the individual

star deflections correspond to the "total"

entries in Table 2.

12
the average intensities the corresponding starlight given by Roach and

Megill [1961] —the resultant "being zodiacal light plus airglow, (3) plot

zodiacal light plus airglow versus corresponding zodiacal light results

of Roach and Rees D-956"] —intercept becomes average airglow, (k) determine zodiacal light, i.e., zodiacal light plus airglow (step 2) minus

average airglow (Step 3)> for each degree of sidereal time, (5) deduce

starlight, i.e., average observed intensity minus zodiacal light

(Step k) minus average airglow (step 3)> for each degree of sidereal

time. This process is repeated as an iteration until further refinements seem to make trivial contributions. We will spare the reader the

details of the iteration and proceed to discuss the final results.

k. THE INTEGRATED STARLIGHT

In Figure 2 the deflections due to individual bright stars appear

as well-defined spikes. The apparent widths exceed the photometer's

field of view (5°) due ^0 the averaging of several observations for each

degree of sidereal time with the attendant spread due to inaccuracies in same for observations extending over a long period of time. The fact

that our observations were made with 5-minute (l-l/^°) intervals also

contributed to a spread in results referred to intervals of 1° in

sidereal time. The faintest star that would be detectable as an individual star lies between visual magnitude 5*0 (corresponding to 5 S^o

(vis) units*") and 6.0 (corresponding to 2 S]_q (vis) units). For our

analysis, we have attempted to underdraw the individual star deflections

(the entries labelled "total" in Table 2) in order to permit a comparison with predicted intensities based on star counts. In Figure 3> we

show plots of the results of our analysis for integrated starlight,

zodiacal light, and airglow as a function of sidereal time for the two

stations. As anticipated, the ratio between the intensities in the

^he field of view of our photometer is about 20 square degrees

5 Sj_q (vis) units thus corresponds to 5 x 20 = 100 tenth magnitude stars or 1 fifth magnitude star.

13
400

300

£ 200

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300

200

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AIRGLOW

HALEAKALA

INTEGRATED

STARLIGHT

40 80 120 160 200 240 280 320 360

SIDEREAL TIME IN DEGREES

Figure 3- The resolution as a function of sidereal time of

the total zenith intensities at Fritz Peak and

Haleakala into the three components: airglow,

zodiacal light and integrated starlight.

Ik
Milky Way and near the galactic pole is now about 10, in substantial

agreement with our earlier remarks

An integration of intensities based on star counts is possible by

reference to the classical study of van Rhijn [1925 ] who published

tables of log Nm

to m(pg) = 18.0 for 10,296 discrete regions of the

celestial sphere.* The results are necessarily highly smoothed since

their basis is the 206 "Selected Areas" the study of which was initiated by Kapteyn in 1906. Two isophotal maps of the Milky Way based on the van Rhijn (Groningen publication il-3 [referred to hereafter as GR k^])

tables have been published. Roach and Pettit [1951] published a map

based on an approximate integration (this map was also included in a paper by Roach, Pettit, Tandberg-Hanssen, and Davis [195^-]) • More

recently, with the help of an electronic computer, Roach and Megill

[1961 ] repeated the integration and published a revised Milky Way map

The difference between the two integrations is not large.

A comparison between our present measurements and the integrations based on star counts is shown in Figure k. Least-squares solutions give the following relationships between the integrated starlight

from the GR ^3 integration (G) and our measurements of total

intensities, S-^

St = 201 + 1.18 G (Haleakala) ,-.\

(corr. coeff., r, = O.89) ^ '

St = 197 + l.CA- G (Fritz Peak) , * (r = 0.73) K }

It is noted that the intercepts which correspond to the non-stellar

contribution are close to 200 S-j_q (vis), as deduced earlier on the

basis of general arguments.

The lower curves in Figure k show plots of the integrated starlight, S, which we have deduced against the predicted values from the

"T^og Nm is the logarithm (base 10 ) of the number of stars per

square degree brighter than magnitude m.

15
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16
GR ^3 integrations. We made successive approximations "by adjusting the

absolute level of the zodiacal light plus airglow until the deduced

integrated starlight plotted against the GR ^3 integrated starlight from

star counts produced curves which went through the origin. A second

requirement was that the two systems should be in agreement at high

galactic latitudes. The quality of the final result may be judged "by

examination of the lower curves in Figure k. It is to be noted that

the scatter of the observational points with respect to straight-line

least-squares solutions is much reduced in going from the upper curves which include zodiacal light and airglow to the lower curves in which

the zodiacal light and airglow have been subtracted out. Since we have

assumed the airglow to be a constant (with respect to sidereal time)

the improvement is due to the refinement resulting- from subtracting the

variable zodiacal light according to the entries of Table 3« It is also

noted that the scatter of the points increases for the brighter regions

(near the galactic plane) probably due to the severe smoothing that

must have entered into the GR ^3 tabulations. The least -squares solutions given below omit some of the more discordant points in the Milky

Way (see legend for Figure k) :

Haleakala S =1.35 G /„\

(r = 0.97) U)

Fritz Peak S = 1.22 G ,, v (r = 0.86) W

Haleakala plus S = 1.26 G

Fritz Peak (r = O.91) (5)

A criticism of our procedure is that we have used our judgment in

selecting solutions which go through the origin and through the points

corresponding to the fainter intensities by omitting some of the discordant high intensity points from the analysis.

17
5- DISCUSSION OF THE OBSERVATIONAL RESULTS

We now propose to compare our observational results with- those

obtained by others working in the general domain of the absolute brightness of the light of the night sky with particular reference to the

integrated starlight and the zodiacal light

.

The intensity of integrated starlight may be considered constant

so that similar photometers should give identical absolute intensities

for the starlight component for the same region of the sky. There

exist ; however, serious discrepancies among three observers. These

will be discussed in some detail later.

Whether the zodiacal light can be considered constant with time is

not so clear. Fluctuations over a few minutes as well as seasonal variations have been reported by several observers, but we are inclined to

agree with the general conclusion reached by Barbier [1955 ] that the

reality of such fluctuations and variations is subject to doubt. We

propose to make a definitive comparison of four independent measurements

of the brightness of the zodiacal light in the ecliptic as a function of

the elongation from the sun, e, not only because of its intrinsic

interest but also because the comparison helps to explain the divergence of the measured integrated starlight results

.

There are two interdependent sources of error encountered in the

interpretation of observations of the light of the night sky. First,

the three principal components are each of significant brightness and

an error in the estimation of any one affects the others . We may call

this the subtraction error. Second, the absolute calibration of the

photometer is critical since an error in calibration affects a particular component both directly by a multiplication error and indirectly by

the possibility of contributing to a subtraction error. The difficulty of minimizing the subtraction error is shown in a paper by Roach, Pettit, Tandberg-Hanssen and Davis [195^] (referred to

hereafter as RPTD) in which the authors proceeded by a series of three

approximations in their evaluation of the zodiacal light, in each

18
successive approximation attempting to reduce the subtraction error.

In Table 5 we list some published zodiacal light intensities

which are compared graphically in Figures 5 and 6- We find the following relationships to hold among the observers:

L = 1.+55 R -20 (6)

¥ = 0-937 R +20 (T)

E = 0-55+ R -IT (8)

where L corresponds to intensity as measured by Elvey and Roach [1937]

(referred to hereafter as LVR), ¥ by J. ¥einberg [1963 h E ^y Els&sser

[1958], and R by RPTD D-95+]. Although we cannot he certain that the

zodiacal light is constant in intensity, we prefer to consider that we here deal with measurement and interpretation differences rather than

intrinsic changes. Considering that the measured intensities extend to

many hundreds of S]_q (vis) units, the additive terms of -20, +20 and -17*

respectively, which reflect differences of subtraction of the nonzodiacal light components among the observers may be taken as of

secondary importance. ¥e are left with the conclusion that the principal

cause of the discrepancies is due to differences of absolute calibrations

among the observers . One of us (FER) has been directly associated with

two Of the measurements (LVR and RPTD) separated in time by 17 years and

in calibration by a factor of 1.^-5' As we shall see later, our present

results lie between the two earlier investigations

¥e now turn to a comparison of the integrated starlight intensities, S, listed by us in Table 2 and those previously reported by Elvey

and Roach [1937] and by Elsasser and Haug [i960]. In the case of the

LVR measurements, we have read off values of the "galactic light" in

S]_o(ph) units shown by them in their Figure 11 corresponding to the

galactic coordinates of the successive zenith observations of the

present study. These were converted into S]_q (vis) units by reversing

the original procedure employed by LVR in their estimation of the

galactic light. * The Elsasser-Haug (EH) measurements of absolute

*In the Appendix A, we explain the conversion from the S]_o(ph)

units used by LVR to the S^q ( vis ) units used in this paper.

19
Table 5.

Comparison Of Four Independent Zodiacal Light

Studies. Brightness In the Ecliptic.

In S^q (vis) Units

X- A ©

MEASUREMENTS DEDUCED

(Present

E JW RPTD LVR Study)

30 1230 2200 2331 - 2740

35 1545 1594 2295 1880

40 630 113Q 1184 1691 1390

45 898 945 1323 1110

50 420 730 755 1063 890

55 610 601 864 710

60 270 520 498 719 590

65 445 426 622 500

70 180 385 371 538 440

75 338 329 468 390

80 130 300 297 414 350

85 270 271 371 320

90 110 250 247 329 290

95 228 229 297 270

100 215 2M 271 250

20
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20

ZODIACAL LIGHT

IN THE ECLIPTIC

LVR

JW

RPTD

40 60 80

ELONGATION, €

100

Figure 5 Four independent published plots of the variation

of the intensity of the zodiacal light in the

ecliptic with elongation angle from the sun (from Table 5).

21
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22
intensity were taken from their Figure 3, again for each of the galactic

coordinates corresponding to our successive zenith readings.

The common observations when plotted showed an obvious correlation

but with a scatter that indicated the need of least-squares solutions.

We find

L = 1.3^ S + 16 (r = 0.8*0 (9)

E = 0.1*3 S + 1*1 (r = O.85)., (10)

We note immediately that the LVR results for the integrated starlight

are relatively high and the EH* low, strengthening the conclusion

reached in the comparison of zodiacal light results that the two investigations differ because of differences of absolute calibration. The

interrelationships are shown graphically in Figure J. In Table 6, we

summarize the relationships among several observers based on both integrated starlight and zodiacal light studies . In the last column a multiplying factor is given to refer the diverse results to the scale of

the present paper (RS).

6. THE GALACTIC LIGHT

The discussion in the preceding section on the intercomparison of

various investigations on the light of the night sky leads directly to

the question of the existence of the so-called "galactic light" which was invoked by Elvey and Eoach D-937] to explain the fact that their deduced

integrated starlight intensities were systematically higher than those

predicted by the star count integrations of Bottlinger [1932]. The

indication in the present study that the LVR absolute calibration was systematically high invites examination of the possibility that the

The Elsasser-Haug results for the integrated starlight and the

earlier Elsasser results for the zodiacal light are based on similar

instrumentation and calibration procedures. In the Elsasser-Haug paper

on integrated starlight [i960], the earlier Elsasser D-958] results for

the zodiacal light were used.

23
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Table 6.

Summary of Relative Calibrations

Deduced from Several Published

Studies of the Integrated Starlight and the Zodiacal Light.

Relative Intensities

(Observed)

Relative Intensities

normalized to RS=1.00

and Z.L. results of column 3.

Investigators* Integrated

Starlight

Zodiacal

Light

LVR=1 .34 EH=0.43 Mean Multiplying

factor

(mean)

EH 0.43 .554 .51 .43 .47 2.13

JW mm .937 .86 .73 .79^ 1.26

RPTD - 1.000 .92 .78 .85 1.1&

RS 1.00 - 1.00 1.00 1.00 1.00

LVR 1.34 1.455 1.34 1.13 1.235 .81

*Code for Investigators

EH

JW

RPTD

RS

LVR

Elsasser, 1958

Elsasser and Haug, 1960

Elsasser, 1963

Weinberg, 1963

Roach, Pettit, Tandberg-Hanssen and Davis, 1954

Present Study

Elvey and Roach, 1937

25
numerical values of the galactic light deduced by them should be significantly reduced, possibly to zero. In the opposite direction, the integrated starlight intensities

reported by Elsasser and Haug [i960] are systematically lower than

those predicted by the star counts of GR k-3* which, in the absence of

an error in absolute calibration, could only occur if there is a systematic error in the star counts themselves . The relationship

between the EH measurements (e) and the GR ^3 integrations (G; found by

us from the entire Milky Way is

E = O.kO G + 72 (r = 0.71) (ll)

Also E» = 0A3 G + 81 (r = 0.7*0 (12)

E" = 0A5 G + 87 (r = 0.75) (13)

where E

1 corresponds to the Elsasser-Haug measurements increased by

light from magnitudes 6 and 7 and E" from magnitudes 6, 7 and 8.

In our previous discussion, we have presented circumstantial

evidence that suggests that the three investigators, LVR, EH and RS are

in disagreement with respect to their absolute calibrations (multiplying

error) and their allowances for airglow plus zodiacal light (subtracting

error). Without passing judgment on which of the three may be most

nearly correct, it is obvious that the galactic light deductions from

the three must be in serious divergence.

A critical matter, as brought out by Henyey and Greenstein [19^1],

is the wide divergence in the integrated starlight deduced from star

counts as reported in the literature. Comparing the integrated starlight deduced from tables of star counts by Seares and Joyner [1928]

*The Elsasser-Haug intensities agree numerically with the star

count integrations of Bottlinger. The Bottlinger integrations based on the star counts of Mt. Wilson Contribution 301 (Seares, et al. [1925])

and those based on GR 43 star counts are in systematic disagreement at

low galactic latitude.

"^Clsasser and Haug estimated that their photometer recorded stars

brighter than magnitude 8 as individual stars . Included in the GR ^3

integration as used, were stars from magnitude 6.

26
and by van Rhijn (GR ^3) they found that, for galactic latitude 0°,

S-^o (phot) = 121 (Seares and Joyner)

S10 (phot) = 201 (van Rhijn)

In order to illustrate the dependence of an estimation of the

galactic light on the several uncertainties in the analysis, it is

convenient to recall that

Galactic light = Total light - (airglow + zodiacal light + integrated starlight).

The numerical values of the galactic light that have been reported are

in the range 10 to 100 Sj_q (phot) units. A typical zenith total light

reading in the Milky Way is 250, of the zodiacal light 60, and of the

airglow 30. For the two values of integrated starlight cited, we thus

obtain

Galactic light = 250 - (30 + 60 + 201) = -kl or = 250 - (30 + 60 + 121) = +39.

It is obvious that the uncertainty in our knowledge of the integrated

starlight will make an estimation of galactic light extremely difficult.

When one adds to the problem of absolute calibration the difficulty of

subtracting out the airglow and zodiacal light, it is apparent that all

galactic light estimates should be considered as provisional.

We know of four independent estimates of the galactic light and

show them in Table 7 with two alternate solutions, one based on values

of the integrated starlight from Seares, van Rhijn, Joyner and Richmond

[1925] and the other on the higher values from GR V3« It is to be

noted that the measurements of Henyey and Greenstein [19^-1 ] are not

subject to a large uncertainty from the integrated starlight term

*Tn the galactic light discussion we use S]_q (phot) rather than

S]_o (vis) in agreement with most of the literature. For a rough orientation, S]_q (vis) ~ 2 S^lq (phot) but see Appendix A for a discussion of

the color index and its effect on S]_q (vis J / S]_q (phot).

27
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28
"because they were able to avoid stars brighter than m (pg) = l6. In

addition to the direct observational results by LVE and by EH, we have

listed revised values based on the empirical relations found in this

study to place their absolute intensities in our system (see Table 6).

The mean galactic light values from Table 7 are 72 S^q (phot)

referred to the Mt. Wilson 301 star counts and 3^ referred to the GR ^-3 star counts'*. A careful study of the literature on the subject of the

galactic light was made by van Houten [1961] who used a value of 12 in

his analysis.

In order to illustrate both the observational and the computational difficulties of evaluating the galactic light, we have plotted

together the observational results** for the zenith of Fritz Peak

(Figure 8) and Haleakala (Figure 9) "based on LVR, RS and EH together

with the predictions from the GR ^-3 star counts . We note that for the

four Milky Way crossings :

LVR > GR ^-3 for all four crossings

RS > GR ^3 for two crossings

RS ~ GR ^3 for one crossing

RS < GR ^-3 for one crossing

EH < GR V3 for all four crossings

7. THE ZODIACAL LIGHT

In our treatment of the mean intensities over a year, we found it

convenient to consider that the zodiacal light as observed in the zenith

is a function only of the ecliptic latitude, p, according to the entries

of Table 3* In an individual observation the zodiacal light component

must vary from the mean value. The nature of the variation is apparent

from an examination of Figure 10 in which we show an isophote map of

In these means we have used the "revised" values for LVR and EH.

**Note that in Figures 8 and 9 we have used S^q (vis ) units.

29
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the portion of the zodiacal light and gegenschein included in the

zenith according to the two coordinates, ecliptic latitude and differential ecliptic longitude*, X - X Q

. It is noted that for any given

ecliptic latitude there is a range of intensities with respect to the

mean values of Table 3 a^d that, during a given night, the observation

locus includes a variety of X - X @ values

.

The procedure adopted by us should be a reasonable approximation

for the purpose of deducing the integrated starlight from the original

mean zenith intensities based on the randomly distributed (with

respect to X - XQ ) 15 to 30 individual readings entering into the

means. However, for a given observation or for a given night the

X - X Q term introduces a variation with respect to the mean that is by

no means trivial.

The point is illustrated in Figure 11 where we have plotted, for

two nights, the individual observations as differences from the over-all

means. For comparison we show the zodiacal light differences deduced

from the isophote map of Figure 10 in conjunction with the means from

Table 3* The parallelism of the two sets of data supports the thesis

that there is a significant variation of zenith intensity (referred to

our means of Table 3) due to the X - X © term in the zodiacal light

.

We plan to make definitive studies of this matter in subsequent

investigations

.

Most of the zodiacal light investigations have dealt with the

brighter regions in the ecliptic (30° < e < 90° ) Although we have no

direct observations of this domain in the present study, we now propose

to refer some published results to our photometric scale.

In Table 5, (column 6), we put the diverse results of four independent investigators of the zodiacal light in the ecliptic into the

In the ecliptic X - X® = e , the elongation angle between the

line of sight and the sun. Away from the ecliptic cos e = cos (X - X Q ) cos (3. Thus,, the correct procedure in physical analyses is to use the

parameter, e, in conjunction with line-of-sight integrations involving

particle density. In the present case, it^ suffices to present the

isophotes as functions of X - X Q and f3 .

33
60

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NOV. 6/7, 1961

- SOLID LINE: OBSERVED RESIDUALS

DASHED LINE: RESIDUALS PREDICTED

FROM ZODIACAL LIGHT

FEB. 3/4, 1962

320 340 360 20 40 60 80 100 120 140

SIDEREAL TIME IN DEGREES

160 180 200 220

Figure 11. The solid lines represent residuals between the total observed intensities

for individual nights and the mean intensities from the ensemble of data of

this study. The dashed lines correspond to residuals between the zodiacal

light from the isophotal map of Figure 10 and the means as a function of p alone of Table 3. The general trends of the two residual curves parallel

each other indicating that the cause is the zodiacal light dependence on \ - \ ft . The systematic displacement of the curves may be interpreted as due to variations in airglow from night to night. The random scatter of

the solid curve is probably chiefly due to instrumental and measurement

errors (see Table 8 for a summary of error estimates).

34
absolute scale of our present study. The resulting intensities constitute a consistent body of data approximately mid-way between the RPTD

and LVR results. It should be noted that, if the calibration on which

this study is based is in error on the high side by a factor of 1.26,

this would (a) eliminate the evidence in our data for galactic light

(eq 5) and (b) reduce the zodiacal light intensities to almost exact

agreement with those recently reported by Weinberg [1963] (Table 6).

The entries of column 6 of Table 5 lead to interesting relationships between the intensity of the zodiacal light and the elongation

from the sun, e, in degrees. For the three cases: (a) the corona F,

(b) the interpolation between the corona F and the observed zodiacal

light of this study, and (c) the zodiacal light, we find in units of H

and H

1 Corona F : log H =6.36-2.5 log e or log H' = 6.22 - 2-5 log e

Interpolation : log H =6.37-2.2^ log e or log H

1 = 6.23 - 2.2^ log e

Zodiacal Light : log H =6-3^-2.20 log e or log H' = 6.20 - 2.20 log e

(Ik)

(15)

(16)

The similarity in the log H - log e relationships for the three

regions has often been mentioned in the literature (see for example

equations (3)> Q±) and (5) of RPTD [195^] )• The three curves merge so smoothly into each other that it has encouraged investigators to examine

the interpolation region to test the hypothesis that the F corona and

the zodiacal light are parts of the same physical phenomenon (see e.g.

Figure 7 in "the paper by Blackwell and Ingham [1961]). Interpretations

of the zodiacal light in terms of the physical composition of the interplanetary medium have resulted in several papers over the past two

decades starting with the classical papers by van de Hulst [19^-7] and by

Allen [19^6]. Such analyses depend on knowledge of both the intensity

See Appendix A for a discussion of units.

35
and the polarization characteristics of the zodiacal light. The present

paper is concerned with only the intensity. For a definitive study of

the polarization, the reader is referred to a recent paper "by Weinberg

[1963]* In addition to an exposition of the polarization Weinberg has

included a useful bibliography of zodiacal light papers.

8. SUMMARY AMD CONCLUSIONS

Our motivation in this study was two-fold: (l) to attempt a summary and discussion of divergent photometric observations of the so- called light of the night sky, and (2) to provide a list of absolute

intensities of specific regions of the sky which can serve as "standard

light sources" for ourselves and other investigators in future studies.

The use of the total intensities in Table 2 as standard light

sources should be tempered by the following considerations

(1) They can be used in the zenith only at latitudes equal to

those of Haleakala (N 20-7°) and Fritz Peak (N 39-9°), but they are potentially useful for other latitudes for observations "off zenith."

(2) A random observation will not agree exactly with the tabulated value due to the possible variation of the airglow. It should

be noted that, although we were able to assume constancy of the airglow with respect to sidereal time , sporadic changes in the airglow

or systematic changes with respect to local times are likely to occur.

(3) A random observation will not agree with the tabulated value

due to the fact that the zodiacal light intensity is a function not

only of the ecliptic latitude as given in Table 3 but also of the

differential longitude, X - XQ , from the sun. This was treated in

Section 7*

(k) There are inherent errors of an instrumental or measurement

nature

.

(5) The evaluation of the two sources of fluctuation mentioned

in (2) and (3) above is consistent with the computed probable errors

of the means. We used about 25 individual observations for the mean

36
intensities for each sidereal time in the case of Haleakala. The

probable error of the mean was about k Sj_q (vis) units. The probable

error of a single observation is therefore about 20 S^q (vis) units.

We show in Table 8 a summary of our estimates of the probable errors

due to the three contributors

.

(6) Although the observations for the two stations constitute

internally consistent ensembles, it is necessary to keep in mind

that the absolute accuracy of the entries in Table 2 is not as good

as that implied by the probable errors based on the scatter of our individual observations

.

We estimate that the total intensities listed in Table 2 are accurate to ± 10$ which implies better than ± 10$ absolute accuracy for

the laboratory calibrations of the standard lights in our photometers

.

This estimate is consistent with the fact that the Haleakala and Fritz

Peak correlations with the GR ^+3 star count integrations [eq, (3) and

(k) ] differ by about 10$. Recently we have installed, in the photometers of both stations, new standard lights which have been given

independent laboratory calibrations . It is hoped that a year of

observations with the new standard lights will yield improved data.

We are of the opinion that the principal cause of the inaccurate

calibrations that have plagued many investigators over the years has

been the difficulty attendant on the use of star crossings. This point

is discussed in some detail in Appendix B.

ACKNOWLEDGMENTS

We are indebted to our colleagues in the Airglow and Aurora

Section of the Central Radio Propagation Laboratory of the National

Bureau of Standards for invaluable assistance in the acquisition of

the observations under analysis in this paper. We wish also to thank

Professor Walter Steiger of the University of Hawaii for his cooperation and assistance in the procuring of the data on Haleakala and for

inviting us to the Hawaii Institute of Geophysics for the academic year

1963-6^. We have been stimulated by many conversations with our

37
Table 8.

Estimated Probable Errors

in S

1Q (vis) units.

Source Mean of

25 Observations

One Random

Observation

Instrumental and

Measurement Errors

Zodiacal light

variations

Airglow variations

1.2

3

2

6

15

10

Total (effective) 4 19

38
colleagues, Dr. J. Weinberg and Dr. M. Huruhata. One of us (FER)

gratefully acknowledges the opportunity to work in Hawaii by the award

of a 1963-6^- Senior Specialist Award at the East-West Center of the

University of Hawaii. Finally, a significant part of the financing of

the project has been through NASA grant R-l8.

39

APPENDIX A

ABSOLUTE UNITS IN NIGHT SKY PHOTOMETRY

The units used in surface photometry are a source of some confusion to the casual reader. We propose to define the units which seem

to us to be appropriate in studies of the light of the night sky and

to show their inter-relationships.

A general rule in the selection of a unit for a particular application is based upon the rapidly growing use of digital computer techniques . We have found that, in observational problems, the use of

three significant digits is optimum— two digits is frequently too

coarse and four digits almost always too fine. In our punched card

formats, we have standardized for several years on three-digit fields.

As a matter of convenience, it is desirable that the unit be chosen so that there is no decimal point for the bulk of the data, thus the

entries are included in the 001 to 999 range.

With these general considerations in mind, we recommend the

following units

(l) For integrated starlight: Sj_q (vis), the number of 10th

magnitude (visual) stars per square degree of sky. The unit is a natural one since its evaluation is based on the traditional practice

of astronomers to express star counts in terms of number of stars per

square degree of sky. Star counts have been based on the photographic

magnitude scale rather than the visual, and we prefer to convert to the

visual scale because its effective wavelength is very close to the

5300 A filter used in the present study. The conversion may be made

from the color index (Cl) by the formula

S10 (vis) = S10 (phot) x lO '^ CI .

The color index of the sun may be taken as 0.57> thus for any surface

corresponding to the sun in color, for example, the zodiacal light,

S10 (vis) / S10 (phot) =1.69 .
The color index of the stars in general changes systematically

with the apparent magnitude — the fainter stars are statistically redder

(larger positive color index) . The integrated starlight depends more

and more on fainter stars as the galactic plane is approached. The

effective color index at the galactic pole is about 0-7 (S10 (vis) /

S-.Q (phot) =1.9) and at the galactic equator about 0.8 (Sj_q (vis) /

S^o (phot) = 2.l). This variation of effective color of integrated

starlight with galactic latitude was used by us in converting the LVR

results published in S-j_q (phot) units to our present scale in Sq_q (vis)

units.

(2) For zodiacal light: H, lO"-^ times the mean radiance of the

sun is recommended. This is a natural unit since the zodiacal light is

the result of sunlight on interplanetary particles .*

(3) For airglow "continuous" emissions: R/lOO A = rayleighs per

100 Angstroms is recommended. The rayleigh has been internationally

adopted as a unit for upper atmosphere emissions [Hunten, Roach and

Chamberlain, 195&]. It is a natural unit since it is easily referred

to the rate of quantal production in upper -atmosphere layers . If the

radiance, B, is measured in 10 quanta • cm • see"-1

• steradian" the

total flux in rayleighs, R, is ki(B** or 1R = 10° quanta • cm'2 • sec"1

sphere" . Since the effective thickness of an upper atmosphere layer is

6 frequently approximately 10 km = 10 cm, the intensity in rayleighs is

approximately equal to the number of quanta • cm J • sec within the

emitting layer. If the upper atmosphere light source is not a discrete

^Attention is called to an earlier paper [RHCD, 195^-1 in which a unit H

1 = lO--^ the radiance at the center of the sun was used. For a wavelength of 5300 A, B (center) = 1-37 B© (mean) and, therefore,

H = 1.37 H'.

*"*Irobably a better statement is that, if B^ is the specific M

radiance in 10 quanta cm • sec • ster*"-*- • A"1

, then B = _ B^d^

over the emission line (or over the domain of a filter In the case of a

ICO continuum and the total flux in rayleighs = hrtB = kit B^d^).

Jo

k2
emission but is of a continuous nature, we use rayleighs/lOO Angstroms

(R/lOO A) as a unit of specific intensity.

The interrelations among the units mentioned in this Appendix are

shown in Table 9*

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APPENDIX B

THE ABSOLUTE CALIBBATION

It is obvious that the absolute calibration of a photometer is

critical in drawing conclusions, for example, as to the existence of the

galactic light. The reader has reason to be disturbed that photoelectric photometry with its extraordinarily high precision when applied

to such problems as eclipsing binary systems should yield such diverse

results in applications to the light of the night sky as those reported

by Elvey and Roach D-937-] on "the one hand and by Els&sser and Haug

[i960] on the other. The difficulties seem to be that (l) we deal with

very low light levels for which good field standards are not readily

available, (2) we are concerned with surface photometry and use relatively large angular circles of sky and, (3) we are striving for absolute

accuracy which is more difficult to attain than relative precision such

as used in conventional stellar photometry.

We have been preoccupied with the problem of the absolute accuracy

of our observations for several years and the present calibration is

based on a serious attempt to solve the problem in our field applications. In our laboratory at the Fritz Peak Observatory, we have

installed as our primary standard a black body which illuminates a magnesium oxide screen. Secondary standards of fluorescent material

irradiated by radioactive material which can be transported to the field

are regularly compared with the laboratory black body. Finally,

tertiary standards, also of fluorescent material irradiated by radioactive material are built into our photometers in such a way that every

sky reading is directly compared with a standard light reading, thus

minimizing the effect of transient electrical variations in the amplifier and recording network.*

*For a detailed discussion of the procedures followed at the

Fritz Peak Observatory in the use of fluorescent standard lights, the

reader is referred to Smith and Alexander [1963 ^

^5
The use of calibration stars of known apparent magnitude has "been

widely practiced especially since, in routine observing programs, many

star crossings may occur. A practical difficulty arises in that, with

the large fields (l° to 5° in diameter) used in typical light-of-thenight-sky photometers, the star deflection may depend on the part of the

photo-cathode illuminated. This is especially true in the case of the

RCA. 931 A (lP2l) photomultiplier which has a highly sensitive region

near the central line of the cathode. Two procedures have been followed

to allow for this effect. One may make a multiplicity of star deflection readings essentially mapping out or averaging the sensitivity field

of the cathode. This procedure was followed by RPTD [195^1 in their

study of the zodiacal light. A second method is to use "Fabry optics"

to focus the telescope objective on the cathode. This has the effect of

spreading a point source out into a disc which, in perfect optics, will

be of uniform intensity and independent of the position of the point

source (such as a star) in the field. Our experience has been that

Fabry optics do significantly improve the reproducibility of stellar

deflections but do not completely eliminate errors as will now be shown.

The design of the zenith photometers used in. the present investigation includes Fabry optics in conjunction with a 1P21 photomultiplier

with the Haleakala telescope and an end-on photomultiplier at Fritz

Peak. An inspection of Figure 2 shows that the star crossings are much

more conspicuous with the 1P21 photomultiplier (Haleakala) than with

the end-on tube (Fritz Peak). Obviously great care would have to be

exercised in using the stellar deflections for calibration purposes.

We think the matter is of sufficient importance to justify a numerical example. In Figure 12 we show a plot of the deflections of

the bright star Arcturus (m^ = 0.2^) which goes through the Haleakala

zenith and Vega (mv

= 0.l4) which goes through the Fritz Peak zenith.

The deflections are given as S^q ( vis ) units based on the calibrations

adopted by us in connection with our calibrated built-in standard

lights. The stellar deflection corresponding to our calibration is

indicated on the plots. It is noted that in both cases the peak

k6
500 -

CO

h-

*>

o

CO 1000

Io

u

_l

li.

UJQ

500 -

VEGA

JAN. 1-2, 1962

FRITZ PEAK

ARCTURUS

APRIL 1-2, 1962

HALEAKALA

-3-2-1 I 2 3

TIME IN DEGREES

Figure 12. Typical time plots of the deflections due to bright stars going through the

field of the zenith photometer. The deflection corresponding to an integration of the entire curve is based on eq. (l8). The "uniform cathode"

line indicates the steady deflection that would result from perfect optics

in conjunction with a photomultiplier with a cathode having uniform

sensitivity (eq.. 19)-

^7
deflection is greater than would have been expected on the basis of our calibration.

Let D be the deflection due to a star, 9 the sidereal time.

Then the area, A, of a D - 9 plot is

A = D (0) d0 (17) o

and the D corresponding to the star is

A 5 = s^rsr W

9^ - 0]_ depends on the latitude of the observer and the portion of the

field traversed by the star. For Vega at Fritz Peak, 2

" el

= 5«°72

and for Arcturus at Haleakala, 9^ - 9-* = 4.°87«

The value of D from eq. (l8) can be compared with that based on the

apparent magnitude of the star m^ and the photometer field (19-6 square

degrees) on the assumption that the cathode is uniformly sensitive . The

pertinent relationship is

log D = 0.4 (10.00 - nu.) - log 19.6

(19) = 0A (10.00 - nv) - 1.29 •

In Figure 12 and Table 10, values of D max and D from eq (l8) and

(19) are compared. We conclude: (a) The use of the peak deflection can

give calibration errors as great as 2 for the 1P21 tube and (b) star

crossings can yield reasonable calibrations if allowance is made for the

variable sensitivity of the cathode surface by way of eq. (l8). The

sense of the error resulting from the use of peak deflections is such

that deduced surface brightnesses will be too small.

In spite of the efforts we have made in this study to achieve good

calibrations, we consider that the absolute accuracy of our present

results may be no better than ± 10$. In contrast with this somewhat

pessimistic estimate, we found that the probable errors of the means in

hQ
Table 10.

D (Star) Vega

(F.F. end on)

Arcturus

(Haleakala, 1P21)

From max. D

From Eq (18)

From Eq (19)

550

413

448

1007

552

409

k9
the columns headed "total" in Table 2 were about k S^q (vis) units

(~l-l/3/o) for Haleakala and 5 S10 (vis) units ( ~l-l/2#) for Fritz

Peak. Thus the intensities for the two stations constitute internally

self-consistent sets of data which can be used with confidence byfuture investigators at the same latitudes even though they may be

found to require systematic absolute corrections

.

It seems necessary to reiterate what was earlier pointed out in

the discussion of the galactic light, namely that the uncertainties and

difficulties associated with absolute calibrations of photometers, com- pounded by the uncertainty in the integrated starlight deduced from

star counts dictate a cautious and even skeptical attitude toward the

acceptance of the reality of the existence of the galactic light . The

uncertainty should probably be resolved by investigations with meticulously calibrated photoelectric photometers attached to astronomical

telescopes. Such a set-up using a very small field of view could, by

avoiding the bright stars which contribute most of the integrated starlight, minimize the uncertainty due to the interpretation of star

counts. However, the problems of absolute calibration and of subtracting out zodiacal light and airglow remain.

50
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Allen, C. W. (191*6), Monthly Notices Roy. Astron. Soc. 106" , 137.

Barbier, D. (1955), Mem. Soc. Roy. Sci. Liege 15, 55.

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Bottlinger, K. F. (1932), Z. Astrophys. h, 370.

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Els&sser, H (1963), Planetary Space Sci. 11, 1015-

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Roach, F. E., and M. H. Rees (1956), The Airglow and the Aurorae , p. 1*1-2,

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Seares, F. H., and M. C. Joyner (1928), Astrophys. J. 67, 2k.

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van de Hulst, H. C. (l^T), Astrophys. J. 105 , 471.

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52

GPO 842-421

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