Mars, Jupiter, Saturn, and Uranus: 3.3-mm brightness temperatures and a search for variations with time or phase angle

ICARUS 13, 276--281 (1970)

Mars, Jupiter, Saturn, and Uranus: 3.3-mm Brightness Temperatures and a Search for Variations with Time or Phase Angle E. E. EPSTEIN, M. M. D W O R E T S K Y , 1 J. W. MONTGOMERY, AND W. G. FOGARTY 2 The Aerospace Corporation, Los Angeles, California 90045 R. A. SCHORN Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91103 R e c e i v e d M a y 4, 1970; revised J u l y 2, 1970 E x t e n s i v e 3.3-ram o b s e r v a t i o n s yield d i s k - a v e r a g e b r i g h t n e s s t e m p e r a t u r e s for Mars, J u p i t e r , S a t u r n , a n d U r a n u s of 180 ° =k 18 °, 153 ° q- 15 °, 125 ° ± 13 °, a n d 105 ° ± 13 ° K (1 a), respectively. T h e v a l u e s for t h e first t h r e e p l a n e t s are c o r r e c t e d t o heliocentric d i s t a n c e s of 1.524, 5.203, a n d 9.540 a.u., respectively. A n y v a r i a t i o n of t h e t e m p e r a t u r e of Mars w i t h p h a s e a n g l e is Jess t h a n a few p e r c e n t ; t h i s u p p e r l i m i t is c o n s i s t e n t w i t h a n e x p e c t e d v a r i a t i o n of~< 3~o. T h e m e a s u r e m e n t s f r o m m i d - 1 9 6 5 t o N o v e m b e r 1969 c o n t a i n no c o n f i r m e d v a r i a t i o n s in t h e b r i g h t n e s s t e m p e r a t u r e s of J u p i t e r a n d S a t u r n larger t h a n ~ 4 a n d ~ 7 ~o, respectively. I . INTRODUCTION

Extensive planetary studies at 3 mm with the 15-ft (4.6-m) antenna of The Aerospace Corporation have continued. Recent Mercury (Epstein et al., 1970) and Venus (Epstein et al., 1968) results have been reported elsewhere. This article reports measurements of Uranus and confirms and extends previous work (Epstein, 1968) on Mars, Jupiter, and Saturn. II. OBSERVATIONS

The dual-antenna-beam detecting system has two identical feed horns (eastwest polarization) near the Cassegrain focus of the antenna. The beamwidths are 3~0. Prior to September 1967 one of the feeds was mounted on-axis and the other was mounted off-axis with a separation corresponding to 12:5 west (on the sky) of 1 Also a t D e p a r t m e n t o f A s t r o n o m y , U n i v e r s i t y of California, Los Angeles. 2 Also a t S t e w a r d O b s e r v a t o r y , U n i v e r s i t y of A r i z o n a , Tucson.

the on-axis feed. Subsequent to September 1967 the feed horns were mounted symmetrically east and west of the Cassegrain focus with a separation corresponding to 24:8. The two antenna beams are alternately pointed at the object being observed. Additional information about the antenna system has been given elsewhere (Cogdell et al., 1970). The calibration of the antenna gain was done with the aid of a standard gain horn and a transmitter in the antenna's far field; the estimated 1-a uncertainty is 90/0 . The calibration of the antenna temperature scale was based on a semitheoretical calculation of the antenna's diffractive efficiency over the solid angle subtended by the Sun and the value 6600 ° ± 200°K (la) for the 3.3-mm brightness temperature of the quiet Sun (Shimabukuro and Staeey, 1968; Reber, 1970). On this calibration scale the average (over a lunation) brightness temperature of the center of the Moon is 197°K, and the mean brightness temperatures of Mercury and Venus are, respectively, 296°=k 7° and 296 ° 4- I°K (la). Secondary calibration was

276

3-MM BRIGHTNESS TEMPERATURES OF PLANETS

obtained from a gas discharge tube (prior to 28 October 1968) or a hot resistive load (after 28 October 1968). The estimated overall absolute calibration uncertainty is 10% . Because of changes in receiver parameters, the wavelength of the centroid of the receiver passband changed from 3.4 mm (88 GHz) to 3.3 mm (91 GHz) in mid-1967; this slight change has been allowed for in the system calibration and does not otherwise affect the results. The radiometer output noise fluctuations for a 1-sec RC time constant varied from ~2.0°K in 1965 to m0.6°K in 1969. Antenna temperatures for Mars varied from ~0.1°K near quadrature to ~0.6°K near opposition; those for Jupiter, Saturn, and Uranus were m 1.5 °, ~ 0.5 °, and m 0.02°K, respectively. Each observation consisted of 3-12 hr of integration time, usually distributed over several days, although for Uranus each observation totaled approximately 15 hr. New observing procedures (described by Dworetsky, Epstein, Fogarty, and Montgomery, 1969) were adopted in early 1969 to cancel the differences in atmospheric emission measured by the dual-beam system and to cancel the effects of detection by the antenna side lobes of emission from the atmosphere and the ground. Epstein et al. (1970) described the manner in which the earlier data were corrected for incomplete cancellation. Prior to September 1968 the apparent antenna temperatures of the Sun and radiosonde measurements of atmospheric precipitable water vapor were used to calculate atmospheric attenuation correction factors (Shimabukuro and Epstein, 1970). Subsequent to September 1968 the water vapor procedure was dropped, and a method for calculating attenuation correction factors from measurements of differential atmospheric emission (Dworetsky et al., 1969) has since been used for nighttime observations and for supplementing the solar measurements. The attenuation correction factors ranged from 1.20 t~ ~ 1.80; the estimated 1-a uncertainty of each correction factor is 3O/o. Each observation has been corrected for estimated residual pointing uncertainties

277

and for the finite size of the planetary disk (assumed to be uniformly bright); see Epstein et al. (1968) for a description of the pointing correction calculation and a justification for the assumption of uniform brightness. The correction factors ranged from 1.02 to 1.09; the estimated 1-a up_certainty of each factor is 2~o. All previously published data have been revised by using an improved data reduction procedure. The 1-a uncertainty associated with each observation was calculated from the scatter in the data and the estimated 1-a uncertainties of the pointing and attenuation correction factors. III. MARS

The disk-average brightness temperatures, T B, are listed in Table I, along with the values corrected to the heliocentric distance corresponding to the semimajor axis of Mars, 1.524 a.u. Previously (Epstein, 1968), the correction factor was set equal to (r/1.524 a.u.)l/2; however, Morrison, Sagan, and Pollack (1969) have suggested t h a t short centimeter wavelength observations of Mars should be scaled approximately as the average of the dayside and nightside heliocentric distance corrections. The nightside TB is very weakly dependent on heliocentric distance because the nightside minimum temperature is primarily a function of the physical properties of the surface layers and is practically independent of heliocentric distance (Soter and Ulrichs, 1967). For a blackbody, the distance correction for the dayside maximum temperature is proportional to (r/1.524 a.u. )1/2, where r is the heliocentric distance. For the magnitudes of the corrections involved, a good approximation to the average of a unity correction for the nightside and an (r/1.524) 1/2 correction for the dayside is (r/1.524) 1/4. Because of the uncertainty in the proper form of the correction for 3-mm observations, we have included in Table I brightness temperatures corrected by both the square-root and fourth-root factors. Figure 1 displays as a function of phase angle the temperatures corrected by the

278

E.E.

EPSTEIN

ET AL.

TABLE I 3.3-mm

B R I G H T N E S S T E M P E R A T U R E S OF I~-A.RSa

Date

Mar. Apr. May Apr. May June June July Aug. Sep. Nov.

T~

23-30, 1967 23-27, 1967 17-20, 1967 29, 1969 8-9, 1969 12-15, 1969 23-30, 1969 25-26, 1969 24-26, 1969 5-13, 1969 19-26, 1969

TB(r/ro)xt 4

(*K)

Phase angle

-16 ° +8 ° +25 ° -24 ° --18 ° +12 ° +22 ° +37 ° +44 ° +46 ° +43 °

174 ° 155 ° 166 ° 188 ° 184 ° 192 ° 203 ° 180 ° 176 ° 177 ° 185 °

Averages:

44444± 44444-

(°K)

12 ° 6° 7° 8° 8° 8° 9° 8° 8° 16 ° 14 °

1 8 0 ° 4- 4 °

Tn(rlro) x'2

(*K)

177 ° 157 ° 168 ° 189 ° 184 ° 190 ° 201 ° 178 ° 172 ° 173 ° 181 °

180 ° 159 ° 170 ° 189 ° 184 ° 188 ° 198 ° 175 ° 169 ° 170 ° 177 °

1 7 9 ° 4- 4 °

1 7 8 ° 4- 4 °

a The values in columns 4 and 5 are corrected to r0 = 1.524 a.u., the semimajor axis, by the factors indicated (see text); the 1-a limits are l i s t e d i n c o l u m n 3.

fourth root factor. We conclude t h a t any variation of the 3-mm brightness temperature with phase angle has an amplitude less t h a t a few percent over the range of phase angles observed. We are not sure why two of the 1967 data points are low relative to the 1969 points near the same phase angles; it is possible t h a t the calibration scale was in error because solar observations for antenna temperature scale calibration were sparse during April and May 1967. There was no systematic difference in the range of longitudes observed in 1967 and in 1969. I f two of the 1967 points are excluded, there is a slight suggestion of a phase variation with an amplitude of ~ 10% over the phase angle interval observed. This apparent ~"

210,

~_~

DUSK

15o--30

I SIDE I -2o -~o

I O

I io

t+DA,t!tl

I 20

I SInE I 40

30

50

PHASEANGLE,~{deg) F I G . 1. B r i g h t n e s s t e m p e r a t u r e s of Mars as a function of phase angle. The 1-a limits are indicated. No significant variation with phase a n g l e is a p p a r e n t .

phase effect may be due to uncertainties in relative calibration and attenuation corrections. We note t h a t this apparent variation seems much too large. That is, if it is assumed t h a t the m i n i m u m possible nighttime 3-mm disk-average temperature at a phase angle ~b of 180 ° (not observable from Earth) is 150°K, which is the infrared temperature of the north polar cap observed by Mariner 7 (Neugebauer et al., 1969), and if we interpret the data of Table I to infer a m a x i m u m 3-mm T B of 195 °K, then the largest possible difference between TB values at ¢ = 0 ° and ~b= 45 ° is 6°K, or only ~ 3 % , compared to the apparent variation of ~ 10 ~ . Dent, Klein, and Aller (1965) found less than 3% phase variation at 3.75 cm. The overall 1967 and 1969 average 3.3-mm uncorrected TB of Mars is 180 ° ± 4°K (la); with the estimated absolute calibration uncertainty included, T B = 180 ° -4- 18°K. IV.

JUPITER

AND SATURN

Figure 2 displays the Jupiter and Saturn observations. All values have been corrected to the heliocentric distance equal to the semimajor axis by the factor

3-MM 170

BRIGHTNESS i

i

i

TEMPERATURES i

i

i

i

I

279

OF PLANETS

'

150

150

ttttt tt I

9C

150 !i!~

I

P

tt I

r

i 1966

I

I

I

t

I

t

1968

1967

19169

FIG. 2. Brightness temperatures of J u p i t e r and Saturn as functions of time. The 1-a limits are indicated. The horizontal lines represent the overall mean values. There is no systematic trend in the brightness temperatures, and the scatter among t h e m is consistent with the 1-a limits.

(r/ro) 1/~, w h e r e r 0 = 5.203 a . u . f o r J u p i t e r a n d 9.540 a . u . f o r S a t u r n . O b l a t e n e s s o f both planets was taken into account in c o m p u t i n g t h e TB v a l u e s . The mean values of th4 3.3-mm brightn e s s t e m p e r a t u r e s a n d t h e i r 1-a l i m i t s a r e 153 ° ± 2 ° ( J u p i t e r ) a n d 125 ° ± 2 ° K (Saturn); with the estimated absolute calibration uncertainty included, the v a l u e s a r e 1 5 3 ° ± 15 ° a n d 1 2 5 ° ± 13°K. T h i s J u p i t e r t e m p e r a t u r e is i n a g r e e m e n t with the other millimeter values comp i l e d b y K e l l e r m a n n (1970) a n d D i c k e l , Degioanni, and Goodman (1970); t h e S a t u r n t e m p e r a t u r e is i n e x c e l l e n t a g r e e ment with the values compiled by Kellerm a n n (1970) a n d S e l i n g (1970). Nominal variations from the mean

values as large as ~11% (Jupiter) and 1 8 % ( S a t u r n ) a p p e a r i n F i g . 2. H o w e v e r , the scatter in the Jupiter and Saturn data is c o n s i s t e n t w i t h t h e 1-a l i m i t s ; i.e., approximately two-thirds of the 1-a limits overlap the mean values. On the assumption of the nonvariability of Jupiter and Saturn, this consistency indicates that our long-term relative calibration, atmospheric attenuation and pointing corrections, and uncertainty estimates are satisfactory. We conclude that our measurem e n t s f r o m m i d - 1 9 6 5 t o N o v e m b e r 1969 contain no confirmed variations in the brightness temperatures larger than the a v e r a g e 1-a l i m i t s o f ~4°/O f o r J u p i t e r and ~ 7% for Saturn. The rings were not taken into account

TABLE II S A T U R N : 3.3-mm B R I G H T N E S S T E M P E R A T t r R E S A N D SATURNICENTRIC LATITUDES OF THE EARTH AND THE SUN Date

Apr. Apr. Aug. Jun.

1966-Feb. 1967-Mar. 1968-Mar. 1969-Nov.

1967 1968 1969 1969



a

b

(°K)

(°K)

(°K)

-1.5 ° --6.9 ° --12.7 ° -17.9 °

-1.3 ° --6.7 ° --13.3 ° --17.1 °

125 ° ± 124 ° ± 123 ° ± 129 ° ±

4° 2 °c 2° 2°

a Saturnieentric latitude of the Earth, referred to the plane of the rings. b Saturnieen~rie la.ti~ude of the Sun, referred to the plane of the rings. c This average includes the observation of November 1965, for which B = +5°.8 and B ' = +30.1.

280

E. E. EPSTEIN

in c o m p u t i n g the disk-average brightness t e m p e r a t u r e s of Saturn. W e have combined the 28 observations into four equally weighted sets {Table II), chosen so t h a t the value of B, the Saturnicentric latitude of the E a r t h referred to the plane of the rings, would be r e a s o n a b l y c o n s t a n t for each set. The q u a n t i t y B ' in Table I I is a similarly defined angle for the Sun. A l t h o u g h the rings began opening up in early 1967, no significant t r e n d is a p p a r e n t in either Fig. 2 or Table I I . This a p p a r e n t absence of a correlation between ring inclination a n d brightness t e m p e r a t u r e is consistent with an estimate of the radii of the ring particles of 300 microns given b y one of t w o models of F r a n k l i n a n d Cook (1965), i.e., a size m u c h smaller t h a n the observing wavelength. We shall continue to m o n i t o r S a t u r n as the rings open up further. V. URANUS

Table I I I contains the results of our four observations of Uranus. The p l a n e t a r y disk was assumed to be circular with the angular d i a m e t e r given in The A m e r i c a n Ephemeris and Nautical Almanac. The weighted average brightness t e m p e r a t u r e is 105 ° + 13°K (la) when each o b s e r v a t i o n is weighted b y t h e reciprocal of the square of the 1-a limit. This average is in excellent agreement with the 3.5-mm value of 1 1 1 ° ± 7°K ( P a u l i n y - T o t h a n d KellerTABLE III 3 . 3 - m m BRIGHTNESS TEMPERATURES OF URANUS

Date

Mar. Jun. Dec. Feb.

16-24, 1969 11-22, 1969 29, 1969-Jan. 7,1970 8-22, I970 Weighted b average:

TB a

(°K)

100° ± 85° i 97 ° ± 125° ±

ET AL.

m a n n , 1970), t h u s verifying the decrease in t h e brightness t e m p e r a t u r e o f U r a n u s with decreasing wavelength. Note added inproof: F r o m the lack of a n y significant t r e n d in the d a t a in Table I I , we h a v e a d o p t e d 10~/o as a conservative u p p e r limit to the ratio (3-mm flux from the rings)/(3-mm flux from the planet) during J u n e - N o v e m b e r 1969. I f we ignore b o t h t h e o b s c u r a t i o n o f t h e ring b y t h e planet and the planet b y t h e ring, t h e n we can use simple g e o m e t r y to conclude t h a t E r F T r / ( 1 2 5 ° K ) <~ 0.1, where E r is the emissivity at 3 m m o f the ring material, F is the fraction o f p r o j e c t e d ring area (during J u n e - N o v e m b e r 1969) which is filled b y particles, and Tr is t h e t e m p e r a t u r e c f the ring material.

ACKNOWLEDGMENTS The authors are pleased to acknowledge the work of T. Mori and G. Berry in maintaining the 15-ft antenna and express their appreciation to 1%. C. Cooley for preparing the improved data reduction program. This work was supported by Air Force Contract FO4701-69-C-066.

REFERENCES

COGDELL, J. R. et al. (1970). High resolution millimeter reflector antennas. I E E E Trans. AP-18, 515. DENT, U . A., KLEIN, M. J., AND ALLER, H. D.

(1965). Measurements of Mars at ~ 3.75 cm from February to June, 1965. Astrophys. J. 142, 1685. DICKEL, J. R., DEGIOANNI, J. J., AND GOODMAN,

G. C. (1970). The microwave spectrum of Jupiter. Radio Sci. 5, 517. DWORETSKY, M. M., EPSTEIN, E. E., FOGARTY, W. G., AND MONTGOMERY, J. W. (1969).

27° 31 ° 27° 22 °

105° ± 13°

a 1-a limits are indicated. b Each observation was weighted by the reciprocal of the square of the 1-a ]i~it.

Sagittarius A: Observations of the galactic center at 3.3 mm. Astrophys. J. 158, L183. EPSTEIN,E. E. (1968). Mars, Jupiter, and Saturn : 3.4-mm Brightness temperatures. Astrophys. J. 151, L149. EPSTEIN, E. E., OLIVER, J. P., SOTE~, S. L., SCHORN, R. A., AND WILSON, W. J. (1968). Venus : On an inverse variation with phase in the 3.4-mm emission during 1965 through 1967. Astron. J. 73, 271. EPSTEIN, E. E., DWORETSKY, M. M., FOGARTY, W. G., MONTGOMERY, J. W., AND COOLEY,

3-MM BRIGHTNESS TEMPERATURES OF PLANETS

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PAULINY-TOTH,I. I. K., AND KELLERMANN,K. I. (1970). Millimeter-wavelength measurements of Uranus and Neptune. Astrophys. Lett., in press. REBER, E. E. (1970). Brightness temperatures of the quiet Sun and new Moon at the 6-mm wavelength. Solar Phys., in press. SELINO, T. V. (1970). Observations of Saturn at )13.75 cm. Astron. J . 75, 67. SHIMABUKU~O, F. I., AND STACEY, J. M. (1968). Brightness temperature of the quiet Sun at centimeter and millimeter wavelengths. Astrophys. J. 152, 777. SHIMABUKURO,F. I., AND EPSTEIN, E. E. (1970). Attenuation and emission of the atmosphere at 3.3 mm. I E E E Trans. AP-18, 485. SOTER, S. L., AND ULRICHS, J. (1967). Rotation and heating of the planet Mercury. Nature 214, 1315.