The 1-mm brightness temperature of titan

ICARUS 45, 618-623 (1981)

The 1-mm Brightness Temperature of Titan T. L. ROELLIG,* D. J. E N N I S , t AND J. R. HOUCK* * Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853, and t Department of Physics, California Institute of Technology, Pasadena, California 91125 Received A u g u s t 22, 1980; revised February 3, 1981 Titan has been observed with the 5-m Hale telescope at an effective wavelength o f 1 m m . Adopting a value o f 2700 km for the radius o f Titan, we find a brightness t e m p e r a t u r e o f 86 _+ 12°K at 1 m m . C o m p a r i n g our results with previous m e a s u r e m e n t s at longer wavelengths, we conclude that the satellite surface is the source of the l-ram radiation. Since our m e a s u r e d brightness temperature is close to the equilibrium temperature of a blackbody at the distance o f Saturn, we believe there is no significant g r e e n h o u s e effect on Titan.

I. I N T R O D U C T I O N

Titan is the only planetary satellite known to have a significant atmosphere. Near- and mid-infrared observations of Titan (8 < h < 30 /.tm) have shown a complex spectrum, with brightness temperatures ranging from 158 to 77°K (Gillett, 1975; McCarthy et a l . , 1980). Two different types of atmospheric models have been constructed to explain these results. Models proposed by Hunten (1977, 1978) and Pollack (1973) have a thick atmosphere (surface pressure 0.4 to 21 bars) with pressure-broadened absorption by atmospheric gases causing a greenhouse effect. In these models the surface temperature is between 100 to 200°K, depending on the details of the model. Other models proposed by Danielson et al. (1973), Caldwell (1977, 1978), and others have a thin atmosphere (surface pressure typically 20 mbar) with a temperature inversion. Usually these models incorporate photolysis products or "Axel dust" as the agent responsible for the inversion. These particles would absorb strongly at visible wavelengths, but their small size would prevent them from being efficient radiators at -30-/zm wavelengths. As a result, the equilibrium temperature of the dust would be higher than that of a blackbody at the distance of Saturn. The dust 618 0019-1035/81/030618-06502.00/0 Copyright © 1981by AcademicPress, Inc. All fights of reproduction in any form reserved.

would then heat the surrounding atmosphere to cause a temperature inversion. Recent observations by McCarthy et al. (1980) give a temperature of 160°K for Axel dust and an atmospheric pressure no greater than 20 mbar down to an opaque layer of uncertain composition. This opaque layer, with a derived temperature of 74°K, could either be a cloud deck or the satellite surface itself. The two different types of models are not mutually exclusive, in that the thin temperature-inversion atmosphere could exist on top of a thick greenhouse regime. Surface temperature measurements of Titan impose a constraint that would differentiate between these models, or at least rule out a greenhouse effect if a low surface temperature is observed. The atmosphere of Titan is known to absorb infrared radiation, so that longer wavelengths are necessary to study the surface directly. Unfortunately, there is a lack of agreement in the published radio brightness temperatures of Titan. Briggs (1974) and Jaffe et al. (1979) have observed Titan at 3.8 and 6 cm, respectively. They have found low brightness temperatures, 99 --_ 35°K at 3.8 cm and 87 ___ 13°K at 6 cm for an assumed radius of 2700 km. Conklin et al. (1977) have found a much higher brightness temperature of 220 ___ 40°K at 3.3 mm, for the same assumed

TITAN radius. As a result of this discrepancy, radio results have been used as evidence of b o t h a hot dense greenhouse a t m o s p h e r e (Hunten, 1978), or a cold thin a t m o s p h e r e (Caldwell, 1978). In an a t t e m p t to resolve this c o n t r o v e r s y , we h a v e m e a s u r e d the brightness temperature of Titan at 1 ram. A wavelength of 1 m m is particularly useful for this purpose, since it is long enough so that the absorption in e v e n a thick a t m o s p h e r e would be minimal. F u r t h e r m o r e , if there is s o m e m e c h a n i s m causing the excess radiation at 3 m m reported b y Conklin et al. (1977), it m a y be a p p a r e n t at 1 m m as well. II. OBSERVATIONS The T i t a n - S a t u r n s y s t e m was o b s e r v e d on M a y 5, 1979, D e c e m b e r 4, 1979, and D e c e m b e r 8, 1979 at the prime focus of the 5-m Hale telescope on P a l o m a r Mountain. The detector used was a c o m p o s i t e bolometer cooled to pumped-liquid-3He temperatures with an electrical N E P of 1 × 10-15 W / H z 1/2. The b o l o m e t e r dewar incorporated a low-pass filter with a cut-on at 750 /~m, while the long-wavelength r e s p o n s e was limited b y diffraction in the telescope and d e w a r to 1500/xm. The p h o t o m e t e r and a t m o s p h e r i c correction p r o c e d u r e s used were similar to those described in Elias et al. (1978). The b e a m profile was determined b y drift-scanning the planets. The b e a m core is roughly Gaussian in shape with a halfp o w e r b e a m width of 55 arcsec. A w a y f r o m the b e a m core the b e a m r e s p o n s e was greater than a pure Gaussian. Standard chopping techniques were used to reduce a t m o s p h e r i c noise. T h e precipitable w a t e r v a p o r ranged f r o m 1.25 to 4.25 m m for the different observations, which gave an effective wavelength ranging f r o m 920 to 1000 btm. Since Saturn is so m u c h brighter than Titan at 1 m m , precautions w e r e taken to avoid confusion caused b y proximity of the planet. The chopping was perpendicular to the S a t u r n - T i t a n plane and the c h o p p e r

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throw was limited to 1'. The S a t u r n - T i t a n plane was scanned in the vicinity of Titan, as well as the position on the opposite side of Saturn (called anti-Titan in the following text). T h e s e scans were obtained with Titan in conjunction on D e c e m b e r 4 and at eastern elongation on M a y 5 and D e c e m b e r 8. T h e results of M a y 5 and D e c e m b e r 4 are s h o w n in Fig. 1. The scan with Titan at conjunction on D e c e m b e r 4 tested for any b e a m a s y m m e t r i e s , and the results indicate that the b e a m is indeed s y m m e t r i c in the vicinity of Titan and anti-Titan. At eastern elongation on M a y 5, the m e a s u r e d flux f r o m T i t a n ' s position was almost exactly one order of magnitude higher than the flux f r o m the anti-Titan position. The results of the scan on D e c e m b e r 8 are similar to those shown in Fig. 1, except that Titan was only 160 arcsec a w a y f r o m Saturn on this date. The next flux f r o m Titan was then obtained by subtracting the anti-Titan flux f r o m the Titan flux. The ratio of T i t a n ' s to S a t u r n ' s t

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ROELLIG, ENNIS, AND HOUCK

1-mm flux, corrected for the partial resolution of Saturn by the beam, was (1.27 _+ 0.10) x 10-~. Translating the flux ratio above into a 1mm brightness temperature requires knowing the sizes of both Titan and Saturn and the brightness temperature of Saturn at 1 mm. The 1-mm brightness temperature used was from Werner et al. (1978) with a value of 145 + 16°K. At the time of the measurements of Werner et al. (1978; February, 1976), the rings of Saturn were at an angle of 22° with respect to the line of sight from the Earth. During our measurements the angles were only 7 and 2°.for May and D e c e m b e r 1979, respectively. If the rings emitted significantly at 1 mm, the changing tilt angle would cause a change in the 1-mm brightness temperature of Saturn. Preliminary results reported by Werner (1980) show that the 1-mm brightness temperature of Saturn changed less than 10% from February 1976 to March 1980, implying little ring contribution to the 1-mm brightness temperatures. Their conclusion is in agreement with unpublished high-resolution 1mm scans obtained b y one of the authors (Ennis) and the far-infrared results of Ward (1977). We have, therefore, made no correction to the l-mm brightness temperature of Saturn for the changing ring aspect. The 1-mm size of Titan is a more difficult problem. Elliot et al. (1975) measured a radius of 2916 km for Titan using occultation techniques. H o w e v e r , due to the presence o f Titan's atmosphere, the 1-mm radius is probably smaller than this figure (Caldwell, 1977). Figure 2 is a plot of 1-mm brightness temperature versus radius. The atmospheric model of Caldwell (1977) gives an estimated radius of 2700 km for the surface of Titan. Using this radius, the 1-mm brightness temperature o f Titan is 86 _+ 12°K including statistical and calibration errors. III. DISCUSSION The brightness temperature measured at 1 mm is in excellent agreement with the

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FIG. 2. Derived 1-mm brightness temperature of Titan plotted against satellite surface radius. The thin lines indicating the error include both statistical and calibration uncertainties. The occultation radius of Elliot et al. (1975)is shown together with the standard satellite surface radius from Caldwell (1977). The brightness temperatures of both rapidly and slowly rotating blackbodies are also indicated. Open circle: 3.8-cm result of Briggs (1974). Solid circle: 6-cm resalt of Jaffe et al. (1979). The 3-mm result of Conklin et al. (1977) is off scale at the top of the figure. previously measured values at 3.8 and 6 cm by Briggs (1974) and Jaffe et al. (1979), respectively. As illustrated in Fig. 2, our results show no indication of the highmillimeter brightness temperature reported by Conklin et al. (1977). The agreement with the longer wavelength radio results is a powerful argument for the transparency of the atmosphere to radio radiation down to 1-mm wavelengths, at least down to a level where the optical depth becomes large for all three wavelengths. Possible candidates to produce absorption at these radio wavelengths are atmospheric gases, clouds, or the satellite surface itself. These possibilities are considered below. (a) Opacity from Atmospheric Gases

Spectroscopic measurements of Titan's atmosphere have shown the presence o f methane, with smaller amounts of C2H~,

TITAN C2H4, and C2H2 (Trafton, 1975, 1978; Gillett, 1975). There have also been significant amounts of H2 reported (Trafton, 1972), but this result has been contradicted by other more recent studies (Munch et al., 1977). These gases are all nonpolar and hence are poor absorbers in the radio- and millimeterwave frequency range. However, with the pressures postulated by some greenhouse models the possibility of pressure-broadened absorption should be explored. For a plane-parallel isothermal atmosphere at 100°K in hydrostatic equilibrium, we find a scale height of approximately 40 km for a mean molecular weight of 16 and a uniform gravitational acceleration of 130 cm see -~. The gravitation acceleration assumes a satellite radius of 2500 km. We have used this simple model to calculate the optical depth, z, through the atmosphere. The absorption coefficient for pressurebroadened methane depends to a certain extent on the exact atmospheric composition, but is no larger than 10-6 atm -z at 1 mm for realistic gas mixtures composed predominantly of methane (Pollack, 1973). With these values we find the ~-= 1 level for l-ram radiation is located at 0.71 atm. At this pressure the condensation temperature for methane is 108°K, almost 2tr higher than our measured l-ram brightness temperature. Therefore, the amount of methane needed to explain our results cannot exist in the gaseous state. We will discuss the possibility of opacity from methane clouds below. Pressure induced opacity is even more unlikely when the 6-cm results of Jaffe et al. (1979) are considered. Since the pressure induced absorption coefficient varies approximately as h -2 for nonpolar gases in this temperature and frequency range (Trafton, 1966; Polack, 1973), the r = 1 level is located at 43 atm for 6-era radiation in the isothermal plane-parallel example above. At this temperature the methane condensation temperature is 185°K at this pressure, much higher even than the 6-cm brightness temperature reported by Jaffe et al.

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Although ammonia has not been detected in Titan's atmosphere, it is prevalent in the atmospheres of the giant planets. Since NH3 is a polar molecule with a strong inversion resonance at 1.25 cm, only a small amount would be needed for efficient absorption of radio waves. However, our 1mm results cannot be explained by ammonia opacity. At 100°K the vapor pressure of ammonia is less than 10-~ atm. Using the results of Field (1959) we find an absorption coefficient of less than 4 x 10-12 atm -1 cm -1 at 1 ram. This is far too low to have a significant opacity effect.

(b) Opacity from Clouds It is possible that a thick cloud deck of methane may exist in the atmosphere of Titan and provide sufficient opacity at 1 mm to hide a warmer surface. For a cloud composed of pure methane droplets of 10/~m radius with a droplet density of l05 cm -3 we find a scatterin extinction coefficient of 8 x 10-7 cm -1 at I ram. Thus, it would require about one scale height of such thick clouds for a Z = 1 attenuation. This is perhaps possible, but the results at 6 cm could not be explained by such a cloud deck, since the scattering efficiency has a h -4 dependence. Therefore, pure-methane clouds would not be sufficient to conceal a warm surface from both 6-cm and 1-mm radiation. (c) The Satellite Surface Since atmospheric and cloud opacity are insufficient to conceal Titan's surface, we believe that the l-ram flux originates from thermal emission from Titan's surface. The emissivity of most planetary materials and ices at radio wavelengths is greater than 0.80 (Heiles and Drake, 1963). Thus, the measured l-ram brightness temperature indicates a surface temperature very close to a uniform temperature blackbody at the distance of Saturn from the Sun. The thinatmosphere model of Caldwell (1978) has the surface temperature nearly constant over the face of the satellite due to heat

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transport by either winds with subsequent condensation or methane ocean currents. Neglecting emissivity effects, this model would have the same surface temperature as we derive from our observations. By considering the energy balance of Titan we can make an additional check of our conclusions. We can use the model of McCarthy et al. (1980) to estimate the power emitted by the atmospheric bands and Axel dust. This model assumes: (1) a bolometric albedo of 0.2; (2) an optically thin Axel dust layer at 160°K, responsible for 25% of the power emitted by Titan: (3) a predominantly methane atmosphere, with 10% of the power emitted by Titan coming from atmospheric bands; and (4) an atmospheric radius of 2900 km. Using this model and a surface radius of 2700 km, we find a blackbody surface temperature of 77°K is needed to balance the absorbed insolation. This temperature is in excellent agreement with our measurements. To summarize, we find the results at 1 mm are consistent with low-pressure models of Titan's atmosphere employing hot Axel dust in explaining the near-infrared results. Our measured 1-mm brightness temperature is in excellent agreement with the radio results of Jaffe et al. (1979) at 6 cm and Briggs (1973) at 3.8 cm. Since we can find no source of atmospheric opacity that would conceal a warm surface at 6 cm, 3.8 cm, and 1 mm, we conclude there is at most a small greenhouse effect on Titan. ACKNOWLEDGMENTS We would like to thank the staff of the Mount Palomar Observatory for their assistance in our observations and M. Werner, J. Pollack, and W. J. Forrest for useful discussions. We would also especially like to thank G. Neugebauer for the use of his laboratory facilities and for sharing some of his telescope time. These observations were made under a special joint California Institute of Technology-Cornell University observing program. This work was supported by National Aeronautics and Space Administration Grant NSG-7324. D. Ennis would like to acknowledge the support of NASA Grant NGL-05-002-207.

Note added in proof. Jaffe, Caldwell, and Owen (1980) report VLA observations of Titan at 1.3-, 2- and 6-cm wavelengths. Their data is best fit by a satellite diameter of 2400 ± 250 km and a brightness temperature of 87 _+ 9°K. Our measured flux scaled to their diameter would yield a surface temperature of 109 + 22°K. The measurements are therefore consistent within their combined errors. If the new radius is correct, then a small greenhouse effect is required. REFERENCES BRIGGS, F. H. (1974). The radio brightness of Titan. Icarus 22, 48-50. CALDWELL, J. (1977). Thermal radiation from Titan's atmosphere. In Planetary Satellites (J. A. Burns, Ed.), pp. 438-450, Univ. of Arizona Press, Tucson. CALDWELL, J. (1978). LOW surface pressure models for Titan's atmosphere. In The Saturn System, pp. 113-126, N A S A CP2068. CONKLIN, E. K., ULICH, B. L., AND DICKEL, J. R. (1977). 3-mm observations of Titan. Bull. Amer. Astron. Soc. 9, 471. DANIELSON, R. E., CALDWELL, J., AND LARACH, D. R. (1973). An inversion in the atmosphere of Titan. Icarus 20, 437-443. ELIAS, J. H., ENNIS, D. J., GEZARI, D. Y., HAUSER, M. G., HOUCK, J. R., Lo, K. Y., MATTHEWS, K., NADEAU, D., NEUGEBAUER, G., WERNER, M. W., AND WESTBROOK, W. E. (1978). 1 millimeter continuum observation of extragalactic objects. Astrophys. J. 220, 25-41, ELLIOT, J. L., VEVERKA, J., AND GOGUEN, J. (1975). Lunar occultation of Saturn. I. Icarus 26, 387-407. FIELD, G. B. (1959). The source of radiation from Jupiter at decimeter wavelengths. J. Geophys. Res. 64, 1169-1177. GILLETr, F. C. (1975). Further observations of the 8 13 micron spectrum of Titan. Astrophys. J. 201, L41-L43. HEILES, C. E., AND DRAKE, F. D. (1963). The polarization and intensity of thermal radiation from a planetary surface, h'arus 2, 281-292. HUNTEN, D. M. (1977). Titan's atmosphere and surface. In Planetary Satellites (J. A. Burns, Ed.), pp. 420-437, Univ. of Arizona Press, Tucson. HUNTEN, D. M. (1978). A Titan atmosphere with a surface temperature of 200K. In The Saturn System, pp. 127-140, NASA CP2068. JAFFE, W., CALDWELL, J., AND OWEN, T, (1979). The brightness temperature of Titan at 6 centimeters from the very large array. Astrophys. J. 232, L75L76. MCCARTHY, J. F., POLLACK, J. B., HOUCK, J. R., AND FORREST, W. J. (1980). 16-30 micron spectroscopy of Titan. Astrophys. J. 236, 701-705. MUNCH, G., TRAUGER, J. R., AND ROESLER, F. L. (1977). A search for the Hz (3,0) S1 line of the spectrum of Titan. Astrophys. J. 173, L 143.

TITAN POLLACK, J. B. (1973). Greenhouse models of the atmosphere of Titan. Icarus 19, 43-58. TRAFTON, L. M. 0966). The pressure-induced monochromatic translational absorption coefficient for homopolar and nonpolar gases and gas mixtures with particular application to H2. Astrophys. J. 146, 558-571. TRAFTON, L. M. (1972). On the possible detection of H2 in Titan's atmosphere. Astrophys. J. 175, 285293. TRAFTON, L. M. (1975). Near-infrared spectrophotometry of Titan. Icarus 24, 443-453.

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TRAFTON, L. M. (1978). Titan's atmosphere: Comments on haze content, methane abundance, band shapes, and hydrogen upper limit. In The Saturn System, pp. 141-147, NASA CP2068. WARD, D. B. (1977). Far-infrared spectral observations of Saturn and its rings. Icarus 32, 437-442. WERNER, M. W. (1981). In preparation. WERNER, M. W., NEUGEBAUER, G., HOUCK, J. R., AND HAUSER, M. G. (1978). One-millimeter brightness temperatures of the planets. Icarus 35, 289296.