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The radio brightness of Titan
1cAFtus
22,48-50
(1974)
The Radio
Brightness
of Titan
F. H. BRIGGS National
Astronomy
and Ionosphere
Ceder,
Cornell
University,
Ithaca, New
York
Received January 5, 1974 Observations of Titan with t)he NRA0 interferometer yield a brightness temperature of 115 + 40°K at 8085MHz, giving an estimate for the mean surface temperature of 135 k 45°K.
Saturn’s moon Titan was observed with the NRAO’ interferometer operating at 8085MHz on 22-25 April 1972. Both Titan and Saturn were within the beams of the interferometer elements, and the data have been previously reduced in a study of Saturn and the rings (Briggs, 1974). Here, these same data are used to determine the radio brightness temperature of Titan. The observations were made with interferometer baselines of 500, 1900, and 2400m. The long baseline data are useful only if Titan’s apparent position is known to within a few tenths of an arc second. The positions of Saturn were determined from a revised ephemeris kindly supplied by T. C. Van Flandern of the U.S. Naval Observatory. The positions of Titan relative to Saturn were calculated using the theory of G. Struve as presented in the Explanatory Supplement to The Astronomical Ephemeris and The American Ephemeris and Nautical Almanac ( 196 1) . In order to test the accuracy of the derived ephemerides, apparent positions were calculated for 43 optical measurements made during 1968 and 1969 by Souli& (1973). The standard deviation of a single measurement from the predicted position was 0.“41 in right ascension and 0.“32 in declination. Since it is likely that much of this error is observational scatter, the ephemeris is satisfactory for the radio observation. The interferometer was calibrated by observing a number of sources whose
positions are well-known (Brosche, Wa,de, and Hjellming, 1973). The interferometer system noise level during the period of the observations has been discussed by Briggs (1973). The Titan data consist of 19 hr of observing time wit’h both polarizations from t’wo baselines. The system noise level for t’he full integration time is 0.58mJy (1 mJy = 1 milliJansky = 10-2~Wm-2Hz-1, in accord with t’he definition recommended by the 15th General Assembly of the I.A.U.). The interferometer confusion level arising from the superposition of weak background sources is quite low at 8085MHz, amounting to a few mJy. Since Titan moves rapidly with respect’ to the background, the error due to confusion is further reduced as integration time accumulates (Berge, 1968 ; Briggs and Drake, 1973). Confusion with fringes generated by Saturn forms a significant source of uncertainty. At the time of the observations the flux density from Saturn was approximately 1600mJy. The primary beams were pointed toward Titan, thus reducing Saturn’s signal by as much as 30%. To reduce the contamination from Saturn, only the data from the two longest baselines were used. With such high resolution, Saturn’s disk is well-resolved, and Saturn appears in the 30-set data records with rms amplitudes of 14 and IOmJy for the 1900- and 2400-m baselines, respectively. The confusing signal becomes randomized when treated in integrations longer than 1Omin since changes in the projected
1 The National Radio Astronomy Observatory is operated by Associated Universities under contract with the National Science Foundation. Copyright 0 1974 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
48
RADIO
BRIGHTNESS
baselines and in Titan’s position relative to Saturn cause rapid variation in the relative fringe phase between the two objects. Since there are 114 lo-min integrations in 19 hr, it can be seen that the uncertainty in the final result due to the presence of Saturn is approximately 1 mJy. With the fringe phases adjusted to Tit’an’s position, the calibrated data were Fourier transformed into a map of a 1.‘5 x 1.‘5 region of sky. The rms noise level of the map was 1.3mJy, which is considerably greater than the system noise limit but in agreement with a sum of system noise and confusion from Saturn. Since the contribution from Saturn is wellknown through t’he average of the several days’ data, the response expected from Saturn could be subtracted from each da,y’s observations and the data again transformed to the sky plane. The rms noise level of this map was 0.68mJy, in bett,er agreement with the anticipated syst#em noise level. Because the interferometer phase is often distorted by varying amounts of water vapor along the lines of sight of the individual antennas of the array, t’here are components of Saturn’s signal which are not completely removed by subtracting an average signal. These residuals should behave randomly so that 0.68mJy can be adopted as the uncertainty in t,he observation. To insure that part of Tit’an’s signal was not inadvertently subtracted by this procedure, artificial data, free from noise and confusion, were generated and propagated through the a’veraging and phase-correcting routines. It was found that Titan’s signal was reduced by less than 1%. The data from which Saturn had been subtracted gave a vector average of 2.05 + i0.23mJy at the position predicted for Titan. Figure 1 shows the result of searching the data for an object in Titan’s orbit but at an orbital longitude in the Titan orbit differing from that calculated for Titan by Al. Also shown are the responses predicted if Titan has flux density 2.05mJy. The positions agree to the sccuracy of the observation. The derived disk brightness temperature is 115 + 40°K assuming a radius for Titan
OF TITAN
FIG. 1. Response as a function of the Saturnicentric longitude of Titan in its orbit. Al = 0 corresponds to the predicted position of Titan. The observed values are represented by dots. The solid curve is the response predicted if Titan has a flux density of 2.05mJy.
of 2,500km (Hunten, 1973). The observed radiation probably comes from the planetary surface since none of the proposed atmospheric constituents (Sagan, 1973) are effective absorbers for this frequency at these temperatures and expected pressures. Those molecules with significant vapor pressures below 15O’K have no permitted transitions at centimeter wavelengths. Ammonia and the complex organic molecules which do absorb at 8 GHz are gaseous in significant quantities only at higher temperatures. The microwave emissivity of the surface must be known to convert the brightness temperature to an actual thermometric surface temperature. Lewis (197 1) has suggested that the moons of the outer planets should be covered by a crust of water ice. Water ice has a dielectric constant of 3.1 at this frequency (Evans, 1965), which leads to a mean emissivity over the disk of about 0.85 (Heiles and Drake, 1963). Most terrestrial rocks have microwave dielectric
F. H. BRIGGS
50
constants of 5-10, while rock powders with density 1 gcme3 typically lie in the range 2-2.5 (Campbell and Ulrichs, 1969), so that it is possible to obtain emissivities from 0.7 to 0.95. A thick layer of frost would reduce the sharpness of the dielectric discontinuity, acting like an antireflection coating, and therefore would increase the emissivity. If the surface is assumed to be a hard layer of water ice, the average surface temperature is 135 5 45°K. Although this value favors the elevated temperatures predicted by greenhouse models for Titan’s atmosphere (Pollack, 1973 ; Sagan, 1973 ; Cess and Owen, 1973), the observation is not precise enough to rule out the temperatures near 80°K which are predicted for a body with Titan’s albedo in equilibrium with the solar insolation, or by the atmospheric temperature inversion model of Danielson, Caldwell, and Larach (1973). It is, however, unlikely that the surface temperature is greater than 200°K.
ACKNOWLEDGMENTS It is a pleasure to acknowledge the advice and encouragement of F. D. Drake, C. Sagan, and J. Veverka, and to thank T. C. Van Flandern for supplying the ephemeris for Saturn, W. Melbourne for commenting on the Titan ephemeris, and B. Beredith and B. Balick for help with the early stages of data reduction. The National Astronomy and Ionosphere Center is operated by Cornell University under contract with the National Science Foundation.
REFERENCES BERGE, G. 1~. (1968). Recent observations of Saturn, Uranus and Neptune at 3.12cm. Astrophys. Lett. 2, 127.
BROSCHE, P., WADE, C. M., AND HJELLMIKG, R. M. (1973). Precise positions of radio sources. IV. Improved solutions and error analysis for 59 sources. Astrophys. J. 183, 805. BRIGGS, F. H., AND DRAKE, F. D. (1973). Radio interferometry of moving sources in the presence of confusion. An a.pplication to Mercury at 2 1-centimeter wavelength. A strophys. J. 182, 601 BRIGGS, F. H. (1973). Radio Emission from Ceres. Astrophys. J. 184, 637. BRIGGS, F. H. (1974). The microwave properties of Saturn’s Rings. Astrophys. J., in press. CAMPBELL, M. J., AND ULRICHS, J. (1969). Tho electrical properties of rocks and their significance for lunar radar observations. J.G.R. 74, 5867. CESS, R., AND OWEN, T. (1973). Titan: The effects of noble gases on an atmospheric greenhouse. Nature 244, 272. DANIELSON, R. E., CALDWELL, J. J., AND LARACH, D. R. (1973). An inversion in t,he atmosphere of Titan. Icarus, in press. EVANS, S. (1965). Dielectric properties of ice and snow-a review. J. Glacial. 5, 773. Explanatory Supplement to The Astronomical Ephemeris and The American Ephemeris and Nautical Almanac, (1961). Her Majesty’s Stationery Office, London. HEILES, C. E., AND DRAKE, F. D. (1963). The polarization and intensity of t’hermal radiat,ion from a planetary surface. lcarus 2, 281. HUNTEN, D. M., ed. (1973). The Atmosphere of Titan, Report of the Titan Atmosphere Workshop. Ames Research Center. POLLACK, J. B. (1973). Greenhouse models of the atmosphere of Titan. Icarlts 19, 43. SAGAN, C. (1973a). The greenhouse of Titan. Icarus 18, 649. SAGAN, C. (1973b). Organic chemistry in the atmosphere. In. “The Atmosphere of Titan, Report of the Titan Workshop” (D. M. Hunten, ed.), Ames Research Center. SOULI~~, G. (1973). Positions de grosses plar&tes et de la lune observees a l’equatorial photographique de ,33m. Astron,. Astrophys. Suppl 6, 311.
22,48-50
(1974)
The Radio
Brightness
of Titan
F. H. BRIGGS National
Astronomy
and Ionosphere
Ceder,
Cornell
University,
Ithaca, New
York
Received January 5, 1974 Observations of Titan with t)he NRA0 interferometer yield a brightness temperature of 115 + 40°K at 8085MHz, giving an estimate for the mean surface temperature of 135 k 45°K.
Saturn’s moon Titan was observed with the NRAO’ interferometer operating at 8085MHz on 22-25 April 1972. Both Titan and Saturn were within the beams of the interferometer elements, and the data have been previously reduced in a study of Saturn and the rings (Briggs, 1974). Here, these same data are used to determine the radio brightness temperature of Titan. The observations were made with interferometer baselines of 500, 1900, and 2400m. The long baseline data are useful only if Titan’s apparent position is known to within a few tenths of an arc second. The positions of Saturn were determined from a revised ephemeris kindly supplied by T. C. Van Flandern of the U.S. Naval Observatory. The positions of Titan relative to Saturn were calculated using the theory of G. Struve as presented in the Explanatory Supplement to The Astronomical Ephemeris and The American Ephemeris and Nautical Almanac ( 196 1) . In order to test the accuracy of the derived ephemerides, apparent positions were calculated for 43 optical measurements made during 1968 and 1969 by Souli& (1973). The standard deviation of a single measurement from the predicted position was 0.“41 in right ascension and 0.“32 in declination. Since it is likely that much of this error is observational scatter, the ephemeris is satisfactory for the radio observation. The interferometer was calibrated by observing a number of sources whose
positions are well-known (Brosche, Wa,de, and Hjellming, 1973). The interferometer system noise level during the period of the observations has been discussed by Briggs (1973). The Titan data consist of 19 hr of observing time wit’h both polarizations from t’wo baselines. The system noise level for t’he full integration time is 0.58mJy (1 mJy = 1 milliJansky = 10-2~Wm-2Hz-1, in accord with t’he definition recommended by the 15th General Assembly of the I.A.U.). The interferometer confusion level arising from the superposition of weak background sources is quite low at 8085MHz, amounting to a few mJy. Since Titan moves rapidly with respect’ to the background, the error due to confusion is further reduced as integration time accumulates (Berge, 1968 ; Briggs and Drake, 1973). Confusion with fringes generated by Saturn forms a significant source of uncertainty. At the time of the observations the flux density from Saturn was approximately 1600mJy. The primary beams were pointed toward Titan, thus reducing Saturn’s signal by as much as 30%. To reduce the contamination from Saturn, only the data from the two longest baselines were used. With such high resolution, Saturn’s disk is well-resolved, and Saturn appears in the 30-set data records with rms amplitudes of 14 and IOmJy for the 1900- and 2400-m baselines, respectively. The confusing signal becomes randomized when treated in integrations longer than 1Omin since changes in the projected
1 The National Radio Astronomy Observatory is operated by Associated Universities under contract with the National Science Foundation. Copyright 0 1974 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
48
RADIO
BRIGHTNESS
baselines and in Titan’s position relative to Saturn cause rapid variation in the relative fringe phase between the two objects. Since there are 114 lo-min integrations in 19 hr, it can be seen that the uncertainty in the final result due to the presence of Saturn is approximately 1 mJy. With the fringe phases adjusted to Tit’an’s position, the calibrated data were Fourier transformed into a map of a 1.‘5 x 1.‘5 region of sky. The rms noise level of the map was 1.3mJy, which is considerably greater than the system noise limit but in agreement with a sum of system noise and confusion from Saturn. Since the contribution from Saturn is wellknown through t’he average of the several days’ data, the response expected from Saturn could be subtracted from each da,y’s observations and the data again transformed to the sky plane. The rms noise level of this map was 0.68mJy, in bett,er agreement with the anticipated syst#em noise level. Because the interferometer phase is often distorted by varying amounts of water vapor along the lines of sight of the individual antennas of the array, t’here are components of Saturn’s signal which are not completely removed by subtracting an average signal. These residuals should behave randomly so that 0.68mJy can be adopted as the uncertainty in t,he observation. To insure that part of Tit’an’s signal was not inadvertently subtracted by this procedure, artificial data, free from noise and confusion, were generated and propagated through the a’veraging and phase-correcting routines. It was found that Titan’s signal was reduced by less than 1%. The data from which Saturn had been subtracted gave a vector average of 2.05 + i0.23mJy at the position predicted for Titan. Figure 1 shows the result of searching the data for an object in Titan’s orbit but at an orbital longitude in the Titan orbit differing from that calculated for Titan by Al. Also shown are the responses predicted if Titan has flux density 2.05mJy. The positions agree to the sccuracy of the observation. The derived disk brightness temperature is 115 + 40°K assuming a radius for Titan
OF TITAN
FIG. 1. Response as a function of the Saturnicentric longitude of Titan in its orbit. Al = 0 corresponds to the predicted position of Titan. The observed values are represented by dots. The solid curve is the response predicted if Titan has a flux density of 2.05mJy.
of 2,500km (Hunten, 1973). The observed radiation probably comes from the planetary surface since none of the proposed atmospheric constituents (Sagan, 1973) are effective absorbers for this frequency at these temperatures and expected pressures. Those molecules with significant vapor pressures below 15O’K have no permitted transitions at centimeter wavelengths. Ammonia and the complex organic molecules which do absorb at 8 GHz are gaseous in significant quantities only at higher temperatures. The microwave emissivity of the surface must be known to convert the brightness temperature to an actual thermometric surface temperature. Lewis (197 1) has suggested that the moons of the outer planets should be covered by a crust of water ice. Water ice has a dielectric constant of 3.1 at this frequency (Evans, 1965), which leads to a mean emissivity over the disk of about 0.85 (Heiles and Drake, 1963). Most terrestrial rocks have microwave dielectric
F. H. BRIGGS
50
constants of 5-10, while rock powders with density 1 gcme3 typically lie in the range 2-2.5 (Campbell and Ulrichs, 1969), so that it is possible to obtain emissivities from 0.7 to 0.95. A thick layer of frost would reduce the sharpness of the dielectric discontinuity, acting like an antireflection coating, and therefore would increase the emissivity. If the surface is assumed to be a hard layer of water ice, the average surface temperature is 135 5 45°K. Although this value favors the elevated temperatures predicted by greenhouse models for Titan’s atmosphere (Pollack, 1973 ; Sagan, 1973 ; Cess and Owen, 1973), the observation is not precise enough to rule out the temperatures near 80°K which are predicted for a body with Titan’s albedo in equilibrium with the solar insolation, or by the atmospheric temperature inversion model of Danielson, Caldwell, and Larach (1973). It is, however, unlikely that the surface temperature is greater than 200°K.
ACKNOWLEDGMENTS It is a pleasure to acknowledge the advice and encouragement of F. D. Drake, C. Sagan, and J. Veverka, and to thank T. C. Van Flandern for supplying the ephemeris for Saturn, W. Melbourne for commenting on the Titan ephemeris, and B. Beredith and B. Balick for help with the early stages of data reduction. The National Astronomy and Ionosphere Center is operated by Cornell University under contract with the National Science Foundation.
REFERENCES BERGE, G. 1~. (1968). Recent observations of Saturn, Uranus and Neptune at 3.12cm. Astrophys. Lett. 2, 127.
BROSCHE, P., WADE, C. M., AND HJELLMIKG, R. M. (1973). Precise positions of radio sources. IV. Improved solutions and error analysis for 59 sources. Astrophys. J. 183, 805. BRIGGS, F. H., AND DRAKE, F. D. (1973). Radio interferometry of moving sources in the presence of confusion. An a.pplication to Mercury at 2 1-centimeter wavelength. A strophys. J. 182, 601 BRIGGS, F. H. (1973). Radio Emission from Ceres. Astrophys. J. 184, 637. BRIGGS, F. H. (1974). The microwave properties of Saturn’s Rings. Astrophys. J., in press. CAMPBELL, M. J., AND ULRICHS, J. (1969). Tho electrical properties of rocks and their significance for lunar radar observations. J.G.R. 74, 5867. CESS, R., AND OWEN, T. (1973). Titan: The effects of noble gases on an atmospheric greenhouse. Nature 244, 272. DANIELSON, R. E., CALDWELL, J. J., AND LARACH, D. R. (1973). An inversion in t,he atmosphere of Titan. Icarus, in press. EVANS, S. (1965). Dielectric properties of ice and snow-a review. J. Glacial. 5, 773. Explanatory Supplement to The Astronomical Ephemeris and The American Ephemeris and Nautical Almanac, (1961). Her Majesty’s Stationery Office, London. HEILES, C. E., AND DRAKE, F. D. (1963). The polarization and intensity of t’hermal radiat,ion from a planetary surface. lcarus 2, 281. HUNTEN, D. M., ed. (1973). The Atmosphere of Titan, Report of the Titan Atmosphere Workshop. Ames Research Center. POLLACK, J. B. (1973). Greenhouse models of the atmosphere of Titan. Icarlts 19, 43. SAGAN, C. (1973a). The greenhouse of Titan. Icarus 18, 649. SAGAN, C. (1973b). Organic chemistry in the atmosphere. In. “The Atmosphere of Titan, Report of the Titan Workshop” (D. M. Hunten, ed.), Ames Research Center. SOULI~~, G. (1973). Positions de grosses plar&tes et de la lune observees a l’equatorial photographique de ,33m. Astron,. Astrophys. Suppl 6, 311.