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The brightness temperatures of Saturn and its rings at 39 microns
ICARUS 30, 747--759 (1977)
The Brightness Temperatures of Saturn and Its Rings at 39 Microns I. G. NOLT,*'1 W. M. SINTON,t L. J. CAROFF,~'1 E. F. ERICKSON,~'1 D . W . STRECKER,~ 1'2 AND J. V. RADOSTITZ *'1 *Department of Physics, University of Oregon, Eugene, Oregon 97.$03, ~[nstitute for Astronomy, University of Hawaii, Honolulu, Hawaii 968~2, and $NASA-Ames Research Center, Moffett Field, California 9~035 Received M a y 10, 1976; revised October 5, 1976 We have resolved the relative rings-to-disk brightness (specific intensity) of Saturn a t 39 ~m (&X "~ 8 ~m) using the 224-cm telescope at M a u n a Kea Observatory, and have also measured the total flux of Saturn relative to Jupiter in the same bandpass from the NASA Learjet Observatory. These two measurements, which were made in early 1975 with Saturn's rings near maximum inclination (b' "~ 25°), determine the disk and average ring (A and B) brightness in terms of an absolute flux calibration of Jupiter in the same bandpass. While present uncertainties in Jupiter's absolute calibration make it impossible to compare existing measurements unambiguously, it is nevertheless possible to conclude the following: (1) observations between 20 and 40 ~m are all compatible (within 2or) of a disk brightness temperature of 94°K, and do not agree with the radiative equilibrium models of Trafton; (2) the rings at large tilt contribute a flux component comparable to t h a t of the planet itself for k ~< 40 ~m ; and (3) there is a decrease of ~ 2 2 % in the relative ring:disk brightness between effective wavelengths of 33.5 and 39 ~m. I. I N T R O D U C T I O N
Saturn's thermal emission, which peaks near 200 cm -I (k = 50 urn), can be readily observed from present-day airborne telescopes; however, the ring and disk components cannot be resolved beyond about 20 ~m because of the diffraction-limited resolution. On the other hand, while the spatial resolution is improved by the larger available aperture of ground-based telescopes, the intervening atmospheric absorption restricts observations to a few atmospheric windows. Given dry conditions at Mauna Kea Observatory (MKO elevation 13,800 ft or 4.2 km) it is possible to achieve measurable signal transmission 1 Guest Observer, M a u n a Kea Observatory, Institute for Astronomy, University of Hawaii. 2 N A S / N R C Resident Research Associate.
in the transmission tail of the 20 um window which extends to ~ 4 0 ~m. However, the low mean atmospheric transmission of a few percent makes absolute flux measurements difficult from ground-based measurements alone. In this study we have combined ground observations of the relative rings-to-disk brightness of Saturn with airborne calibration measurements. The result is medium resolution (Ak 8 ~m) measurements of the separate disk and rings thermal emission near 40 urn, with Jupiter serving as the primary calibration reference. The first direct measurement of Saturn's thermal emission was a broadband determination by Aumann et al. (1969) and yielded an effective temperature of 97 ± 4°K. The ring flux was assumed to be negligible based upon an indication at
747 Copyright O 1977 by Academic Press. Inc. All rights of reproduction in any form reserved.
ISSN 0019-1035
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NOLT E7' AL.
that time of a limiting ring brightness temperature of 60°K. While suhsequent measurements by Armstrong et al. (1972) gave a somewhat lower broadband brightness temperature than this, the ring contribution was no longer considered to be negligible. Unpublished evidence was cited for "m increase in ring brightness with the increasing Saturnicentrie declination angle during this epoch. By 1973 a definite consensus had developed in favor of a "large" particle ring model (Pollack et al., 1973; C.ook et al., 1973) and a likely change in ring temperature with tilt angle (Murphy, 1974). Thus any measurement of Saturn's thermal emission during the present epoch includes a significant and probably tiltdependent flux component. Progress in understanding Saturn's thermal properties re
Saturn flux for comparison to Jupiter's. Jupiter was chosen as a calibration source because of its availability and because its temperature is only slightly higher than Saturn's. Its ir spectrum has recently been measured in the region of interest (Erickson et al., 1976). Itowever, the absolute flux calibration of Jupiter is under critical review at the present time. In Section II we describe the aircraft observations and subsequent data analysis leading to our result for a total flux of Saturn referred to Jupiter. In Section III the ground-based results are described. These deal primarily with the determination of the relative ring and disk brightness, but also provide a secondary calibration check relative to the bright hmar limb. In Section IV we derive the brightness temperatures which fit the constraints of these new data. Finally, in Section V the results are discussed in relation to other d'~ta and to the present theoretical models for the atmosphere emission spectrum and the rings. II. AIRBORNE OBSEIIVATIONS As noted above, the airborne and ground-based observations were carried out wi~h the same detector-filter instrumentati
BRIGHTNESS TEMPERATURE
l i
FROM TELESCOPE--.._
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749
OF S A T U R N
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BLOCKING FILTER
(OPT,ONAL)
i ' I/
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\ \ \ \ \ \
FOCUSING MIRROR /
DETECTOR
KRS-5 WINDOW
BCIF 2 MIRROR
\ \ COLD APERTURE \ GOLDMESH YOSHINAGA
FIG. l. Schematic of filter-detector system. The filter consists of a 200-#m-thick Yoshinaga-type filter containing ZnO and A1203 in a black polyethylene matrix, and a 1000 lpi gold mesh. B o t h filter elements are behind the defining 1-mm-diameter focal plane aperture. In addition, as room temperature filter components there are the KRS-5 vacuum window, and a BaF2 reststrahlen mirror, plus the optional alkali halide "subtractive" filter to verify the spectral content of the signal.
The aircraft observations were made on February 10 and 12, 1975, from approximately 13.5 km (45,000 ft) aboard the Learjet observatory. Data were obtained on both Jupiter and Saturn during each flight at roughly equal elevations. The beam size of ~ 2 arcmin was greater than the diffraction-broadened angular sizes of both Jupiter and Saturn. The major contribution to noise was pointing error, and our analysis attempts to account for this, using the known value of sky plus system noise obtained during the sky scans. For sources such as Saturn and Jupiter which do not overfill the beam, errors in pointing always act in such a way as to reduce the signal. In addition, pointing fluctuations will occur on a time scale which is long when compared to the system response time ( ~ 1 0 0 msec), so that there will typically be stretches of data containing many points where the planet was accurately positioned in the diaphragm, stretches where the signal is definitely low, and transitional regions. However, rather than trusting to a technique where selections of "good d ata" were made by eye, the following
quantitative procedure was used. First, data which were obviously bad were removed. The remaining data were divided into bins, one for each individual right or left beam scan. In each of the bins we selected some fraction f with highest signal level. Let us assume initially that these points correspond to times when the noise due to pointing error was negligible compared to the other sources of noise. We then take the mean of these points to give the (uncorrected) signal level for that bin. Now, points chosen in this way will give too large a mean signal level since we have chosen data where the pointing fluctuations are negligible and where fluctuations from the sky plus system noise tend to increase the signal. In order to determine the size of the correction needed to give the proper mean, the same operation was performed on the sky runs. We first selected the top f points in a given sky run, calculated the mean, and found its deviation from the true mean (zero in this case). Averaging this value (of the deviation) over all the sky data gave the magnitude of the correction to be applied to the signal mean obtained from the
NOLT-ET AL.
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FIG. 2. Source spectra, system response, and atmosphere transmission used in defining the effective wavelengths of our measurements. In (a) the 90°K blackbody spectrum (dashed line) approximates the rings, and Trafton's model for a 95°K effective temperature (solid line) disk spectrum. Insert (b) is the measured relative response of the detector-filter system ; and (c) shows the atmosphere transmission as calculated by V. Kunde for Mauna Kea and the two indicated values of the total precipitable waler vapor. The same x-axis frequency scale applies to all three panels above. source. If unlimited integration time were available, it is clear t h a t the best choice of f would be to make it quite small. I n practice, if f is too small the statistical errors will be too large compared to the quality of data. If f is too large, then pointing errors will begin to dominate. B y plotting the mean signal level as a function of f, we determined t h a t the result was insensitive to f up to a value of ~0.1. I n our bandpass the observed signal ratio of S a t u r n : J u p i t e r was 0.164 =L 0.01 on F e b r u a r y 10 and 0.176 + 0 . 0 0 5 on F e b r u a r y 12. Here the errors reflect l z of the distribution of the means in each bill about the mean signal for each flight. The weighted average of the observed signal ratios for the two flights gives the total flux ratio of Saturn to Jupiter of RTOT
=
0.174 :k 0.006.
(1)
This ratio can be written as as~[Bsr~A + asaf[Bs('JA RTOT
,
(2)
where
[ B x ] . = [ Bx(v) tA(v)dv J and where J refers to Jupiter; S to S a t u r n ; d to Saturn's disk; r to Saturn's rings; A to observations from aircraft altitude; tA(v) is the combined transmission of the atmosphere (from Learjet altitude), filter, and detector system; Bx is the surface intensity of object x at the detector, in ergs sec 1 cm-2 sr-1 Hz-1; ~t is the solid angle subtended by the object, fU refers only to the unobscured ring; and v is the frequency. The factor ~" accounts for partial occultation of the disk by the rings and is given by ~" = [-~a,. + e-.r(0)fUl,offfUl,
BRIGHTNESS TEMPERATURE OF SATURN where the superscripts u and o refer to unocculted and occulted, respectively; and e-,r(°) is the m e a n transmission of the rings in the bandpass and along a direction 0 relative to the ring plane normal. Defining [tI~B~]A as the total emission f r o m S a t u r n (rings plus disk) incident on the telescope in the bandpass of the instrument, we can then write [nsBs-]A = RTOT~j['B~]A.
(3)
Here flj = 1.99 X 10 -8 sr for 11 F e b r u a r y 1975, and EB:3~ is calculated f r o m a knowledge of tA@) and the brightness t e m p e r a t u r e curve T~(v) for Jupiter. Specifically,
[B~JA
=/I~[TB(v),
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tA(~)dv
751
(5.7 4- 0.6) X 10 -'° ergs sec-' cm -~ sr -1,
-
(4) w h e r e / ~ ( T , v) is the radiation intensity of a b l a c k b o d y at t e m p e r a t u r e T and frequency v. The measured filter-detector response (Fig. 2b) was multiplied b y the atmospheric transmission, which was calculated as described b y Augason (1975) to obtain t , ( , ) ; u n c e r t a i n t y due to atmospheric effects in (4) is less t h a n 1%, because (4) applies only to Jupiter. Since the d a t a on S a t u r n and J u p i t e r were t a k e n within a few minutes of each other, and both at m e a n elevation angles of 25 °, it is unlikely t h a t atmospheric conditions along the line of sight were significantly different. T h e atmospheric transmission averaged over the bandpass was calculated to be in = 86%. A difference in aircraft altitude of 4-3000 feet is calculated to i m p l y a variation in [~ of +~:~%; this p r o b a b l y exceeds the u n c e r t a i n t y in atmospheric effects between the J u p i t e r and S a t u r n
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FIG. 3. It.aster scan geometry. This figure shows the three-line 40 X 60-arcsec raster pattern which was used to obtain the data shown in Fig. 4b. The defining cold aperture of l-ram diameter is shown projected to scale on the rings, disk, and sky positions; the latter two separated by the chopping distance. The data were recorded automatically in a step-integrate fashion for 24 equally spaced increments along each leg. Each three-line scan took ~ 2 rain to complete with an integration duty cycle of ~50%.
NOLT ET AL.
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(Erickson et al., 1976) in the shape of the brightness temperature curve. Wright (1976) has estimated that the brightness temperature of Armstrong et al. should be reduced by approximately 17°K. Thus, the absolute calibration of (5) m a y be high by as much as 22°K, considering the error quoted by Armstrong et al. Defining the effective wavelength as
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FIG. 4. Signal scans for a poin~ source and Saturn. Part (a) shows the instrumental beam profile observed for the pseudopoint source II/C 10216. In (b) we show the averaged result fron: 13 scans which were selected f()r I/A centering on the basis of their E-W ansa deflection symmetry and which have been shifted in declination a~ required to maximize the serial correlation coet[ieient. The quantity 1)(39) is the peak disk displacement, and A (39) the corresponding ansa value. Both east aIld west, ansa se.ul segments were (!olnhined here for a total of 26 scans in the ansae average. observations because of their (,,lose proximity in time and elevation angle. For TB(V) we have used TB(v) = 145 + (, -- 180)(0.14), 180 ~< , ~ 2 3 0 e m ', =
:5~
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230 ~< v ~< 3 5 0 c m ~. This continuum shape was obtained from a far-infrared spectrum of Jupiter (Erickson et al., 1976), which shows that rotation'd ammonia absorption do not strongly affect the present analysis. The spectrum was normalized to the 45- to 80-urn results of Armstrong et al. (1972). This T~(u) also corresponds well with the measurements of H o u c k et al. (1975). The error shown in (4) is an estimated standard deviation due to the measurement, uncertainty
gives for the airborne observations [-using tAts)I, v,,tV~ = 252 em -I or X,,fc~ = 39.7 #m. The passband for our airt)orne measurements is A~A = 50.8 cm -1, or A)~A ~ 8.1 #m. llI. 11EIATIVE RING AND DISK INTENSITY MEASUREMENTS A few weeks prior to the above measurements, a series of ground-based observations was made at M a u n a Kea Observatory (MKO) with sufficient spatial resolution to establish the relative ring and disk flux components. The 224-cm telescope at M K O provides a diameter of the first Airy dark ring of 8 arcsec at 39 tml. Moreover, the latitude and high altitude of this site permitted Saturn observations along an ideal zenith trajectory and through the shortest air path of any large telescope. Preliminary studies of atmospheric transmission beyond 30 t~m had established that under dry conditions useful measurements couhl be made at effective wavelengths approaching 40 t~nl (Nolt et al., 1973, 1974). Thus, this is the longest-wavelength window, short of the submillimeter windows that begin near 200 t~m, which is available for groundbased observations, and the observed extinction properties are therefore of general interest. The 39 #m measurements were ot)tained on 25/26 and 27,/28 J a n u a r y 1975; the extinction was 0.84 and 0.79 mag (air mass)-~, respectively, if fit, in the conven-
753
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NOLT E T AL.
tional way to a linear dependence in air mass. [-For the intervening night of 26/27 January, the 20-gm extinction was 0.33 mag (air mass)-1. -] A root air mass dependence, which is implied by a random line model (Goody, 1952), is found to give a better fit to the signal variation on both nights over the measured range of one to two air masses. B y this model the zenith extinction was 1.9 and 2.1 mag, respectively. These values correspond to ~ 1 5 % transmission, which agrees reasonally well with the atmosphere spectral characteristics shown in Fig. 2c. The same detector-filter system discussed in Section II was used with the M K O infrared photometer. The maximum p h o t o m e t e r chopping amplitude of 15", which is achieved by a translating-mirror chopper, made equatorial drift scans impractical. Instead we used the computercontrolled raster scan procedure, illustrated in Fig. 3, which allowed the centering to be established in both dimensions. Inasmuch as the beam profile was only partly filled b y the A and B rings, we chose the cusp of Cassini's division as a fiducial point for the ring reading. The distance between the two outer raster segmen*s was set t,) match the distance between the ansae of Cassini's division. The centering of the raster and the separation of its line segments were monitored closely through a dichroic mirror eyepiece. The general seeing was ~--0.5" and it was possible frequently to see the actual bifurcation of Cassini's division ( ~ 0 . 5 " ) by the cross hairs on both outer scan segments. This confirmed the accurate scan generation by the computer control. In the final analysis we selected a subset of scans (13 out of 22 total) which showed no significant a s y m m e t r y in the two ansae signal deflections. B y comparing the computed change in peak ansa deflection per arc second of lateral displacement (~--10%) to the single scan ansae a s y m m e t r y (generally less t h a n the ~ 5 % noise limit of
a single scan), we feel that the standard centering error was less than 0.5" for the selected set of scans. The centering or registration in the orthogonal scan direction, which is less critical, was fixed by computing the maximally correlated average deflection segments for the disk and ring. Figure 4 shows the beam profile and source deflections. From the signal displacements defined here, we obtain a relative rings:disk signal ratio of R~ = A / D = 0.45 ± 0.02.
(7)
The signal ratio establishes the relative brightness (specific intensity) ratio of the rings to disk after a correction is made for the different effective source solid angles subtended at the two positions. An experimental measurement of the solid angle correction factor was made b y measuring the 20 **m signal by the same procedure that we employed at 39 gm and using established 20-gm rings and disk brightnesses, all of which are summarized in Table I. Using the results of M u r p h y (1973) and Rieke (1975), we calculate brightness ratios for the average A, B-ring intensity (our aperture subtends essentially equal A- and B-ring areas) to the disk center of 0.83 and 0.81, respectively. Since tile measured 20 pm signal ratio determined analogously to the result by (7) is 0. 53 ± 0.01, we conclude t h a t the filled fraction of the aperture 1)y the ring at 20 gm was 65 4-2(70. At an ef: feetive wavelength of 39 ~m, the t)eam filling factor becomes 63 ± 2%, if we allow for + , ~)/cC / further reduction due to diffraction at this longer wavelength. This latter correction was computed by an exact model calculation of the Airy diffraction and geometrical factors involved. This same diffraction model calculation showed that 14% of the geometrically subtended A- and B-ring signal is lost from the aperture by diffraction. (l{adiation from the C ring, which lies just
BRIGHTNESS TEMPERATURE OF SATURN beyond the aperture edge and is not included in the computer model, could shift this value a few percent at most.) Furthermore, combining this model result with the geometrically filled aperture fraction subtended at the rings position of 68% provides a calculated effective beam filling fuctor for the rings position of 60 ± 2%. This agreement between model calculation and measurement of the filling factor correction is very satisfying. After making the correction based upon the above result, we arrive at the following rings:disk brightness ratio
BR~ =- [Bs~]~/[Bsd]G = (0.45 ± 0.02)/(0.63 -4- 0.02) = 0.71 ± 0.04, (8) where [ ]a is calculated using ta(v), the transmission function for the MKO observations. Again the quoted errors include the estimated dispersion (1~) of the data and uncertainty in the beam filling factor. Defining the effective wavelength as in (6) and using the transmission function tG(v) gives hetfG = 38.5 #m. No correction is necessary in the above analysis for scattered or diffracted disk radiation at the ansae position. Tests on each night showed no detectable signal (to within a few percent of the peak amplitude) at an aperture position 10 arcsec from the polar limb of the planet. This is consistent with the expected diffraction beam profile, and confirms the absence of any significant scattering by optical elements in front of the defining aperture. IV. BRIGHTNESS TEMPERATURES We now have two measurements of Saturn at a nominal wavelength of 39 #m: the average brightness of the combined A and B rings relative to the disk given by (8), and the ratio of system's total flux to that of Jupiter given by (2). Together, these two measurements determine the absolute intensities of the disk and the
755
rings relative to the absolute brightness of Jupiter at the same wavelength. In terms of arbitrary emission spectra, but assuming a uniform disk brightness, the simultaneous solution of (2) and (8) can be written as
FBa]A x
1 + (O~r/~O~)BR~(1 + C~)
,
(9)
where 1 + C~ = {EBs']a/EBsa]A} {[Bsd]~/ [Bs'JG} accounts for the slight difference in bandpass between the aircraft and ground-based observations. In order to solve this relationship we make the approximation Cx = 0 and assume the two spectra are Planckian over the bandpasses of our measurement. This leads to brightness temperatures for the rings and disk of 89 ± 2.5 and 98 ± 2.5°K, respectively, at a nominal (mean) wavelength of 39 t~m. From Table I we see that this brightness temperature of the rings implies temperatures approximately equal to those observed at ~ 2 0 and 33.5/~m. Such a result, of course, is quite consistent with the largeparticle ring model (Pollack et al., 1973; Cook et al., 1973) and would indicate that the rings radiate a Planckian spectrum to wavelengths >40 ~m. However, this conclusion concerning the rings is contingent upon the assumed Jupiter disk-average absolute brightness and its internal consistency with the absolute flux calibrations of the other measurements between 20 and 34/~m. The other groups' results rely upon stellar standards whose absolute flux calibration is not currently in question. Consequently, the reported equal disk and B-ring brightness temperature of 91 ± 2°K at 33.5 t~m, which is referred to a Tau for absolute calibration (Rieke, 1975), provides a significant reference point; any decrease of Jupiter's absolute calibration alone would affect only our result at 39 ~m
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NOLT ET' A L . I [
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FIG. 5. Thermal emissi(m spectrum of Saturn. The graph shows all the present mea~sureInents of Saturn's resolved disk emission between 20 and 40 gin. The syml)ols refer to the corresponding entries in Table I as follows: &, Murphy (1973); ®, Morrison (1974); 0 , Rieke (1975); O, Nolt et al. (1974); and e, this paper. Brightness temperature is plotted in (b), arid the corresponding outgoing (specific) intensity in (a); both versus frequency in wavenumber. The nominal fiher bandpass is shown by the horizontal bars. The uncertainty of the measurement is given by the vertical bar. In some cases the error is too slnall to be shown on this scale. These results are compared to blackbody spectra (dashed lines in upper figure), and Trafton's (1967) model atmosphere spectrum for an effective temperature of 99°K (solid line). For completeness, we also show the brightness temperatures and the flux equivalenls of the ring model corrected aircraft measurements as given by Rieke (1975), where lhe rectangles represent the range of the ring model (~ol're(.tions. •rod p r o d u c e "~ subse(tuent decrease in S a t u r n ' s ring brightness t e m p e r a t u r e over the relatively short f r e q u e n c y interval t)et w e e n the two filter b a n d s which are c e n t e r e d at 33.5 and 39 t~m. T h e conclusion of essentially c o n s t a n t ring brightness 1)etween 20 and 40 t~m t h u s couhl c h a n g e d e p e n d i n g u p o n t h e resolution ()f the present calibration (tuestion. F o r this same calil)ration, t h e disk brightness t e m p e r a t u r e results show an
increase with w a v e l e n g t h between 33.5 and 39 t~m of 91 ± 2 to 98 -4- 2.5°K, respectively. As Fig. 5 illustrates, a slightly s t r o n g e r g r a d i e n t in disk brightness t e m p e r a t u r e is shown by model a t m o s p h e r e calculations to result f r o m the c h a n g e in a t m o s p h e r i c o p a c i t y in m o v i n g f u r t h e r f r o m the S(0) line of H,z at 28 u m (Trafton, 1967). On the basis of this model we can examine how our brightness ternp e r a t u r e solution depends u p o n the unk n o w n source s p e c t r u m in the m e a s u r e d b a n d w i d t h which is reflected t h r o u g h t h e p a r a m e t e r Cx. F o r example, we h a v e ass u m e d T r a f t o n ' s model s p e c t r u m (for 9 5 ° K effective t e m p e r a t u r e ) for the disk emission and P l a n c k i a n b e h a v i o r for the rings (see Fig. 2a) and h a v e c o m p u t e d the r e s u l t a n t brightness t e m p e r a t u r e s . In this case, Cx = --0.13, and the resulting solution is "~ disk brightness t e m p e r a t u r e of ~ 9 9 ° K at 39.7 um ( = X,.ffA), ~ 9 6 O K at 38.5 #m ( = X,,f(;), and a m e a n ring brightness of 88°K. In other words a reasonable range of S a t u r n ' s spectral b e h a v i o r in our m e a s u r e d b a n d p a s s of a b o u t S u m centered at ~ 3 9 um implies an u n c e r t a i n t y of the order of ± I ° K between the limits of P l a n c k i a n and radiation-equilibrium model s p e c t r a for the disk emission. This uncertainty, which derives from the u n k n o w n source s p e c t r u m or, e
BRIGHTNESS TEMPERATURE OF SATURN This result for the disk at a wavelength of 38.5 zm is 93 q- 4°K. The ring-average brightness temperature is 85 ± 4°K in this case, which indicates, by comparison to other data in Table I, some inconclusive evidence for a small drop in ring brightness temperature with increasing wavelength. V. DISCUSSION AND CONCLUSIONS Table I summarizes all measurements between 20 and 39 ~m which separate the rings and disk flux components. With these measurements, we can compose low-resolution spectra of the rings and disk to about 39 ~m. In Fig. 5 we show the disk spectrum defined by the data assembled in Table I. We show as well the brightness values which Rieke (1975) has derived from aircraft measurements at longer wavelengths which do not resolve directly the ring and disk components. Thus Fig. 5 summarizes all present experimental measurements which provide some degree of spectral resolution of Saturn's thermal emission spectrum. Unfortunately, the absence of any common calibration reference for the measurements by the various groups introduces the uncertainties associated with the absolute calibration in each case. In particular, Wright (1976) has recently proposed a recalibration of Jupiter's infrared brightness temperature, which could reduce our brightness temperature values for Saturn at 39 ~m by as much as ~ 8 ° K . (The relative change in units of temperature between Jupiter and Saturn is approximately in the ratio of 2:1, respectively.) Such a large change in absolute flux calibration, without a corresponding change in the 33.5-~m result (Rieke, 1975), would effectively transform the unambiguous change in relative ring:disk brightness between 33.5 and 39 t~m into a changing ring brightness temperature. Also, in view of the present uncertainties of Jupiter's
757
absolute brightness at 40 ~m we can make no meaningful conclusions concerning the possible spectral structure associated with the 28-~m rotational feature of H~ (Trafton, 1967; T r a f t o n and Munch, 1969) in the 30- to 40-~m range. We can, however, state some definite conclusions regarding the comparison of the disk brightness and the class of radiative-equilibrium models over the 20- to 40-~m range. Since any downward adjustment in Jupiter's absolute flux can only worsen the existing disagreement, which is apparent in Fig. 5b, it is clear that this class of radiative-equilibrium models with zero-helium abundance (Trafton, 1967) does not agree with observation. While the results of Gautier and Grossman (1972) suggest that finite helium abundance may give better agreement as a consequence of a relative elevation of the 20-~m brightness, any significant change appears to require an unreasonably large helium abundance. A meaningful determination of the helium abundance, similar to that recently accomplished for Jupiter by Houck et al. (1975), apparently will require Saturn measurements of higher spectral resolution than yet available in order to obtain a satisfactory inversion for the unknown Saturnian temperature profile. (In the absence of a s-~tisfactory model atmosphere solution, Saturn's temperature profile must also be assumed to be unknown.) Even in the event that the disk brightness were to be reduced by 8°K, all the results between 20 and 40 ~m would still be within 2~ of 94°K. In view of the same calibration uncertainties, we can conclude little concerning the precise spectrum of the rings emission. It is clear that the rings contribute a significant thermal flux component during the present epoch of large ring tilt. Indeed, at 40 ~m the total flux component of the rings currently is approximately equal to that of the planet itself
758
NOLT ET AL.
in E a r t h - b a s e d o b s e r v a t i o n s . C o n s e q u e n t l y , c o r r e c t i o n s for t h e r i n g flux c o n t a m i n a t i o n will c e r t a i n l y h a v e t o be c o n s i d e r e d in a n y E a r t h - b a s e d s p e c t r a l m e a s u r e m e n t s of t h e t h e r m a l e m i s s i o n w h i c h do n o t i s o l a t e t h e d i s k c o m p o n e n t , or o c c u r d u r i n g t h e s h o r t p e r i o d of " e d g e - o n " r i n g p r o j e c t i o n in 1980. A s e c o n d r e s u l t for t h e rings w h i c h is i n d e p e n d e n t of a b s o l u t e c a l i b r a t i o n concerns t h e r e l a t i v e r i n g : d i s k b r i g h t n e s s as a f u n c t i o n of w a v e l e n g t h . T h e r e is c l e a r l y a d e c r e a s e in t h e b r i g h t n e s s of t h e rings r e l a t i v e t o t h e d i s k ; t h e m e a s u r e m e n t s of R i e k e (1975) i m p l y a v a l u e of ~ 0 . 9 0 a t 33.5 # m in c o n t r a s t to t h e a v e r a g e r i n g : d i s k r a t i o of 0.71 :t: 0.04 a t 39 ~m g i v e n b y (8) a b o v e . T h e r e still r e m a i n s t h e q u e s t i o n of h o w the rings' brightness varies with the S a t u r n i c e n t r i e l a t i t u d e of t h e S u n (B'). All t h e m i d i n f r a r e d m e a s u r e m e n t s , as s u m m a r i z e d in T a b l e I, were m a d e o v e r a v e r y s m a l l c h a n g e of t i l t angle a n d so a d d l i t t l e information beyond the picture presented b y M u r p h y (1974) a n d , m o r e r e e e n t l y , b y K a w a t a a n d h ' v i n e (1975). I n t h i s conn e c t i o n it is i m p o r t a n t t o n o t e t h e poss i b i l i t y t h a t 45-#m r a d i o m e t r i c r i n g m e a s u r e m e n t s f r o m t h e P i o n e e r 11 S a t u r n p a s s a g e in S e p t e m b e r 1979 c o u l d p r o v i d e t h e c r i t i c a l r i n g e d g e - o n d a t u m (B' ~-e 5 °) for c o m p a r i s o n t o t h e p r e s e n t b a s e l i n e d a t a for l a r g e tilt. T h e r i n g b r i g h t n e s s c h a n g e a t 40 ~,m for i n t e r m e d i a t e t i l t c o u l d b e s t be o b t a i n e d b y r e p e a t i n g t h e M a u n a K e a m e a s u r e m e n t in 1976-1977, before t h e r i n g p r o j e c t i o n is t o o s m a l l for a c c u r a t e measurement. ACKNOWLEDGMENTS Many people contributed to the success of this effort as it ew)lved over the past 5 years. We appreciate helpful contributions from and discussions with R. M. Cameron, l~. J. l)(mnelly, H. C. Ford, J. T. Jefferies, V. Kunde, R. E. Murphy, L. M. Trafton, and F. C. Witteborn. We also are most grateful to the staff at MKO for their excellent hospitality and assistance, and to the
Airborne Science Office and, particularly, the Learjet flight crew for their vital contributions to the success of the airborne observations. We also would like to thank J. V. Harwood and J. S. Gibbons for their talented programming assistance, and Greg Buck for programming and technical assistance throughout the program. This work was supported in part by NASA Grant NGR 39-003-034. REFERENCES
ARMSTRONG,K. R., HARPER, l). A., Jr., AND LOW, F. J. (1972). Far-infrared brightness temperatures of the planets. Astrophys. J. 178, L89-L92. AUGASON, G. C., ~'IoRD, A. J., WITTEBORN, F. C., ERICKSON, E. F., SWIFT, C. D., C:kROFF, L.J., ANn KUNZ, L. W. (1975). Water vapor absorption spectra of the upper atmosphere (45-185 cm 1). Appl. Opt. 14, 2146-2150. AUMANN, H. H., (~ILLESPIE, C. M., JR., AND Low, F. J, (1969). The internal powers and effective temperatures of Jupiter and Saturn. Astrophys. J. 157, L69-L72. COOK, A. F., FRANKLIN, F. A., AND PALLUCONI, F. I). (1973). Saturn's Rings. Icarus 18, 317-337. ERICKSON, n. F., STRECKER, ]). W., GOORVITCIt, I)., SIMPSON, J. P., SCAnGLE, J. D., CAROFF, L. J., AND WITTEBORN, F. C. (1976). Spectra of Venus and Jupiter from 28 to 120 microns. To be published. (~AUT1ER, l)., AND (}ROSSMAN, K. (1972). A new method f()r the determination of the mixing ratio hydrogen to helium in the giant planets. J. Atmos. Sci. 29, 788-792. GEOFFR1ON, A. R., KORNER, ~{., ~kNI) SINTON, W. M. (1960). Isothermal contours of the Moon. Lowell Obs. Bull. 5, 1-15. GooDY, R. M. (1952). A statistical model for water-vapor absorption. Quart. J. Roy. Met. Soc. 78, 165-169 HOUCK, J. R., POLLACK,J. B., SCHAAK,l)., REED, R. A., AND S(;MMERS, A. (1975). Jupiter: Its infrared spectrum from 16 to 40 microns. Science 189, 720-722. K:
BRIGHTNESS TEMPERATURE OF SATURN NOLT, I. G., RADOSTITZ~J. V., AND DONNELLY, R. J. (1973). 35 micron photometry: Filter design and atmosphere transmission data. Publ. Astron. Soc. Pacific 85, 535. NOLT, I. G., RADOSTITZ,J. V., DONNELLY, R. J., MURPHY, R. E., AND FORD, H. C. (1974). Thermal emission of Saturn's Rings and disk at 34 microns. Nature 248, 659-660. PALLUCONI, F. D., AND PETTENGILL, G. H. (Eds.) (1974). The Rings of Saturn. NASA SP-343. POLLACK, J. B., SUMMERS, A., AND BALDWIN, B. (1973). Estimates of the size of the particles in
759
the Rings of Saturn and their cosmogonic implications. Icarus 20, 263-278. RIEKE, G. H. (1975). The thermal radiation of Saturn and Its Rings. Icarus 26, 37-44. TRAFTON, L. M. (1967). Model atmospheres of the major planets. Astrophys. J. 147, 765-781. TRAVrON, L. M., AND MUNCH, (~. (1969). The structure of the atmospheres of the major planets. J. Atmos. Sci. 26, 813-825. WRmHT, E. L. (1976). Recalibration of the farinfrared brightness temperatures of the planets. Astrophys. J. 210, 250-253.
The Brightness Temperatures of Saturn and Its Rings at 39 Microns I. G. NOLT,*'1 W. M. SINTON,t L. J. CAROFF,~'1 E. F. ERICKSON,~'1 D . W . STRECKER,~ 1'2 AND J. V. RADOSTITZ *'1 *Department of Physics, University of Oregon, Eugene, Oregon 97.$03, ~[nstitute for Astronomy, University of Hawaii, Honolulu, Hawaii 968~2, and $NASA-Ames Research Center, Moffett Field, California 9~035 Received M a y 10, 1976; revised October 5, 1976 We have resolved the relative rings-to-disk brightness (specific intensity) of Saturn a t 39 ~m (&X "~ 8 ~m) using the 224-cm telescope at M a u n a Kea Observatory, and have also measured the total flux of Saturn relative to Jupiter in the same bandpass from the NASA Learjet Observatory. These two measurements, which were made in early 1975 with Saturn's rings near maximum inclination (b' "~ 25°), determine the disk and average ring (A and B) brightness in terms of an absolute flux calibration of Jupiter in the same bandpass. While present uncertainties in Jupiter's absolute calibration make it impossible to compare existing measurements unambiguously, it is nevertheless possible to conclude the following: (1) observations between 20 and 40 ~m are all compatible (within 2or) of a disk brightness temperature of 94°K, and do not agree with the radiative equilibrium models of Trafton; (2) the rings at large tilt contribute a flux component comparable to t h a t of the planet itself for k ~< 40 ~m ; and (3) there is a decrease of ~ 2 2 % in the relative ring:disk brightness between effective wavelengths of 33.5 and 39 ~m. I. I N T R O D U C T I O N
Saturn's thermal emission, which peaks near 200 cm -I (k = 50 urn), can be readily observed from present-day airborne telescopes; however, the ring and disk components cannot be resolved beyond about 20 ~m because of the diffraction-limited resolution. On the other hand, while the spatial resolution is improved by the larger available aperture of ground-based telescopes, the intervening atmospheric absorption restricts observations to a few atmospheric windows. Given dry conditions at Mauna Kea Observatory (MKO elevation 13,800 ft or 4.2 km) it is possible to achieve measurable signal transmission 1 Guest Observer, M a u n a Kea Observatory, Institute for Astronomy, University of Hawaii. 2 N A S / N R C Resident Research Associate.
in the transmission tail of the 20 um window which extends to ~ 4 0 ~m. However, the low mean atmospheric transmission of a few percent makes absolute flux measurements difficult from ground-based measurements alone. In this study we have combined ground observations of the relative rings-to-disk brightness of Saturn with airborne calibration measurements. The result is medium resolution (Ak 8 ~m) measurements of the separate disk and rings thermal emission near 40 urn, with Jupiter serving as the primary calibration reference. The first direct measurement of Saturn's thermal emission was a broadband determination by Aumann et al. (1969) and yielded an effective temperature of 97 ± 4°K. The ring flux was assumed to be negligible based upon an indication at
747 Copyright O 1977 by Academic Press. Inc. All rights of reproduction in any form reserved.
ISSN 0019-1035
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NOLT E7' AL.
that time of a limiting ring brightness temperature of 60°K. While suhsequent measurements by Armstrong et al. (1972) gave a somewhat lower broadband brightness temperature than this, the ring contribution was no longer considered to be negligible. Unpublished evidence was cited for "m increase in ring brightness with the increasing Saturnicentrie declination angle during this epoch. By 1973 a definite consensus had developed in favor of a "large" particle ring model (Pollack et al., 1973; C.ook et al., 1973) and a likely change in ring temperature with tilt angle (Murphy, 1974). Thus any measurement of Saturn's thermal emission during the present epoch includes a significant and probably tiltdependent flux component. Progress in understanding Saturn's thermal properties re
Saturn flux for comparison to Jupiter's. Jupiter was chosen as a calibration source because of its availability and because its temperature is only slightly higher than Saturn's. Its ir spectrum has recently been measured in the region of interest (Erickson et al., 1976). Itowever, the absolute flux calibration of Jupiter is under critical review at the present time. In Section II we describe the aircraft observations and subsequent data analysis leading to our result for a total flux of Saturn referred to Jupiter. In Section III the ground-based results are described. These deal primarily with the determination of the relative ring and disk brightness, but also provide a secondary calibration check relative to the bright hmar limb. In Section IV we derive the brightness temperatures which fit the constraints of these new data. Finally, in Section V the results are discussed in relation to other d'~ta and to the present theoretical models for the atmosphere emission spectrum and the rings. II. AIRBORNE OBSEIIVATIONS As noted above, the airborne and ground-based observations were carried out wi~h the same detector-filter instrumentati
BRIGHTNESS TEMPERATURE
l i
FROM TELESCOPE--.._
•/•.• /~
749
OF S A T U R N
HELIUMBATH I
BLOCKING FILTER
(OPT,ONAL)
i ' I/
/ /
/
/ /
\ \ \ \ \ \
FOCUSING MIRROR /
DETECTOR
KRS-5 WINDOW
BCIF 2 MIRROR
\ \ COLD APERTURE \ GOLDMESH YOSHINAGA
FIG. l. Schematic of filter-detector system. The filter consists of a 200-#m-thick Yoshinaga-type filter containing ZnO and A1203 in a black polyethylene matrix, and a 1000 lpi gold mesh. B o t h filter elements are behind the defining 1-mm-diameter focal plane aperture. In addition, as room temperature filter components there are the KRS-5 vacuum window, and a BaF2 reststrahlen mirror, plus the optional alkali halide "subtractive" filter to verify the spectral content of the signal.
The aircraft observations were made on February 10 and 12, 1975, from approximately 13.5 km (45,000 ft) aboard the Learjet observatory. Data were obtained on both Jupiter and Saturn during each flight at roughly equal elevations. The beam size of ~ 2 arcmin was greater than the diffraction-broadened angular sizes of both Jupiter and Saturn. The major contribution to noise was pointing error, and our analysis attempts to account for this, using the known value of sky plus system noise obtained during the sky scans. For sources such as Saturn and Jupiter which do not overfill the beam, errors in pointing always act in such a way as to reduce the signal. In addition, pointing fluctuations will occur on a time scale which is long when compared to the system response time ( ~ 1 0 0 msec), so that there will typically be stretches of data containing many points where the planet was accurately positioned in the diaphragm, stretches where the signal is definitely low, and transitional regions. However, rather than trusting to a technique where selections of "good d ata" were made by eye, the following
quantitative procedure was used. First, data which were obviously bad were removed. The remaining data were divided into bins, one for each individual right or left beam scan. In each of the bins we selected some fraction f with highest signal level. Let us assume initially that these points correspond to times when the noise due to pointing error was negligible compared to the other sources of noise. We then take the mean of these points to give the (uncorrected) signal level for that bin. Now, points chosen in this way will give too large a mean signal level since we have chosen data where the pointing fluctuations are negligible and where fluctuations from the sky plus system noise tend to increase the signal. In order to determine the size of the correction needed to give the proper mean, the same operation was performed on the sky runs. We first selected the top f points in a given sky run, calculated the mean, and found its deviation from the true mean (zero in this case). Averaging this value (of the deviation) over all the sky data gave the magnitude of the correction to be applied to the signal mean obtained from the
NOLT-ET AL.
750
50
T
CM
F o
2 "
40
WAVELENGTH, ~ m 55 25
....\
20
---
90K
--
95K MODEL
17
BLACK-BODY
g (1) O
b
Ca)
,
"2o II 1.0
1.0
i
I
.... ~ - - -
I-
I0
Z 0
w C12 w T O69 O
6") Z < IZ: I1
I1
--
0.5 mm ,
200
500 400 500 WAVENUMBER, c m -t
H20
__0 600
FIG. 2. Source spectra, system response, and atmosphere transmission used in defining the effective wavelengths of our measurements. In (a) the 90°K blackbody spectrum (dashed line) approximates the rings, and Trafton's model for a 95°K effective temperature (solid line) disk spectrum. Insert (b) is the measured relative response of the detector-filter system ; and (c) shows the atmosphere transmission as calculated by V. Kunde for Mauna Kea and the two indicated values of the total precipitable waler vapor. The same x-axis frequency scale applies to all three panels above. source. If unlimited integration time were available, it is clear t h a t the best choice of f would be to make it quite small. I n practice, if f is too small the statistical errors will be too large compared to the quality of data. If f is too large, then pointing errors will begin to dominate. B y plotting the mean signal level as a function of f, we determined t h a t the result was insensitive to f up to a value of ~0.1. I n our bandpass the observed signal ratio of S a t u r n : J u p i t e r was 0.164 =L 0.01 on F e b r u a r y 10 and 0.176 + 0 . 0 0 5 on F e b r u a r y 12. Here the errors reflect l z of the distribution of the means in each bill about the mean signal for each flight. The weighted average of the observed signal ratios for the two flights gives the total flux ratio of Saturn to Jupiter of RTOT
=
0.174 :k 0.006.
(1)
This ratio can be written as as~[Bsr~A + asaf[Bs('JA RTOT
,
(2)
where
[ B x ] . = [ Bx(v) tA(v)dv J and where J refers to Jupiter; S to S a t u r n ; d to Saturn's disk; r to Saturn's rings; A to observations from aircraft altitude; tA(v) is the combined transmission of the atmosphere (from Learjet altitude), filter, and detector system; Bx is the surface intensity of object x at the detector, in ergs sec 1 cm-2 sr-1 Hz-1; ~t is the solid angle subtended by the object, fU refers only to the unobscured ring; and v is the frequency. The factor ~" accounts for partial occultation of the disk by the rings and is given by ~" = [-~a,. + e-.r(0)fUl,offfUl,
BRIGHTNESS TEMPERATURE OF SATURN where the superscripts u and o refer to unocculted and occulted, respectively; and e-,r(°) is the m e a n transmission of the rings in the bandpass and along a direction 0 relative to the ring plane normal. Defining [tI~B~]A as the total emission f r o m S a t u r n (rings plus disk) incident on the telescope in the bandpass of the instrument, we can then write [nsBs-]A = RTOT~j['B~]A.
(3)
Here flj = 1.99 X 10 -8 sr for 11 F e b r u a r y 1975, and EB:3~ is calculated f r o m a knowledge of tA@) and the brightness t e m p e r a t u r e curve T~(v) for Jupiter. Specifically,
[B~JA
=/I~[TB(v),
3a(v)dv/f
tA(~)dv
751
(5.7 4- 0.6) X 10 -'° ergs sec-' cm -~ sr -1,
-
(4) w h e r e / ~ ( T , v) is the radiation intensity of a b l a c k b o d y at t e m p e r a t u r e T and frequency v. The measured filter-detector response (Fig. 2b) was multiplied b y the atmospheric transmission, which was calculated as described b y Augason (1975) to obtain t , ( , ) ; u n c e r t a i n t y due to atmospheric effects in (4) is less t h a n 1%, because (4) applies only to Jupiter. Since the d a t a on S a t u r n and J u p i t e r were t a k e n within a few minutes of each other, and both at m e a n elevation angles of 25 °, it is unlikely t h a t atmospheric conditions along the line of sight were significantly different. T h e atmospheric transmission averaged over the bandpass was calculated to be in = 86%. A difference in aircraft altitude of 4-3000 feet is calculated to i m p l y a variation in [~ of +~:~%; this p r o b a b l y exceeds the u n c e r t a i n t y in atmospheric effects between the J u p i t e r and S a t u r n
et al.
N ~" ~" 6".6
1 / /
I0
/ \ I+)
"
--
\1 /
t (+} \ /
T
FIG. 3. It.aster scan geometry. This figure shows the three-line 40 X 60-arcsec raster pattern which was used to obtain the data shown in Fig. 4b. The defining cold aperture of l-ram diameter is shown projected to scale on the rings, disk, and sky positions; the latter two separated by the chopping distance. The data were recorded automatically in a step-integrate fashion for 24 equally spaced increments along each leg. Each three-line scan took ~ 2 rain to complete with an integration duty cycle of ~50%.
NOLT ET AL.
752
(Q)
/ / / ~
POINTSOURCE
(Erickson et al., 1976) in the shape of the brightness temperature curve. Wright (1976) has estimated that the brightness temperature of Armstrong et al. should be reduced by approximately 17°K. Thus, the absolute calibration of (5) m a y be high by as much as 22°K, considering the error quoted by Armstrong et al. Defining the effective wavelength as
X~.-:-
~ff=
/
~t(v)dv
/f
t(~)dv
(6)
A39 I ....
1_
!
__I
--30"
1
[
d
+30"
0
FIG. 4. Signal scans for a poin~ source and Saturn. Part (a) shows the instrumental beam profile observed for the pseudopoint source II/C 10216. In (b) we show the averaged result fron: 13 scans which were selected f()r I/A centering on the basis of their E-W ansa deflection symmetry and which have been shifted in declination a~ required to maximize the serial correlation coet[ieient. The quantity 1)(39) is the peak disk displacement, and A (39) the corresponding ansa value. Both east aIld west, ansa se.ul segments were (!olnhined here for a total of 26 scans in the ansae average. observations because of their (,,lose proximity in time and elevation angle. For TB(V) we have used TB(v) = 145 + (, -- 180)(0.14), 180 ~< , ~ 2 3 0 e m ', =
:5~
--
(~ --
(5)
'-)30)(0.22),
230 ~< v ~< 3 5 0 c m ~. This continuum shape was obtained from a far-infrared spectrum of Jupiter (Erickson et al., 1976), which shows that rotation'd ammonia absorption do not strongly affect the present analysis. The spectrum was normalized to the 45- to 80-urn results of Armstrong et al. (1972). This T~(u) also corresponds well with the measurements of H o u c k et al. (1975). The error shown in (4) is an estimated standard deviation due to the measurement, uncertainty
gives for the airborne observations [-using tAts)I, v,,tV~ = 252 em -I or X,,fc~ = 39.7 #m. The passband for our airt)orne measurements is A~A = 50.8 cm -1, or A)~A ~ 8.1 #m. llI. 11EIATIVE RING AND DISK INTENSITY MEASUREMENTS A few weeks prior to the above measurements, a series of ground-based observations was made at M a u n a Kea Observatory (MKO) with sufficient spatial resolution to establish the relative ring and disk flux components. The 224-cm telescope at M K O provides a diameter of the first Airy dark ring of 8 arcsec at 39 tml. Moreover, the latitude and high altitude of this site permitted Saturn observations along an ideal zenith trajectory and through the shortest air path of any large telescope. Preliminary studies of atmospheric transmission beyond 30 t~m had established that under dry conditions useful measurements couhl be made at effective wavelengths approaching 40 t~nl (Nolt et al., 1973, 1974). Thus, this is the longest-wavelength window, short of the submillimeter windows that begin near 200 t~m, which is available for groundbased observations, and the observed extinction properties are therefore of general interest. The 39 #m measurements were ot)tained on 25/26 and 27,/28 J a n u a r y 1975; the extinction was 0.84 and 0.79 mag (air mass)-~, respectively, if fit, in the conven-
753
BRIGHTNESS TEMPERATURE OF SATURN
Cr~
O4 ~9
¢9
°°
~
¢9
¢D
0
"~
oO
°
°
d
I
I ~d d d
~
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c'q aS
E~
~
1
~ 1
~
E~
"E
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.o ~-~
O
L~
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o
754
NOLT E T AL.
tional way to a linear dependence in air mass. [-For the intervening night of 26/27 January, the 20-gm extinction was 0.33 mag (air mass)-1. -] A root air mass dependence, which is implied by a random line model (Goody, 1952), is found to give a better fit to the signal variation on both nights over the measured range of one to two air masses. B y this model the zenith extinction was 1.9 and 2.1 mag, respectively. These values correspond to ~ 1 5 % transmission, which agrees reasonally well with the atmosphere spectral characteristics shown in Fig. 2c. The same detector-filter system discussed in Section II was used with the M K O infrared photometer. The maximum p h o t o m e t e r chopping amplitude of 15", which is achieved by a translating-mirror chopper, made equatorial drift scans impractical. Instead we used the computercontrolled raster scan procedure, illustrated in Fig. 3, which allowed the centering to be established in both dimensions. Inasmuch as the beam profile was only partly filled b y the A and B rings, we chose the cusp of Cassini's division as a fiducial point for the ring reading. The distance between the two outer raster segmen*s was set t,) match the distance between the ansae of Cassini's division. The centering of the raster and the separation of its line segments were monitored closely through a dichroic mirror eyepiece. The general seeing was ~--0.5" and it was possible frequently to see the actual bifurcation of Cassini's division ( ~ 0 . 5 " ) by the cross hairs on both outer scan segments. This confirmed the accurate scan generation by the computer control. In the final analysis we selected a subset of scans (13 out of 22 total) which showed no significant a s y m m e t r y in the two ansae signal deflections. B y comparing the computed change in peak ansa deflection per arc second of lateral displacement (~--10%) to the single scan ansae a s y m m e t r y (generally less t h a n the ~ 5 % noise limit of
a single scan), we feel that the standard centering error was less than 0.5" for the selected set of scans. The centering or registration in the orthogonal scan direction, which is less critical, was fixed by computing the maximally correlated average deflection segments for the disk and ring. Figure 4 shows the beam profile and source deflections. From the signal displacements defined here, we obtain a relative rings:disk signal ratio of R~ = A / D = 0.45 ± 0.02.
(7)
The signal ratio establishes the relative brightness (specific intensity) ratio of the rings to disk after a correction is made for the different effective source solid angles subtended at the two positions. An experimental measurement of the solid angle correction factor was made b y measuring the 20 **m signal by the same procedure that we employed at 39 gm and using established 20-gm rings and disk brightnesses, all of which are summarized in Table I. Using the results of M u r p h y (1973) and Rieke (1975), we calculate brightness ratios for the average A, B-ring intensity (our aperture subtends essentially equal A- and B-ring areas) to the disk center of 0.83 and 0.81, respectively. Since tile measured 20 pm signal ratio determined analogously to the result by (7) is 0. 53 ± 0.01, we conclude t h a t the filled fraction of the aperture 1)y the ring at 20 gm was 65 4-2(70. At an ef: feetive wavelength of 39 ~m, the t)eam filling factor becomes 63 ± 2%, if we allow for + , ~)/cC / further reduction due to diffraction at this longer wavelength. This latter correction was computed by an exact model calculation of the Airy diffraction and geometrical factors involved. This same diffraction model calculation showed that 14% of the geometrically subtended A- and B-ring signal is lost from the aperture by diffraction. (l{adiation from the C ring, which lies just
BRIGHTNESS TEMPERATURE OF SATURN beyond the aperture edge and is not included in the computer model, could shift this value a few percent at most.) Furthermore, combining this model result with the geometrically filled aperture fraction subtended at the rings position of 68% provides a calculated effective beam filling fuctor for the rings position of 60 ± 2%. This agreement between model calculation and measurement of the filling factor correction is very satisfying. After making the correction based upon the above result, we arrive at the following rings:disk brightness ratio
BR~ =- [Bs~]~/[Bsd]G = (0.45 ± 0.02)/(0.63 -4- 0.02) = 0.71 ± 0.04, (8) where [ ]a is calculated using ta(v), the transmission function for the MKO observations. Again the quoted errors include the estimated dispersion (1~) of the data and uncertainty in the beam filling factor. Defining the effective wavelength as in (6) and using the transmission function tG(v) gives hetfG = 38.5 #m. No correction is necessary in the above analysis for scattered or diffracted disk radiation at the ansae position. Tests on each night showed no detectable signal (to within a few percent of the peak amplitude) at an aperture position 10 arcsec from the polar limb of the planet. This is consistent with the expected diffraction beam profile, and confirms the absence of any significant scattering by optical elements in front of the defining aperture. IV. BRIGHTNESS TEMPERATURES We now have two measurements of Saturn at a nominal wavelength of 39 #m: the average brightness of the combined A and B rings relative to the disk given by (8), and the ratio of system's total flux to that of Jupiter given by (2). Together, these two measurements determine the absolute intensities of the disk and the
755
rings relative to the absolute brightness of Jupiter at the same wavelength. In terms of arbitrary emission spectra, but assuming a uniform disk brightness, the simultaneous solution of (2) and (8) can be written as
FBa]A x
1 + (O~r/~O~)BR~(1 + C~)
,
(9)
where 1 + C~ = {EBs']a/EBsa]A} {[Bsd]~/ [Bs'JG} accounts for the slight difference in bandpass between the aircraft and ground-based observations. In order to solve this relationship we make the approximation Cx = 0 and assume the two spectra are Planckian over the bandpasses of our measurement. This leads to brightness temperatures for the rings and disk of 89 ± 2.5 and 98 ± 2.5°K, respectively, at a nominal (mean) wavelength of 39 t~m. From Table I we see that this brightness temperature of the rings implies temperatures approximately equal to those observed at ~ 2 0 and 33.5/~m. Such a result, of course, is quite consistent with the largeparticle ring model (Pollack et al., 1973; Cook et al., 1973) and would indicate that the rings radiate a Planckian spectrum to wavelengths >40 ~m. However, this conclusion concerning the rings is contingent upon the assumed Jupiter disk-average absolute brightness and its internal consistency with the absolute flux calibrations of the other measurements between 20 and 34/~m. The other groups' results rely upon stellar standards whose absolute flux calibration is not currently in question. Consequently, the reported equal disk and B-ring brightness temperature of 91 ± 2°K at 33.5 t~m, which is referred to a Tau for absolute calibration (Rieke, 1975), provides a significant reference point; any decrease of Jupiter's absolute calibration alone would affect only our result at 39 ~m
75(i
NOLT ET' A L . I [
~ I00
WAVELENGTH, ,u. 5040 50 25
20
5
~
(a)
C
:
/'
i
..
(b)
"140 o
17
120
ea I00 80 I00
200
500
400
500
600
WAVENUMBER, c m -I
FIG. 5. Thermal emissi(m spectrum of Saturn. The graph shows all the present mea~sureInents of Saturn's resolved disk emission between 20 and 40 gin. The syml)ols refer to the corresponding entries in Table I as follows: &, Murphy (1973); ®, Morrison (1974); 0 , Rieke (1975); O, Nolt et al. (1974); and e, this paper. Brightness temperature is plotted in (b), arid the corresponding outgoing (specific) intensity in (a); both versus frequency in wavenumber. The nominal fiher bandpass is shown by the horizontal bars. The uncertainty of the measurement is given by the vertical bar. In some cases the error is too slnall to be shown on this scale. These results are compared to blackbody spectra (dashed lines in upper figure), and Trafton's (1967) model atmosphere spectrum for an effective temperature of 99°K (solid line). For completeness, we also show the brightness temperatures and the flux equivalenls of the ring model corrected aircraft measurements as given by Rieke (1975), where lhe rectangles represent the range of the ring model (~ol're(.tions. •rod p r o d u c e "~ subse(tuent decrease in S a t u r n ' s ring brightness t e m p e r a t u r e over the relatively short f r e q u e n c y interval t)et w e e n the two filter b a n d s which are c e n t e r e d at 33.5 and 39 t~m. T h e conclusion of essentially c o n s t a n t ring brightness 1)etween 20 and 40 t~m t h u s couhl c h a n g e d e p e n d i n g u p o n t h e resolution ()f the present calibration (tuestion. F o r this same calil)ration, t h e disk brightness t e m p e r a t u r e results show an
increase with w a v e l e n g t h between 33.5 and 39 t~m of 91 ± 2 to 98 -4- 2.5°K, respectively. As Fig. 5 illustrates, a slightly s t r o n g e r g r a d i e n t in disk brightness t e m p e r a t u r e is shown by model a t m o s p h e r e calculations to result f r o m the c h a n g e in a t m o s p h e r i c o p a c i t y in m o v i n g f u r t h e r f r o m the S(0) line of H,z at 28 u m (Trafton, 1967). On the basis of this model we can examine how our brightness ternp e r a t u r e solution depends u p o n the unk n o w n source s p e c t r u m in the m e a s u r e d b a n d w i d t h which is reflected t h r o u g h t h e p a r a m e t e r Cx. F o r example, we h a v e ass u m e d T r a f t o n ' s model s p e c t r u m (for 9 5 ° K effective t e m p e r a t u r e ) for the disk emission and P l a n c k i a n b e h a v i o r for the rings (see Fig. 2a) and h a v e c o m p u t e d the r e s u l t a n t brightness t e m p e r a t u r e s . In this case, Cx = --0.13, and the resulting solution is "~ disk brightness t e m p e r a t u r e of ~ 9 9 ° K at 39.7 um ( = X,.ffA), ~ 9 6 O K at 38.5 #m ( = X,,f(;), and a m e a n ring brightness of 88°K. In other words a reasonable range of S a t u r n ' s spectral b e h a v i o r in our m e a s u r e d b a n d p a s s of a b o u t S u m centered at ~ 3 9 um implies an u n c e r t a i n t y of the order of ± I ° K between the limits of P l a n c k i a n and radiation-equilibrium model s p e c t r a for the disk emission. This uncertainty, which derives from the u n k n o w n source s p e c t r u m or, e
BRIGHTNESS TEMPERATURE OF SATURN This result for the disk at a wavelength of 38.5 zm is 93 q- 4°K. The ring-average brightness temperature is 85 ± 4°K in this case, which indicates, by comparison to other data in Table I, some inconclusive evidence for a small drop in ring brightness temperature with increasing wavelength. V. DISCUSSION AND CONCLUSIONS Table I summarizes all measurements between 20 and 39 ~m which separate the rings and disk flux components. With these measurements, we can compose low-resolution spectra of the rings and disk to about 39 ~m. In Fig. 5 we show the disk spectrum defined by the data assembled in Table I. We show as well the brightness values which Rieke (1975) has derived from aircraft measurements at longer wavelengths which do not resolve directly the ring and disk components. Thus Fig. 5 summarizes all present experimental measurements which provide some degree of spectral resolution of Saturn's thermal emission spectrum. Unfortunately, the absence of any common calibration reference for the measurements by the various groups introduces the uncertainties associated with the absolute calibration in each case. In particular, Wright (1976) has recently proposed a recalibration of Jupiter's infrared brightness temperature, which could reduce our brightness temperature values for Saturn at 39 ~m by as much as ~ 8 ° K . (The relative change in units of temperature between Jupiter and Saturn is approximately in the ratio of 2:1, respectively.) Such a large change in absolute flux calibration, without a corresponding change in the 33.5-~m result (Rieke, 1975), would effectively transform the unambiguous change in relative ring:disk brightness between 33.5 and 39 t~m into a changing ring brightness temperature. Also, in view of the present uncertainties of Jupiter's
757
absolute brightness at 40 ~m we can make no meaningful conclusions concerning the possible spectral structure associated with the 28-~m rotational feature of H~ (Trafton, 1967; T r a f t o n and Munch, 1969) in the 30- to 40-~m range. We can, however, state some definite conclusions regarding the comparison of the disk brightness and the class of radiative-equilibrium models over the 20- to 40-~m range. Since any downward adjustment in Jupiter's absolute flux can only worsen the existing disagreement, which is apparent in Fig. 5b, it is clear that this class of radiative-equilibrium models with zero-helium abundance (Trafton, 1967) does not agree with observation. While the results of Gautier and Grossman (1972) suggest that finite helium abundance may give better agreement as a consequence of a relative elevation of the 20-~m brightness, any significant change appears to require an unreasonably large helium abundance. A meaningful determination of the helium abundance, similar to that recently accomplished for Jupiter by Houck et al. (1975), apparently will require Saturn measurements of higher spectral resolution than yet available in order to obtain a satisfactory inversion for the unknown Saturnian temperature profile. (In the absence of a s-~tisfactory model atmosphere solution, Saturn's temperature profile must also be assumed to be unknown.) Even in the event that the disk brightness were to be reduced by 8°K, all the results between 20 and 40 ~m would still be within 2~ of 94°K. In view of the same calibration uncertainties, we can conclude little concerning the precise spectrum of the rings emission. It is clear that the rings contribute a significant thermal flux component during the present epoch of large ring tilt. Indeed, at 40 ~m the total flux component of the rings currently is approximately equal to that of the planet itself
758
NOLT ET AL.
in E a r t h - b a s e d o b s e r v a t i o n s . C o n s e q u e n t l y , c o r r e c t i o n s for t h e r i n g flux c o n t a m i n a t i o n will c e r t a i n l y h a v e t o be c o n s i d e r e d in a n y E a r t h - b a s e d s p e c t r a l m e a s u r e m e n t s of t h e t h e r m a l e m i s s i o n w h i c h do n o t i s o l a t e t h e d i s k c o m p o n e n t , or o c c u r d u r i n g t h e s h o r t p e r i o d of " e d g e - o n " r i n g p r o j e c t i o n in 1980. A s e c o n d r e s u l t for t h e rings w h i c h is i n d e p e n d e n t of a b s o l u t e c a l i b r a t i o n concerns t h e r e l a t i v e r i n g : d i s k b r i g h t n e s s as a f u n c t i o n of w a v e l e n g t h . T h e r e is c l e a r l y a d e c r e a s e in t h e b r i g h t n e s s of t h e rings r e l a t i v e t o t h e d i s k ; t h e m e a s u r e m e n t s of R i e k e (1975) i m p l y a v a l u e of ~ 0 . 9 0 a t 33.5 # m in c o n t r a s t to t h e a v e r a g e r i n g : d i s k r a t i o of 0.71 :t: 0.04 a t 39 ~m g i v e n b y (8) a b o v e . T h e r e still r e m a i n s t h e q u e s t i o n of h o w the rings' brightness varies with the S a t u r n i c e n t r i e l a t i t u d e of t h e S u n (B'). All t h e m i d i n f r a r e d m e a s u r e m e n t s , as s u m m a r i z e d in T a b l e I, were m a d e o v e r a v e r y s m a l l c h a n g e of t i l t angle a n d so a d d l i t t l e information beyond the picture presented b y M u r p h y (1974) a n d , m o r e r e e e n t l y , b y K a w a t a a n d h ' v i n e (1975). I n t h i s conn e c t i o n it is i m p o r t a n t t o n o t e t h e poss i b i l i t y t h a t 45-#m r a d i o m e t r i c r i n g m e a s u r e m e n t s f r o m t h e P i o n e e r 11 S a t u r n p a s s a g e in S e p t e m b e r 1979 c o u l d p r o v i d e t h e c r i t i c a l r i n g e d g e - o n d a t u m (B' ~-e 5 °) for c o m p a r i s o n t o t h e p r e s e n t b a s e l i n e d a t a for l a r g e tilt. T h e r i n g b r i g h t n e s s c h a n g e a t 40 ~,m for i n t e r m e d i a t e t i l t c o u l d b e s t be o b t a i n e d b y r e p e a t i n g t h e M a u n a K e a m e a s u r e m e n t in 1976-1977, before t h e r i n g p r o j e c t i o n is t o o s m a l l for a c c u r a t e measurement. ACKNOWLEDGMENTS Many people contributed to the success of this effort as it ew)lved over the past 5 years. We appreciate helpful contributions from and discussions with R. M. Cameron, l~. J. l)(mnelly, H. C. Ford, J. T. Jefferies, V. Kunde, R. E. Murphy, L. M. Trafton, and F. C. Witteborn. We also are most grateful to the staff at MKO for their excellent hospitality and assistance, and to the
Airborne Science Office and, particularly, the Learjet flight crew for their vital contributions to the success of the airborne observations. We also would like to thank J. V. Harwood and J. S. Gibbons for their talented programming assistance, and Greg Buck for programming and technical assistance throughout the program. This work was supported in part by NASA Grant NGR 39-003-034. REFERENCES
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the Rings of Saturn and their cosmogonic implications. Icarus 20, 263-278. RIEKE, G. H. (1975). The thermal radiation of Saturn and Its Rings. Icarus 26, 37-44. TRAFTON, L. M. (1967). Model atmospheres of the major planets. Astrophys. J. 147, 765-781. TRAVrON, L. M., AND MUNCH, (~. (1969). The structure of the atmospheres of the major planets. J. Atmos. Sci. 26, 813-825. WRmHT, E. L. (1976). Recalibration of the farinfrared brightness temperatures of the planets. Astrophys. J. 210, 250-253.