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The 15 August 1980 occultation by the Uranian system: Structure of the rings and temperature of the upper atmosphere
ICARUS 52, 454-472 (1982)
The 15 August 1980 Occultation by the Uranian System" Structure of the Rings and Temperature of the Upper Atmosphere 1 B. SICARDY AND M. COMBES Observatoire de Paris, 92190 Meudon, France
A. B R A H I C Universitd de Paris VII et Observatoire de Paris, 92190 Meudon, France
P. B O U C H E T AND C. PERRIER European Southern Observatory, La Silla, Chile AND
R. COURTIN LPSP 91370 Verrieres le Buisson, France Received F e b r u a r y 22, 1982; revised A u g u s t 3, 1982 A stellar occultation by U r a n u s and its rings was o b s e r v e d on A u g u s t 15, 1980, from the European Southern O b s e r v a t o r y (Chile), at the 3.6-m telescope equipped with an infrared (2.2 Ixm) photometer. The recording presents the best signal-to-noise ratio obtained since the discovery of the Uranian rings in March 1977. The nine rings were observed, and the profiles o f f i n g s a , 13, and were resolved, the ring a exhibiting a double structure. Strong diffraction peaks are visible in the ring profile suggesting an opaque ring with very sharp edges. A broad and faint structure e x t e n d s outward from the rl ring, on a radial scale of about 55 km. Apart from the ring occultations, unexplained sharp and deep e v e n t s were recorded, and no interpretation is possible until future observations are made. F u r t h e r m o r e , the stellar light curve during the immersion of the star behind the planet provides (via an inversion computation) the temperature profile of the upper a t m o s p h e r e of U r a n u s . The temperature is close to 145 -+ 10°K at the 3 × 10-2-mbar pressure level and is nearly constant (155 - 15°K) in the pressure interval from 10 -~ to 10 3 mbar. The thermal inversion is as strong as the inversion on N e p t u n e but is located at higher altitudes. This high stratospheric temperature is consistent with the upper limit of the brightness temperature at 8 p.m only if CH4 follows its saturation law.
ing ring segment, which in turn allows a kinematic model of the system to be derived (when all the data from different occultation observations are collected). Since their discovery on 10 March 1977 (Elliot et al., 1977a; Millis et al., 1977; Bhattacharyya and Kuppuswamy, 1977), the systematic observation of occultations (Elliott et al., 1978; Millis and Wasserman, 1978; Nicholson et al., 1978; Elliot et al., 1981a; Nicholson et al., 1981; Elliot et al., 1981b) showed that seven out of nine rings now identified fit elliptical orbits in uniform pre-
I. I N T R O D U C T I O N
The observation of a stellar occultation by the Uranian system is interesting for two reasons. First, it provides an opportunity to observe Uranus' rings at high resolution, and second, it allows us to probe the upper Uranian atmosphere. The occultation by the ring system provides the precise locations of each occult1 Based on observations collected at the E u r o p e a n Southern Observatory, La Silla, Chile. 454 0019-1035/82/120454-19502.00/0 Copyright @ 1982by AcademicPress, Inc. All fightsof reproduction in any form reserved.
15 AUGUST 1980 OCCULTATION BY URANUS
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cession, the other two being circular. If confinement, why do the ~qand 8 rings (and only due to the oblateness of the planet the possibly others) exhibit a " b r o a d " (-50 precession rate may provide the values of km) and diffuse component in addition to the zonal harmonic coefficients J2 and J4 of the narrow and dense component? (iv) Why Uranus' gravity potential. These coeffi- does the profile of the e ring present the cients give some information about the inte- same structure in the different parts of the rior of the planet (Elliot et al., 1981b). ring's orbit in spite of its variations of On the other hand, the occultation pro- width, and how may this structure be stafiles are presently the best probes of the ble? Possible answers involving self-gravidensity distribution inside the rings, be- tation in the rings or tidal torque exchange cause of their high resolution (about 2 km). between a ring and satellites orbiting close The Uranian ring system was quite surpris- to its edges have been proposed by ing when discovered because it raised, and Goldreich and Tremaine (1979, 1980). still raises, unanswered questions, such as: The observed structures are complex, (i) How the rings may be so confined (eight and they are linked to fundamental quesof them are a few kilometers wide, the ninth tions such as the origin, the evolution, and being a few tens of kilometers wide), with the stability of rings, the accretion mechavery sharp edges? Without any external nisms, and the formation of the solar sysconstraint, a system of colliding particles tem. So far, the only way to find out the orbiting around a central massive body whole structure of the Uranian rings is to spreads radially under the effects of differ- observe as many occultations as possible, ential rotation and collision. (ii) Why are each of them providing a "scan" of the ring some of the rings locked in precession as a system (Fig. 1). whole without being disrupted by differenOn the other hand, the star was also octial precession? (iii) In spite of this strong culted by the upper atmosphere of the
I 1" I
N
l
10 I I*kmI 08,16,80
08/15180
0~0
/ ??-0~0
~ W
FIG. 1. The path of the star KM 12 relative to the Uranian system. The dashed line represents interruptions of observations due to "synchronization stops" (see text) or passage of clouds.
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SICARDY ET AL.
planet: the stellar light curve during immersion, or emersion, is the result of differential bending of starlight, due to the gradient of refractivity in the Uranian atmosphere. An inversion computation developed by Vapillon et al. (1973) gives, from the stellar light curve, the refractivity profile and the temperature profile of the upper atmosphere. The result is a constraint for the models describing deeper regions of Uranus' atmosphere. Uranus is very different from the other giant planets in various respects: its internal energy source, if it exists, is small in magnitude; the general atmospheric circulation and seasonal pattern are expected to depend on the position of the rotation axis of the planet; in contrast with the other giant planets, Uranus does not exhibit any emission of molecular species in the infrared; and furthermore, the results of the 1977 occultation (Dunham et al., 1980) seemed to indicate that Uranus' stratosphere was colder than those of the other giant planets. The occultation experiment is expected to provide new data on the structure and composition of the upper atmosphere. In this paper, we will present the first results derived from the 15 August 1980 occultation, observed from the European Southern Observatory (ESO) at La Silla, Chile, with the 3.6-m telescope. One should note that this occultation was unique compared with previous ones because of its high signal-to-noise ratio, relative to previous observations, and because it was observed simultaneously from three stations close to each other [Cerro Las Campanas Observatory (CLCO), which lies 30 km north of ESO, and Cerro Tololo Inter American Observatory (CTIO), 100 km south of ESO]. A comparison between the three observations, in view of the good signal-to-noise ratio, allows without doubt the identification of faint and broad, or fine and narrow, structures in the rings. It is also possible to compare the light curve during immersion or emersion in the planetary atmosphere;
this light curve presents numerous strong and short spikes due to inhomogeneities in the atmosphere. The correlation of these spikes when observed from one station or another is a critical test for the understanding of the structure of the Uranian upper atmosphere. The comparison of ring profiles and temperature profiles will be published in subsequent papers (French et al., 1982; Elliot et al., 1982). Section II describes our observations, Section III the results related to the rings, and Section IV presents the results concerning the atmosphere of Uranus. II. OBSERVATIONS
Uranus and its ring system occulted the star KM 12 [star number 12 on the list of Klemola and Marsden (1977)] on the night from 15 to 16 August, 1980. We observed this phenomenon with the ESO infrared photometer/spectrophotometer attached to the 3.60 telescope (La Silla, Chile), equipped with an InSb photovoltaic detector cooled at 63°K. In order to increase the contrast between the star and the planet, an infrared filter (K band, h = 2.2 p.m, Ah = 0.5 p~m) corresponding to a methane band was used. In that way the contribution of the planet and its rings was about 35 times weaker than the total flux (star + planet + rings). Thus the signal-to-noise was significantly increased by comparison with previously observed stellar occultations by Uranus. The star was centered in a 7.5-arcsec diaphragm and the chopping frequency was 20 Hz, with an amplitude of 20 arcsec. The signal was traced in real time on a strip chart and was simultaneously recorded on a magnetic tape with the same sample step of 0.1 sec. The effective total time constant of the recording system was 0.1 sec. The diaphragm of the photometer had a diameter of 7.5 arcsec, and the response of the receptor decreased significantly when the star was moved by about 1.5 arcsec from the center of the aperture. The geometry of the occultation is shown in Fig. 1, and the interruptions of observa-
15 AUGUST 1980 OCCULTATION BY URANUS tion are indicated on the path of the star KM 12. Some of these interruptions are due to passages of cirrus. The others come from electronic problems: every l0 sec, a cesium clock controlled the UT recorded on the tape and some of these synchronizations could not be made immediately, which led to these "synchronization stops." The paths of the star as observed from CLCO and CTIO are indistinguishable
457
from the line traced in Fig. l, considering the scale of the sketch. During the first part of observation, i.e., before the immersion of the star behind the planet (the Sun was then still in the sky), the telescope was guided so that the signal was maximum. This procedure, however, led to some variations of the signal caused by decenterings (see Fig. 2). During this part of the observation, transitory passages of cirrus caused
PRE-IMMERSION
0
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S
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0
200
400
600
1000
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seconds after
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200
400
600
800
FIG. 2. A general view of the nine ring occultations. The sudden increase of flux during preimmersion occultation by ring ot is due to a recentering of the star in the diaphragm. The very high noise observed during preimmersion occultations by the rings is due to passages of cirrus (it was then still daylight). The variations in the flux observed during postemersion are seeing effects. Note the presence of two supplementary events (a and b) and the diffraction peaks associated with the ~/ ring occultation (especially in the preimmersion recording).
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SICARDY ET AL.
very high noise, the last passage occuring at 21 : 52 UT, as visible in Fig. 2. It prevented the observation of the preimmersion occultation of the ring e. All the other ring occultations were observed thereafter. After the immersion of the star KM 12 behind the planet's disk (the Sun was set then), the telescope was monitored by a guide-probe. The seeing was good and the guiding star did not suffer displacements greater than 1 arcsec. Thus the variations of signal detected during postemersion occultations (see Fig. 2) cannot be artifacts caused by decenterings, as occurred during the preimmersion observations. Most of these variations are probably due to clouds which modified the transparency of the sky. The immersion of the star in the atmosphere of Uranus was clearly observed, with, however, some possible guiding problems due to the procedure described above (signal maximum in the diaphragm). The emersion light curve is not usable because the star was not centered in the diaphragm when it reappeared. III. RING OCCULTATIONS Figure 2 gives a general view of the nine ring occultations (preimmersion and postemersion). A comparison with previous recordings shows the quality of the signal-tonoise ratio of the 15 Aug. 1980 occultation (this ratio was better for postemersion events because the Sun was set then). Also visible in Fig. 2 are two of the six isolated events reported by Bouchet et al. (1980) from the original ESO observation. Figure 3 presents the detailed profiles of identified rings, the time step of 0.1 sec corresponding to a radial distance (in the plane of the rings) of 0.82 and 0.84 km for preimmersion and postemersion events, respectively. Table I lists the mid-times, the durations (i.e., the full-width at half-maximum, FWHM), the fractional depths, and the projected (i.e., in the sky-plane, not the ringplane) apparent widths corresponding to each duration. For the value of the radial velocity of the star in the sky-plane, we
took 7.4 and 7.5 km/sec, for preimmersion and postemersion events, respectively. The uncertainty in the durations is 0.1 sec, i.e., -0.7 km for the projected apparent widths. The fractional depths given in Table I do not take into account that part of the flux due to the planet. During the ring occultations, this part of the flux represented less than 1% of the total flux. Thus subtracting the contribution of the planet would increase the fractional depths of Table I by less than 1%, which is negligible here. The main cause of error comes from the noise in the data, which varies from one ring to the other, so that error bars have been attributed to each fractional depth in Table I. Besides, the mid-times do not take into account the time constant of the demodulator, and each of them must be corrected by about -0.1 sec to obtain the actual midtimes. We will now consider some of the properties of the rings inferred from the occultation profiles. Qualitative results are given here and quantitative properties, together with more theoretical interpretations, will be considered in a subsequent paper. Rings 6, 5, 4. The projected apparent widths (FWHM) of these rings are comparable to the minimum apparent width allowed by the diffraction pattern: as shown by Elliot et al. (1981a) and by Nicholson et al. (1982a), when the actual projected width of a ring is smaller than roughly 2 kin, then the apparent width (FWHM) becomes constant. At h -- 2.2 ixm, for Uranus at D = 18.8 AU from the Earth, and for a stellar diameter reduced to Uranus' distance of 1.8 km, the value of this constant is about 3 km. This is the minimum apparent width (FWHM) that can be obtained in an occultation profile. In this situation, the apparent fractional depth of the profile decreases not only with the optical depth "r of the ring, but also with its actual width W. It is interesting to note that the profile of ring 5 is significantly deeper at postemersion than at preimmersion (Fig. 3). This may indicate that the occulting segment is
15 AUGUST 1980 OCCULTATION BY URANUS
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FIG. 3. T h e d e t a i l e d p r o f i l e s o f t h e n i n e o c c u l t a t i o n s . T h e t i m e s t e p o f 0.1 s e c r e p r e s e n t s a r a d i a l d i s t a n c e o f 0 . 8 2 a n d 0 . 8 4 k m in t h e p l a n e o f t h e r i n g s f o r p r e i m m e r s i o n a n d p o s t e m e r s i o n p r o f i l e s , respectively. The intervals between the thick marks represent 1 sec.
wider and/or more opaque at postemersion than at preimmersion. As previously shown by Elliot et al. (1981a) and Nicholson et al. (1982a), some elliptical rings present a variation of width with radius (the rings or, 13, and ~). It is therefore quite possible that azimuthal variations of width and optical depth exist in ring 5 since its eccentricity (e = 1.77 x 10 -3) lies between the eccentricities o f the ot and ~ rings [e = 0.72 x 10 -3 and e = 7.92 x
10 -3, respectively, see Elliot et al. (1981b)]. Observations at shorter wavelength with smaller stars would be needed to show these variations in ring 5. R i n g et. Unlike rings 6, 5, and 4, the et ring is resolved in postemersion profiles. In the case where the apparent width of a ring is greater than 5 km, the fractional depth of the profile is a function of the apparent optical depth "ca only (i.e., it is not affected by diffraction effects and the finite size of the
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SICARDY ET AL. TABLE I
Ring
Immersion 15 August 1980 (UT)
Emersion 16 August 1980 (UT)
Duration (sec) i
6 5 4 c~ I~ "q -/ e
22:11 : 16.85 22 : 10 : 21.22 22:09:50.5 22:05:25.28 22:03:27.4 22:00:23.3 21 : 59 : 28.75 21:58:07.25 --
00:45:58.4 00 : 46 : 50.42 00:47:31.32 00:51:51.8 00:53:42.45 00:56:41.75 00 : 57 : 35.5 00:58:55.6 01:04:45.1
0.5 0.5 0.4 0.55 0.8 0.4 0.5 0.5 --
Fractional depth
e
0.4 0.45 0.45 1.2 1.5 0.5 0.6 0.5 8.0
i
0.22 0.35 0.29 0.74 0.53 0.16 0.53 0.70
- 0.02 -+ 0.02 +- 0.015 - 0.005 -+ 0.015 -+ 0.02 -+ 0.015 -+ 0.01 --
Projected width, FWHM e
0.24 0.46 0.35 0.60 0.30 0.25 0.90 0.71 0.97
-+ 0.015 - 0.01 -+ 0.015 -+ 0.001 -+ 0.01 - 0.015 +- 0.005 -+ 0.01 +-- 0.005
(km) i
e
3.7 3.7 2.9 4.0 5.9 2.9 3.7 3.7 --
3.4 3.4 3.4 9.0 11.2 3.7 4.5 3.7 60
N o t e . These times do n o t take into account the time c o n s t a n t of the re c e pt or (0.1 sec).
star). This fractional depth is simply given by 1 - e -~a. We report in Table II the apparent radial width of resolved rings, as well as their normal optical depth ~-,. r. is given by • , = % sin B, B being the inclination of the Earth above the ring plane. Here sin B = 0.90. For postemersion segments of ring a, we obtained an apparent radial width of 10.1 km and "r, = 0.82. Furthermore, one should note that an "irregular" structure is visible in the postemersion profile (Fig. 3) of ring a. This structure was anticipated by Hubbard and Zellner (1980), and is also well identified on postemersion profiles given by Elliot et al. (1981b) and by Nicholson et al. (1982a). This may be due to the presence of a density fluctuation, or more probably to the presence of two ringlets instead of one as T A B L E II Ring
N o r m a l optical depth
Radial width, FWHM (km) i
e
6.6
10.0 12.6 67.5
i
e
0.68 --- 0.03
0.82 -+ 0.03 0.32 -+ 0.01 ->3
previously thought. The distance between the two ringlets, for the segment observed at postemersion, would be 4.2 km. Because of the eccentricity of ring a, this distance would vary along the ring, and the two components would be too close to each other in the preimmersion profile to be separated. Like ring e (Nicholson et al., 1978) and ring 13 (Elliot et al., 1981a), ring oL has a width/radius relation. This relation is well represented by a linear fit for the 13 and e rings, but this fit is not so satisfactory for ring a because the dispersion of points is higher (Nicholson et al., 1982a). The presence of two ringlets in ring a may explain the scattering of widths around a linear fit. As shown by Goldreich and Tremaine (1979), precessing models of elliptical rings, whose widths vary linearly with radius, may be understood in terms of self-gravity in the ring. On the other hand, the "splitting" of ring ot into two components could be explained by the presence of a small satellite (inside the ring) which could have produced a gap. The presence of this satellite might also explain the p o o r e r agreement concerning the linear relation width versus radius in the case of ring or. Ring 13. Just as for ring a, both occulting segments of ring 13 can be resolved. The
15 AUGUST 1980 OCCULTATION BY URANUS apparent radial widths and normal optical depths of these segments are given in Table II. This ring presents a smooth profile, with no significant "irregularities." Ring 0. This ring is not resolved, and is quite similar to rings 6, 5, and 4 described above. On the other hand, one of the most interesting results of the 15 August 1980 occultation was the clear confirmation of a broad component associated with the narrow component of ring -q. This broad component is described below. Ring ~1. The low speed of the ring shadow ( - 8 km/sec) and the signal-to-noise ratio of the observations allowed the unambiguous detection of diffraction peaks caused by the sharp edges of ring ~. The highest peak in the preimmersion profile (Figs. 2 and 3) represents 22% of the total flux, whereas it is reduced to 12% in the postemersion profile. Note also that the postemersion profile is significantly deeper and wider than the preimmersion profile (Fig. 3 and Table I). A postemersion profile has been synthesized by Nicholson et al. (1982a), who described the ring ~/ as an opaque strip with a projected width of 3 km. The first diffraction peaks, which may represent 40% or more of the total flux, are smoothed by the following effects: the finite size of stellar disk (whose diameter was estimated to be 1.8 km) and the time constant of the receptor (0.1 sec). The greater diffraction peaks observed in the preimmersion profiles may be interpreted in several ways: the width of the preimmersion segment may correspond to a particular value for which the peaks are enhanced, or, more likely, the star's diameter has been overestimated so that the smoothing effect is less important than initially thought. In any case, it is quite interesting to note that the ring ~/, which is circular (Elliot et al., 1981b), seems to present azimuthal variations of width and/or optical depth. R i n g 8. Both preimmersion and postemersion profiles are relatively noisy. The
461
fractional depth and the width of ring 8 make it similar to ring -/, apart from the fact that diffraction peaks are not visible. This absence of peaks must be due in part to a broad component located in the inner part of ring 8, with a projected width of about 15 km (Elliot et al., 1981b; Nicholson et al., 1982a). This broad component is not visible on our profiles because of the noise in the data. Ring ~. The widest of Uranus' rings was observed only at postemersion because of the passage of clouds during the preimmersion occultation. The edges of this ring are sharp, as indicated by the diffraction peaks. As pointed out by Nicholson et al. (1978), the width of ring e is a linear function of its radius. The new data from the present occultation confirm this property (Nicholson et al., 1982a). Furthermore, the fine structures of ring • are identical to those shown by Nicholson et al. (1978), relative to 10 March 1977 and to 10 April 1978. This confirms that ring ~ precesses as a whole, with no distortion due to differential precession on a scale of a few years. Note that the deepest part of ring reaches a fractional depth of 97%, indicating the presence of a nearly opaque component. Broad components. Another consequence of the good signal-to-noise ratio was the detection of a broad component associated with the narrow component of ring -q. In preimmersion and postemersion profiles (Fig. 4), the broad ring is delimited at its outer edge by a small feature (with a fractional depth of 10%) located at 56 and 55 km from the narrow component (which is circular), respectively. It is quite interesting to note that the broad component does not seem to have the same shape and the same location relative to the narrow component on preimmersion and postemersion profiles. This should be viewed as only a possibility, considering the higher noise of preimmersion data; further observations are needed to confirm this variation of position and shape of the broad component.
462
SICARDY ET AL.
.9
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22:11:21.9
22:00:28.3
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"6 -
00:56:36.8
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FIG. 4. The broad components of ring r I (right). Note the small component (cross) at the edge of the broad component. The latter does not seem to have the same shape and location on the preimmersion and postemersion profiles. On the left, features indicating the possible presence of broad and diffuse components associated with ring 6. Time interval between tick marks is 10 sec.
On the other hand, there seems to be some rapid variation of optical depth in the broad component, on a scale of 100 km or so. The typical optical depth of the broad component as observed from CLCO is 0.03 (Nicholson et al., 1982a) versus 0.07 for ESO observations ( - 3 0 km from CLCO) and 0.1 for CTIO profiles [-135 km from CLCO, see Elliot et al. (1980)]. We suspect the presence of other broad structures close to ring 6 (Fig. 4), but they are not confirmed by other teams and should await further observations. I s o l a t e d events. Apart from the identified ring occultations, we observed isolated events (Bouchet et al., 1980) which are not correlated with isolated events detected at CLCO and CTIO (Elliot, Matthews, private communications). This rules out the possibility of occultations by supplementary rings, or by satellites larger than 100 km. Similar isolated events were observed during previous observations (Millis and Wasserman, 1978; Hubbard and Zellner, 1980). The majority of the events are due to seeing effects. For instance, in our data the signal sometimes decreases on a time scale of about 10 sec, with a drop of 20%, and then
increases again, the minimum exhibiting a sharp and deep drop in signal. Such an event is likely to be due to a rapid decentering of the star caused by scintillation. Although the diaphragm of the photometer had a diameter of 7.5 arcsec, the response of the receptor decreased significantly when the star was moved by about 1.5 arcsec from the center of the aperture. However, for the events listed in Table III the surrounding signal is not noisy, and the drops are sharp and deep (Fig. 5), which makes their interpretation more difficult. These events are interesting in themselves T A B L E III Event
Time 16 August 1980 (UT a)
Duration (sec)
Fractional depth
a b c d e f
00:59:56.1 01:01 : 54.25 01 : 46 : 30.4 02 : 01 : 27.85 02 : 05 : 55.0 02 : 06 : 59.45
0.25 0.3 0.45 1.7 0.4 0.5
0.29 0.30 0.30 0.58 0.27 0.24
a These times do n o t take into account the time constant of the receptor (0.1 sec).
15 AUGUST 1980 OCCULTATION BY URANUS , f , , , , , , , f
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d 02:01:27.9
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FIG. 5, The profiles of six isolated events, o b s e r v e d during the postemersion part of the occultation (see Table III). The steps on the time axis c o r r e s p o n d s to 1 sec.
because they are not yet explained, and their origin should be clarified to avoid some ambiguities with other " r e a l " events. An observation with two telescopes close to each other (a few hundreds of meters) is now needed to provide a better understanding of their cause. In conclusion, the occultation of the star KM 12 by Uranus' rings was important for a better knowledge of the density profiles of the rings (owing to the good signal-to-noise ratio and the low speed of the star relative to Uranus). In addition, the data of 15/16 August 1980 allowed an improvement in the kinematic model describing the rings as precessing orbits (Elliot et al., 1981b). Three of nine ring profiles were resolved (or, 13, and e). Ring ot presents a double structure which may be caused by the presence of a gap inside the ring, ring 13exhibits a smooth structure, and ring Cs profile confirms the existence of a fixed structure (on a time scale of a few years). These conclusions are valid as long as the features considered are bigger than about 2 km (smaller details are smoothed by diffraction, the finite size of the stellar disk, and the time constant of the detector). The ring ~/occultation profile shows diffraction peaks, indi-
cating a narrow (3 km) opaque ring with very sharp edges. The difference in the height of peaks between preimmersion and postemersion profiles must be investigated. The narrow components contrast with the "broad" (a few tens of kilometers) and faint structures associated with rings -q and (and possibly 6). Other observations are needed to provide a better description of these broad structures, and also to find out the origin of some isolated events whose signature is not clearly different from the rings' signatures.
IV. T H E O C C U L T A T I O N BY T H E P L A N E T A R Y ATMOSPHERE
IV.1. The Occultation Light Curve
The occultation light curve is shown in Fig. 6. It is dominated by numerous spikes which are usually assumed to be due to small density fluctuations in the atmospheric structure. It may be noticed that in the first part of the curve, down to the midoccultation level, the drop of the flux was more rapid in the Dunham et al. (1980) data, considering the differences in the stellar velocity between the two occultations.
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SICARDY ET AL.
?,
absolute zero f[ux seconds after 2 2 : 3 6 , 1 7 UT 100
200
300
FIc. 6. The light curve during the immersion of the star behind the planet. The flux from Uranus has
not been removed from the curve shown here, so that the absolute zero flux is reached when no signal enters the photometer. Note the presence of numerous narrow and strong "spikes" due to small temperature inhomogeneities in Uranus' atmosphere. In contrast, light curves of the 15 August 1980 occultation recorded simultaneously at Las C a m p a n a s and Cerro Tololo observatories are very similar to the curve we obtained (French et a l . , 1982). So, from this first look, we see that the 15 August 1980 occultation leads to a value of the mean temperature that is higher than the value derived by D u n h a m et al. (1980).
IV.2. The Inversion Method
The inversion of occultation light curves is a well-known procedure. The method used for the present analysis is based upon the integral inversion o f the Abelian equation relating the refraction angle to to both the refractive index Ix and the altitude r0. ~ ( Po) = -
fi
' 2po • dlx
o Ix( r) . dr
[ ( r - Ix(r)) 2 - (r0" Ix(r0))2] -1/2 • dr,
(II.1)
where po is the impact p a r a m e t e r and ro the altitude of closest a p p r o a c h of a given starlight ray. The integral inversion of (II.1) leads to an explicit expression of the refractive index and of the altitude (Abelian integral):
Ix(ro) = exp
~ Jo
ro = po/ix(ro).
(11.2)
This method has already been used for the occultation of 13 Sco by Jupiter. For a detailed discussion the reader is referred to Vapillon et al. (1973) and C o m b e s et al. (1975). V e v e r k a et al. (1974) have used, for various stellar occultations by planets, a similar procedure improved by French et al. (1978). Briefly described, our method consists in using the observational data (i.e., the astrometric position of the star relative to Uranus and the occultation light curve) to derive the refraction angle o~(t) and the impact p a r a m e t e r p ( t ) versus time. This in turn allows Eq. (II.2) to be solved (this is the inversion properly speaking), leading to the determination of the atmospheric refractivity v(h) = Ix(h) - 1 as a function of the altitude h. The origin of the altitude h is usually chosen at the level where the drop of the stellar flux represents half of the full stellar flux ("half-light level"). F r o m the refractivity profile, one can deduce the num-
15 AUGUST 1980 OCCULTATION BY URANUS ber density versus altitude h and finally the vertical temperature profile T(h) through the hydrostatic equation
dT(h) T(h)
-
-
dr(h) v(h)
th g dh k T(h) '
(II.3)
where rh is the mean molecular weight, g the gravity, and k Boltzmann's constant. The inversion requires the knowledge of the initial stellar flux and the zero light level. Furthermore, the horizontal focusing effects of the spherical atmosphere must be taken into account. A set of assumptions have to be made when using the above procedure: 1. The atmosphere is assumed to be spherically symmetric. Otherwise stated, there are no horizontal gradients in the refractive index. 2. The differential refractivity is the major source of stellar light attenuation. In other words, extinction due to scattering and absorption can be neglected. 3. The star is considered to be a point source.
4. The atmosphere is assumed to be a perfect gas in hydrostatic equilibrium. Hydrogen and helium are the major constituents. They are assumed to be well mixed. Table IV gives the values of the different parameters used for the inversion.
IV.3. Baselines and Initial Condition In order to integrate Eq. (11.3) an initial condition is needed. We have imposed T0(h0) at the arbitrary level h0 • To has been fixed (80 < To < 200°K) at the highest altitude where reasonable results are expected T A B L E IV PARAMETERS OF THE INVERSION Perpendicular stellar velocity Molecular weight Gravity Specific refractivity (at 1 b a r and 0°C) A d o p t e d half-light time (UT)
6.790 k m / s e c H2 : 2 g mole-X He : 4 g mole -~ 818 c m sec -2 H 2 : 1 . 3 6 x 10 -4 He : 0.34 × 10 -4 22:38:09.0
465
(h0 - 50 km). Out of the interval (80, 200°K), the values of To lead to clearly unrealistic lapse-rates in the overlying atmosphere. Other authors used a different boundary condition (Wasserman and Veverka, 1973; French et al., 1978) which is equivalent to imposing an isothermal lapse-rate in the overlying atmosphere. What we need in the inversion computation is the normalized flux, that is, F = (~ OOp)/(4~0- ~p), where ~ is the recorded flux, 4ap the flux from the planet, and ~0 the total flux before immersion (due to the full stellar flux plus the planetary flux). The value of ~0 that we derived from the light curve is ~0 = 53,600 -+ 1,000 counts/sec, the error bars indicating the dispersion of the values around the mean level. To derive 6p, we consider the residual flUX ~ r = 750 --- 100 counts/sec. We have ~br = dpp + ~bs, where +s is the flux due to the star, which does not reach zero, even when the star is well behind the planet. This flux is not negligible and corresponds to a maximum refraction angle of about 0.9 arcsec. The minimum value of +s has been computed by Elliot et al. (1977b), who found (16H/3p) ~o, where H is the scale height of the probed atmosphere (H = kT/thg) and p the apparent distance of the star to the center of the planet at half-light time. Thus, +s >- (16H/3p) +0 = 750 --- 50 counts/sec taking T = 150 -+ 10°K. Then +p = dpr - t~s is estimated to 0 -< +p - 150 counts/sec. We report in Fig. 8b the uncertainties in the temperature profiles due to the uncertainties in ~b0 (=53,600 --- 1,000 counts/sec) and in d~p (0 -< ~bp -< 150 counts/sec). In the same way, the upper and lower baselines may be estimated by different methods and in particular (French et al., 1978) by fitting the observed light curve to the light curve obtained for an isothermal atmosphere. It might be noted that these methods, as well as our method, introduce some arbitrary features in the upper and lower parts of the thermal profile. But as discussed be-
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SICARDY ET AL.
low, significant results cannot be derived outside the altitude range ( H to - 3 H).
IV.4. Significance o f the Results It must be emphasized that the various authors agree on basic conclusions concerning the limits of significance of the results derived from the inversion method (Vapillon et al., 1973; C o m b e s et al., 1975; W a s s e r m a n n and V e v e r k a , 1973; French et al., 1978). The significance of the derived temperature in the outer atmospheric layers is limited due to various effects: - - T h e noise in the light curve induces errors in the refractivity profiles at the highest altitudes. These errors propagate into the calculated t e m p e r a t u r e profile. M o r e o v e r , starting the inversion at a finite level in the atmosphere, since one cannot integrate to infinity, leads to an initial error in the refractivity profile. An inaccurate determination of the stellar flux prior to occultation has a similar effect (Fig. 8).
- - T h e initial condition on T0(h0) or (dT/
dh) also introduces severe limitations on the significance of the results. As the number density increases exponentially, it can be shown that the influence of To(ho) becomes negligible as deeper atmospheric levels are probed (Fig. 7). - - P h o t o n noise and/or photometric uncertainties in the residual flux result as well in uncertainties in the t e m p e r a t u r e profile in the deepest probed atmospheric layers (Fig. 8). The conclusion of such an error analysis is that, while the inversion method is the best usable procedure, significant temperature profiles cannot be inferred f r o m the uppermost part of the light curve. In practice, and quite independently from the choice of the integration starting point and/or the initial condition, one cannot obtain significant temperature information a b o v e the halflight level. The most accurate results are obtained in the atmospheric range correb
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220 (K}
i 100
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'
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FIG. 7. The temperature profiles, derived from the inversion described in Section IV.2, are shown for different boundary conditions (temperature fixed at 80, 140, and 200°K at an altitude, above the half-light level, of 50 km). (a) Temperature as a function of pressure. (b) Temperature as a function of altitude above the half-light level.
{K}
15 AUGUST 1980 OCCULTATION BY URANUS b
467
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-200
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FIG. 8. Influence of varying the different parameters. (a) Variation of q, the hydrogen fraction by number (q = nn2/(nn~ + nHz)). (b) Variations of the total initial flux ~b0and of the residual flux d~r(see text). (i) ~b0= 53,600 counts/sec, t~r = 75 counts/sec ("nominal"). (ii) d~0= 54,600 cps, d~r= 75 cps. (iii) dp0 = 52,600 CpS, ~br = 75 CpS. (iv) d~0= 53,600 cps, d~r = 150 cps. (v) ~b0= 53,600 cps, ~br = 0 cps.
sponding to a residual stellar flux of 0.1 to 0.3. Indeed the inversion p r o c e d u r e must be stopped when " n e g a t i v e " values of the residual flux are induced by the noise fluctuations. As a c o n s e q u e n c e the p r o b e d atmospheric range is limited to approximately 3 scale heights below the midoccultation level. Usually the t e m p e r a t u r e profiles derived from stellar or radio occultations exhibit small t e m p e r a t u r e fluctuations. Such a fine structure is mainly due to small flux fluctuations at low frequency. High-frequency fluctuations, denoted " s p i k e s , " translate into much smaller t e m p e r a t u r e fluctuations. Figure 7 shows typical t e m p e r a t u r e fluctuations due to low-frequency flux variations and to spikes. As stressed previously, the inversion method can be used only if the atmosphere is assumed to be spherically stratified. Spikes m a y be induced b y atmospheric scintillation in a turbulent atmosphere or by density fluctuations in a hor-
izontally stratified a t m o s p h e r e (therefore spherically symmetric). W a s s e r m a n n and V e v e r k a have shown convincingly that the inversion method is efficient even in the case of a " s p i k y " light curve. N e v e r t h e less, one must k e e p in mind that if the atmospheric structure is far from spherically symmetric, or if severe ray-crossing occurs, the fine structure of the t e m p e r a t u r e profile may be questionable. In contrast, it must be emphasized that if spherical stratification is a correct assumption, the thermal fine structure is more significant than the derived lapse-rate and t e m p e r a t u r e mean value. IV.5. R e s u l t s
The result of the numerical integration of Eq. (II.3), for a set of values of the boundary condition T0(h0), is shown in Fig. 7. As a consequence of the previous conclusions on the validity of the results, the atmospheric range has been limited to the inter-
468
SICARDY ET AL.
val from +50 to - 1 50 km. From the inversion procedure and from Eq. (I1.3), one can simultaneously derive the temperature and the number density versus altitude. The corresponding pressure is thus affected in a quite complex way by the various uncertainties in the temperature, density, and altitude. The T ( P ) profile is given in Fig. 7a. It can be seen from Eq. (11.3) that the mean molecular weight of the atmosphere has a direct influence on the retrieved thermal profile. Following Courtin et al. (1978), an estimate of the hydrogen to helium mixing ratio can be obtained from inversion of infrared brightness temperatures of Uranus. A reasonable estimate is q = 0.9 0.1 in the well-mixed atmosphere. Figure 8 shows the influence of varying the H2/He ratio and the full-light or the zero-light levels, assuming the same boundary condition To(ho). It appears that the boundary condition is responsible for the largest uncertainty on the T(h) profile. We shall not present in this paper any results on the small temperature fluctuations of the T ( P ) profile. The observations of the 15 August occultation obtained from Cerro Tololo, ESO, and Las Campanas observatories have been used to compare the atmospheric structure of Uranus at points separated by - 1 0 0 km along the planetary limb. The results will be published in a common paper of the three teams (French et al., 1982). The main result of this comparative study is that the observed correlation of the three light curves is strong. Turbulence does not dominate the structure of the upper atmosphere, which is strongly layered with a horizontal coherence scale of at least several h u n d r e d kilometers. Most (95%) of the refraction effect is produced inside an atmospheric layer, the thickness of which is 2 H (Combes et al., 1971), corresponding to a horizontal coherence length L -~ 4 ~ (R being the planetary radius and H the scale height). Similar conclusions may be derived from French et al. (1978). For Uranus, L - 4000 km. Thus the above conclusion gives confidence in the thermal
profile derived from the inversion method. Comparison of the light curves obtained at ESO, Cerro Tololo, and Las Campanas observatories reveals a large general agreement (French et al., 1982). Nevertheless, our light curve (ESO) shows a loss of signal relative to the other two curves over the interval 40 to 70 sec after the mid-occultation, probably due to a tracking inaccuracy, which results in a lower temperature (by -5°K) from the -80- to -120-km altitude levels. The thermal profile derived by Nicholson et al. (1982b) from Las Campanas observations results in a mean temperature colder by - 2 0 ° K above the 10-2-mbar pressure level. In contrast, the thermal profile derived by French et al. (1982) from Cerro Tololo observations is in good agreement with our result in the upper atmosphere. These differences are due to small but real differences in the observed light curves and to different methods of determining the zero-light and full-light levels. IV.6. Discussion
In view of the various uncertainties in the retrieved temperature profile discussed in Section IV.5, a conservative conclusion may be that the temperature of the stratosphere of Uranus is nearly constant in the 10-3 to 10-2-mbar pressure range with a mean value of 155 - 15°K. Below this the temperature seems to decrease down to 145°K at the 3.10-2-mbar level. From our result and in agreement with similar results from French et al. (1982) and Nicholson et al. (1982b), it may be concluded that the stratospheric temperature of Uranus is, in contrast with previous studies, as high as the stratospheric temperature of Neptune in the 10-2- to 10-3-mbar pressure range. The low value attributed previously to the Uranian stratospheric temperature was based on the Dunham et al. (1980) occultation observations but also to the lack of CH4 and C2H6 emission features at 7.7 and 12 txm, respectively (Gillett and Rieke, 1977). In Fig. 9 we plotted the
15 AUGUST 1980 OCCULTATION BY URANUS "~ 10"/~
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I
469
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l
100
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I
200
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Temperature (K}
FIG. 9. Comparison between the temperature profiles obtained from the occultation of star SAO 158687 by Uranus on 10 March 1977 (Dunham et al., 1980) and the profiles derived from 15/16 August 1980 occultation (present work). We took three different boundary conditions for these profiles (see Fig. 7) in order to s h o w the clear discrepancy b e t w e e n the 1977 and 1980 results.
profiles obtained by Dunham et al. (1980) and the profiles derived from the present work. Dunham et al. (1980) derived a mean value of the tem_perature of 95°K in the 3.10 -4- to 2.10-2-mbar pressure range as a result of the occultation of SAO 158687 by Uranus on 10 March 1977. It seems almost impossible to relate this large discrepancy to observations uncertainties since the Dunham et al. results were derived from four observations (immersion and emersion recorded at both Cape Town and the KAO), while our result is in agreement with two other independent observations at Las Campanas and Cerro Tololo. Variations in the upper atmosphere of Uranus with time, while unexpected, may be responsible for the observed discrepancy. New observations of stellar occultations are needed to firmly establish such variations effects (Fig. 9). The low stratospheric temperature (95°K) derived by Dunham et al. (1980) was in agreement with the upper limit of the brightness temperature at 8 and 12 I~m obtained by Gillett and Rieke (1977), leading to TB (8 Ixm) < 100°K. It must be examined whether or not our result is in conflict with this upper limit. We have computed the expected emission in the Ch4 v4 band at 8.0 I~m in two cases, which may be considered as limit-cases for the structure of the atmosphere of Uranus (Fig. 10).
1. A CH4 "supersaturated" model similar to the radiative-convective equilibrium model computed by Wallace (1975) with a constant CH4/H2 mixing ratio, with T = BO°K in the stratosphere above the 0.1mbar pressure level. It may be noticed that the related vertical thermal profile is close to the N profile obtained by Courtin et al. (1978) from the inversion of the available infrared brightness temperatures at h > 10 Ixm. Thus it is only necessary to estimate the brightness temperatures resulting from this model at h < 10 Ixm and more especially at 8 Ixm. We obtained TB (8 I~m) close to 110°K, which considerably exceeds the upper limit obtained by Gillett and Rieke (1977). 2. A second model in which CH4 follows its saturation low, similar to Wallace's saturated model (1980) but with a warmer stratosphere (T = 150°K above the 0.1-mbar pressure level). Such a model leads to a thermal profile close to the Courtin et al. profile I (1978) and is also in agreement with ir available data. The discrepancy between I and N profiles is due to divergent observational data at 300 cm -~. So here again only an estimate of TB (8 ~m) is needed. We obtained TB (8 I~m) = 89°K significantly lower than the observational upper limit. So, there is no conflict between Gillett and Rieke's upper limit and the high stratospheric temperature derived from the occultation for a saturated C H 4 distribution.
470
SICARDY ET AL. I
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Present work 11.0 20
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I [~---------~ ~ 120
I I 160 200 Temperature (K)
FIG. 10. Comparison of temperature profiles. Here we show the profiles derived from Wallace's (1975) models, the Courtin et al. (1978) retrieved profiles from infrared measurements, and the results of the present work (with three different boundary conditions, see Fig. 7).
But in this case (saturated CH4) the stratospheric temperature should be, following Wallace (1975), 125°K at most, and even less if the cooling of the upper atmosphere by C2H6 and C2H2 (not observed but possibly present) is taken into account. Additional heating could be due to non-LTE processes or to the presence of aerosols. Appleby (1980) has computed various nonLTE models for Uranus. From his results non-LTE processes do not seem to be sufficient to explain the observed temperature (Fig. 10). Additional heating could also be due to aerosols. But it may be impossible to maintain an aerosol layer at these altitudes (Dunham et al., 1980). The magnitude of the needed additional heating is not well defined. Indeed, the derived temperature profile depends upon the assumed atmospheric composition. If helium is strongly depleted the temperature profile would shift toward lower temperature by -15°K. From what is known on the
internal structure of the planet and on the lack (or weakness) of the internal energy source on Uranus, such a depletion of helium cannot be excluded. Even if helium is not significantly depleted in the whole planet it may be depleted in the P < 10-2 mbar pressure range due to gravitational separation, which may take place in this range (N - 1014 cm -3) for values of the eddy mixing coefficient of about 105-106 cm 2 sec -~. Such values are plausible by comparison with Jupiter. A detailed aeronomical model of Uranus, including helium depletion but also the photochemistry of C H 4 , C2H6, and C2H2, is needed to explain quantitatively the observational results. This study seems to establish, in contrast with previous studies, that the stratospheric temperatures would be similar in both Uranus and Neptune at P < 10-2 mbar. The lack of CH4 emission at 8 ixm would indicate that the temperature inver-
15 AUGUST 1980 OCCULTATION BY URANUS
sion on Uranus is located at a higher atmospheric level (P < 1 mbar) than on Neptune (P - 10 mbar). New observations at 17.8 and 19.6 I~m by Tokunaga et al. (1982) seem to be in agreement with these qualitative conclusions.
471
COURTIN, R., D. GAUTIER, AND A. LACOMBE (1978). On the thermal structure of Uranus from infrared measurements. Astron. Astrophys. 63, 97-101. DERMOTT, S. F. (1981). The "braided" F-ring of Saturn. Nature 290, 454-457. DUNHAM, E., J. L. ELLIOT, AND P. J. GIERASCH (1980). The upper atmosphere of Uranus: Mean temperature and temperature variations. Astrophys. J. 235, 279-284. CONCLUSION ELLIOT, J. L., E. DUNHAM, AND D. MINK (1977a). The rings of Uranus. Nature 267, 328-330. The mean temperature of the Uranian at- ELLIOT, J. L., R. G. FRENCH, E. DUNHAM, P. J. mosphere in the pressure range between GIERASCH, I. VEVERKA, C. CHURCH, AND C. SA10-3 and 10-2 mbar is about 155 -+ 15°K and GAN (1977b). Occultation of ~ geminorum by Mars. II. The structure and extinction of the Martian upper decreases to 145°K at the 3 x 10-2-mbar atmosphere. Astrophys. J. 217, 661-679. pressure level. This temperature profile ELLIOT, J. L., E. DUNHAM, L. H. WASSERMAN,R. L. would shift toward colder temperature (by MILLIS, AND J. CHURMS (1978). The radii of Ura15°K) if hydrogen is the only atmospheric nian rings ct, 13, ~, 8, e, "q, 4, 5 and 6 from their constituent, due to global depletion of heoccultations of SAO 158687. Astron. J. 83, 980992. lium or to gravitational separation. This high stratospheric temperature is compati- ELLIOT, J. L., J. A. FROGEL, J. H. ELIAS, J. S. GLASS, R. G. FRENCH, D. J. MINK, AND W. LILLER (1981a). ble with the upper limit of the brightness The 20 March 1980 occultation by the Uranian rings. temperature at 8 ~m (Gillett and Rieke, Astron. J. 86, 127-134. 1977) if CH4 follows its saturation law, but a ELLIOT, J. L., R. G. FRENCH, J. A. FROGEL, J. H. ELIAS, D. J. MINK, AND W. LILLER (1981b). Orbits quantitative explanation of such a high of nine Uranian rings. Astron. J. 86, 444-455. stratospheric temperature remains to be ELLIOT, J. L., et al. (1982). In preparation. found. FRENCH, R. G., J. L. ELLIOT, AND P. J. GIERASCH (1978). Analysis of stellar occultation data. Effects ACKNOWLEDGMENTS of photon noise and initial conditions. Icarus 33, 186-202. We thank F. Gutitrrez, at La Silla Observatory FRENCH, R. G., J. L. ELLIOT, B. SICARDY, AND P. (ESO), who promptly wrote a fast acquisition program NICHOLSON (1982). The upper atmosphere of before the observation. We are grateful to J. Appleby Uranus: A critical test of isotropic turbulence and R. French for rereading the text and giving advice, models. Submitted. and also to J. Elliot and P. Nicholson for helpful comGILLETT, F. C., AND G. H. RIEKE (1977). 5--20 micron ments. This work was supported by RCP 544 Anobservations of Uranus and Neptune. Astrophys. J. neaux, by the ATP Planttologie, the Observatoire de 218, L141-LI44. Paris, and the Universit6 de Pads. GOLDREICH, P., AND S. TREMAINE (1979). Towards a theory for the Uranian rings. Nature 277, 97-99. REFERENCES GOLDREICH, P., AND S. TREMAINE (1980). Disk-satelAPPLEBY, J. (1980). Atmospheric Structures o f the lite interactions. Astrophys. J. 241, 425-441. Giant Planets from Radiative-Convective Equilib- HUBBARD, W. B., AND B. H. ZELLNER(1980). Results rium Models. Ph.D. thesis, SUNY, Stony Brook. from the 10 March 1977 occultation of the Uranus BHATTACHARYYA, J. C., AND K. KUPPUSWAMY system. Astron. J. 85, 1663-1669. (1977). A new Satellite of Uranus. Nature 267, 331- KLEMOLA, A. R., AND B. G. MARSDEN (1977). Pre332. dicted occultations by the rings of Uranus, BOUCHET, P., C. PERRIER, AND B. SICARDY (1980). 1977-1980. Astron. J. 82, 849-851. IAU Circular No. 3503. MILLIS, R. L., L. H. WASSERMAN,AND P. V. BIRCH COMBES, M., J. LECACHEUX, AND L. VAPILLON (1977). Detection of rings around Uranus. Nature (1971). First results of the occultation of 13 Sco by 267, 330-331. Jupiter. Astron. Astrophyhs. 15, 235-238. MILLIS, R. L., AND L. H. WASSERMAN (1978). The COMBES, M., L. VAPILLON, AND J. LECACHEUX occultation of BD-15°3969 by the rings of Uranus. (1975). The occultation of 13 Sco by Jupiter. IV. DiAstron. J. 83, 993-998. vergences with other observers in the derived tem- NICHOLSON, P. D., S. E. PERSSON, K. MATTHEWS, P. perature profiles. Astron. Astrophys. 45, 399-403. GOLDREICH, AND G. NEUGEBAUER (1978). The
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rings of Uranus: Results of the 10 April 1978 occultation. Astron. J. 83, 1240-1248. NICHOLSON, P. D., K. MATTHEWS, AND P. GOLDREICH (1981). The Uranus occultation of 10 June 1979. I. The rings. Astron. J. 86, 596-606. NICHOLSON, P. D., K. MATTHEWS, AND P. GOLDREICH (1982a). Radial widths, optical depths, and eccentricities of the Uranian rings. Astrophys. J. 87, 433-447. NICHOLSON, P. D., et al. (1982b). In preparation. TOKUNAGA, A. T., G. S. ORTON, AND J. CALDWELL (1982). New observational constraints on the temperature inversion of Uranus and Neptune. Submitted. VAPILLON, L., M. COMBES, AND J. LECACHEUX
(1973). The 13 Scorpii occultation by Jupiter. II. The temperature and density profiles of the Jovian upper atmosphere. Astron. Astrophys. 29, 135-149. VEVERKA, J., L. H. WASSERMAN, J. L. ELLIOT, AND C. SAGAN (1974). The occultation of 13 Scorpii by Jupiter. I. The structure of the Jovian upper atmosphere. Astron. J. 79, 73-84. WASSERMAN, L., AND J. VEVERKA (1973). On the reduction of occultation light-curve. Icarus 20, 322-345. WALLACE, L. (1975). On the thermal structure of Uranus. Icarus 25, 538-544. WALLACE, L. (1980). The structure of the Uranus atmosphere. Icarus 43, 231-259.
The 15 August 1980 Occultation by the Uranian System" Structure of the Rings and Temperature of the Upper Atmosphere 1 B. SICARDY AND M. COMBES Observatoire de Paris, 92190 Meudon, France
A. B R A H I C Universitd de Paris VII et Observatoire de Paris, 92190 Meudon, France
P. B O U C H E T AND C. PERRIER European Southern Observatory, La Silla, Chile AND
R. COURTIN LPSP 91370 Verrieres le Buisson, France Received F e b r u a r y 22, 1982; revised A u g u s t 3, 1982 A stellar occultation by U r a n u s and its rings was o b s e r v e d on A u g u s t 15, 1980, from the European Southern O b s e r v a t o r y (Chile), at the 3.6-m telescope equipped with an infrared (2.2 Ixm) photometer. The recording presents the best signal-to-noise ratio obtained since the discovery of the Uranian rings in March 1977. The nine rings were observed, and the profiles o f f i n g s a , 13, and were resolved, the ring a exhibiting a double structure. Strong diffraction peaks are visible in the ring profile suggesting an opaque ring with very sharp edges. A broad and faint structure e x t e n d s outward from the rl ring, on a radial scale of about 55 km. Apart from the ring occultations, unexplained sharp and deep e v e n t s were recorded, and no interpretation is possible until future observations are made. F u r t h e r m o r e , the stellar light curve during the immersion of the star behind the planet provides (via an inversion computation) the temperature profile of the upper a t m o s p h e r e of U r a n u s . The temperature is close to 145 -+ 10°K at the 3 × 10-2-mbar pressure level and is nearly constant (155 - 15°K) in the pressure interval from 10 -~ to 10 3 mbar. The thermal inversion is as strong as the inversion on N e p t u n e but is located at higher altitudes. This high stratospheric temperature is consistent with the upper limit of the brightness temperature at 8 p.m only if CH4 follows its saturation law.
ing ring segment, which in turn allows a kinematic model of the system to be derived (when all the data from different occultation observations are collected). Since their discovery on 10 March 1977 (Elliot et al., 1977a; Millis et al., 1977; Bhattacharyya and Kuppuswamy, 1977), the systematic observation of occultations (Elliott et al., 1978; Millis and Wasserman, 1978; Nicholson et al., 1978; Elliot et al., 1981a; Nicholson et al., 1981; Elliot et al., 1981b) showed that seven out of nine rings now identified fit elliptical orbits in uniform pre-
I. I N T R O D U C T I O N
The observation of a stellar occultation by the Uranian system is interesting for two reasons. First, it provides an opportunity to observe Uranus' rings at high resolution, and second, it allows us to probe the upper Uranian atmosphere. The occultation by the ring system provides the precise locations of each occult1 Based on observations collected at the E u r o p e a n Southern Observatory, La Silla, Chile. 454 0019-1035/82/120454-19502.00/0 Copyright @ 1982by AcademicPress, Inc. All fightsof reproduction in any form reserved.
15 AUGUST 1980 OCCULTATION BY URANUS
455
cession, the other two being circular. If confinement, why do the ~qand 8 rings (and only due to the oblateness of the planet the possibly others) exhibit a " b r o a d " (-50 precession rate may provide the values of km) and diffuse component in addition to the zonal harmonic coefficients J2 and J4 of the narrow and dense component? (iv) Why Uranus' gravity potential. These coeffi- does the profile of the e ring present the cients give some information about the inte- same structure in the different parts of the rior of the planet (Elliot et al., 1981b). ring's orbit in spite of its variations of On the other hand, the occultation pro- width, and how may this structure be stafiles are presently the best probes of the ble? Possible answers involving self-gravidensity distribution inside the rings, be- tation in the rings or tidal torque exchange cause of their high resolution (about 2 km). between a ring and satellites orbiting close The Uranian ring system was quite surpris- to its edges have been proposed by ing when discovered because it raised, and Goldreich and Tremaine (1979, 1980). still raises, unanswered questions, such as: The observed structures are complex, (i) How the rings may be so confined (eight and they are linked to fundamental quesof them are a few kilometers wide, the ninth tions such as the origin, the evolution, and being a few tens of kilometers wide), with the stability of rings, the accretion mechavery sharp edges? Without any external nisms, and the formation of the solar sysconstraint, a system of colliding particles tem. So far, the only way to find out the orbiting around a central massive body whole structure of the Uranian rings is to spreads radially under the effects of differ- observe as many occultations as possible, ential rotation and collision. (ii) Why are each of them providing a "scan" of the ring some of the rings locked in precession as a system (Fig. 1). whole without being disrupted by differenOn the other hand, the star was also octial precession? (iii) In spite of this strong culted by the upper atmosphere of the
I 1" I
N
l
10 I I*kmI 08,16,80
08/15180
0~0
/ ??-0~0
~ W
FIG. 1. The path of the star KM 12 relative to the Uranian system. The dashed line represents interruptions of observations due to "synchronization stops" (see text) or passage of clouds.
456
SICARDY ET AL.
planet: the stellar light curve during immersion, or emersion, is the result of differential bending of starlight, due to the gradient of refractivity in the Uranian atmosphere. An inversion computation developed by Vapillon et al. (1973) gives, from the stellar light curve, the refractivity profile and the temperature profile of the upper atmosphere. The result is a constraint for the models describing deeper regions of Uranus' atmosphere. Uranus is very different from the other giant planets in various respects: its internal energy source, if it exists, is small in magnitude; the general atmospheric circulation and seasonal pattern are expected to depend on the position of the rotation axis of the planet; in contrast with the other giant planets, Uranus does not exhibit any emission of molecular species in the infrared; and furthermore, the results of the 1977 occultation (Dunham et al., 1980) seemed to indicate that Uranus' stratosphere was colder than those of the other giant planets. The occultation experiment is expected to provide new data on the structure and composition of the upper atmosphere. In this paper, we will present the first results derived from the 15 August 1980 occultation, observed from the European Southern Observatory (ESO) at La Silla, Chile, with the 3.6-m telescope. One should note that this occultation was unique compared with previous ones because of its high signal-to-noise ratio, relative to previous observations, and because it was observed simultaneously from three stations close to each other [Cerro Las Campanas Observatory (CLCO), which lies 30 km north of ESO, and Cerro Tololo Inter American Observatory (CTIO), 100 km south of ESO]. A comparison between the three observations, in view of the good signal-to-noise ratio, allows without doubt the identification of faint and broad, or fine and narrow, structures in the rings. It is also possible to compare the light curve during immersion or emersion in the planetary atmosphere;
this light curve presents numerous strong and short spikes due to inhomogeneities in the atmosphere. The correlation of these spikes when observed from one station or another is a critical test for the understanding of the structure of the Uranian upper atmosphere. The comparison of ring profiles and temperature profiles will be published in subsequent papers (French et al., 1982; Elliot et al., 1982). Section II describes our observations, Section III the results related to the rings, and Section IV presents the results concerning the atmosphere of Uranus. II. OBSERVATIONS
Uranus and its ring system occulted the star KM 12 [star number 12 on the list of Klemola and Marsden (1977)] on the night from 15 to 16 August, 1980. We observed this phenomenon with the ESO infrared photometer/spectrophotometer attached to the 3.60 telescope (La Silla, Chile), equipped with an InSb photovoltaic detector cooled at 63°K. In order to increase the contrast between the star and the planet, an infrared filter (K band, h = 2.2 p.m, Ah = 0.5 p~m) corresponding to a methane band was used. In that way the contribution of the planet and its rings was about 35 times weaker than the total flux (star + planet + rings). Thus the signal-to-noise was significantly increased by comparison with previously observed stellar occultations by Uranus. The star was centered in a 7.5-arcsec diaphragm and the chopping frequency was 20 Hz, with an amplitude of 20 arcsec. The signal was traced in real time on a strip chart and was simultaneously recorded on a magnetic tape with the same sample step of 0.1 sec. The effective total time constant of the recording system was 0.1 sec. The diaphragm of the photometer had a diameter of 7.5 arcsec, and the response of the receptor decreased significantly when the star was moved by about 1.5 arcsec from the center of the aperture. The geometry of the occultation is shown in Fig. 1, and the interruptions of observa-
15 AUGUST 1980 OCCULTATION BY URANUS tion are indicated on the path of the star KM 12. Some of these interruptions are due to passages of cirrus. The others come from electronic problems: every l0 sec, a cesium clock controlled the UT recorded on the tape and some of these synchronizations could not be made immediately, which led to these "synchronization stops." The paths of the star as observed from CLCO and CTIO are indistinguishable
457
from the line traced in Fig. l, considering the scale of the sketch. During the first part of observation, i.e., before the immersion of the star behind the planet (the Sun was then still in the sky), the telescope was guided so that the signal was maximum. This procedure, however, led to some variations of the signal caused by decenterings (see Fig. 2). During this part of the observation, transitory passages of cirrus caused
PRE-IMMERSION
0
aO
S
"4"
c
seconds before 22,10:10.8
UT
0
200
400
600
1000
12'00
10;0
12;0
-4"
POST- E M E R S I O N tN
o
J cO
~o
S -4>.
seconds after
00,45,05.8
UT
ev
o
200
400
600
800
FIG. 2. A general view of the nine ring occultations. The sudden increase of flux during preimmersion occultation by ring ot is due to a recentering of the star in the diaphragm. The very high noise observed during preimmersion occultations by the rings is due to passages of cirrus (it was then still daylight). The variations in the flux observed during postemersion are seeing effects. Note the presence of two supplementary events (a and b) and the diffraction peaks associated with the ~/ ring occultation (especially in the preimmersion recording).
458
SICARDY ET AL.
very high noise, the last passage occuring at 21 : 52 UT, as visible in Fig. 2. It prevented the observation of the preimmersion occultation of the ring e. All the other ring occultations were observed thereafter. After the immersion of the star KM 12 behind the planet's disk (the Sun was set then), the telescope was monitored by a guide-probe. The seeing was good and the guiding star did not suffer displacements greater than 1 arcsec. Thus the variations of signal detected during postemersion occultations (see Fig. 2) cannot be artifacts caused by decenterings, as occurred during the preimmersion observations. Most of these variations are probably due to clouds which modified the transparency of the sky. The immersion of the star in the atmosphere of Uranus was clearly observed, with, however, some possible guiding problems due to the procedure described above (signal maximum in the diaphragm). The emersion light curve is not usable because the star was not centered in the diaphragm when it reappeared. III. RING OCCULTATIONS Figure 2 gives a general view of the nine ring occultations (preimmersion and postemersion). A comparison with previous recordings shows the quality of the signal-tonoise ratio of the 15 Aug. 1980 occultation (this ratio was better for postemersion events because the Sun was set then). Also visible in Fig. 2 are two of the six isolated events reported by Bouchet et al. (1980) from the original ESO observation. Figure 3 presents the detailed profiles of identified rings, the time step of 0.1 sec corresponding to a radial distance (in the plane of the rings) of 0.82 and 0.84 km for preimmersion and postemersion events, respectively. Table I lists the mid-times, the durations (i.e., the full-width at half-maximum, FWHM), the fractional depths, and the projected (i.e., in the sky-plane, not the ringplane) apparent widths corresponding to each duration. For the value of the radial velocity of the star in the sky-plane, we
took 7.4 and 7.5 km/sec, for preimmersion and postemersion events, respectively. The uncertainty in the durations is 0.1 sec, i.e., -0.7 km for the projected apparent widths. The fractional depths given in Table I do not take into account that part of the flux due to the planet. During the ring occultations, this part of the flux represented less than 1% of the total flux. Thus subtracting the contribution of the planet would increase the fractional depths of Table I by less than 1%, which is negligible here. The main cause of error comes from the noise in the data, which varies from one ring to the other, so that error bars have been attributed to each fractional depth in Table I. Besides, the mid-times do not take into account the time constant of the demodulator, and each of them must be corrected by about -0.1 sec to obtain the actual midtimes. We will now consider some of the properties of the rings inferred from the occultation profiles. Qualitative results are given here and quantitative properties, together with more theoretical interpretations, will be considered in a subsequent paper. Rings 6, 5, 4. The projected apparent widths (FWHM) of these rings are comparable to the minimum apparent width allowed by the diffraction pattern: as shown by Elliot et al. (1981a) and by Nicholson et al. (1982a), when the actual projected width of a ring is smaller than roughly 2 kin, then the apparent width (FWHM) becomes constant. At h -- 2.2 ixm, for Uranus at D = 18.8 AU from the Earth, and for a stellar diameter reduced to Uranus' distance of 1.8 km, the value of this constant is about 3 km. This is the minimum apparent width (FWHM) that can be obtained in an occultation profile. In this situation, the apparent fractional depth of the profile decreases not only with the optical depth "r of the ring, but also with its actual width W. It is interesting to note that the profile of ring 5 is significantly deeper at postemersion than at preimmersion (Fig. 3). This may indicate that the occulting segment is
15 AUGUST 1980 OCCULTATION BY URANUS
® -E
6
4
5
22:11:16.9 I
459
22:09:50.5
22:10:21.2
22:03:27.4
-22:05:25.3
I
I
I
-I
\s ® "E
6
00:45:58.6 I
5
4
00:46:50.6 I
00:47:31.5
00:51:52.
00:53:42.5
I
I
--
b
_
:[
eo E 22:00:23.3 I
21:59:28.8
" 21:58:07.3
,
-t
E 00:56:42. I
2 I
30:58:55.8 I
,
,
,
,
,
,
I
. . . . .
,
,
FIG. 3. T h e d e t a i l e d p r o f i l e s o f t h e n i n e o c c u l t a t i o n s . T h e t i m e s t e p o f 0.1 s e c r e p r e s e n t s a r a d i a l d i s t a n c e o f 0 . 8 2 a n d 0 . 8 4 k m in t h e p l a n e o f t h e r i n g s f o r p r e i m m e r s i o n a n d p o s t e m e r s i o n p r o f i l e s , respectively. The intervals between the thick marks represent 1 sec.
wider and/or more opaque at postemersion than at preimmersion. As previously shown by Elliot et al. (1981a) and Nicholson et al. (1982a), some elliptical rings present a variation of width with radius (the rings or, 13, and ~). It is therefore quite possible that azimuthal variations of width and optical depth exist in ring 5 since its eccentricity (e = 1.77 x 10 -3) lies between the eccentricities o f the ot and ~ rings [e = 0.72 x 10 -3 and e = 7.92 x
10 -3, respectively, see Elliot et al. (1981b)]. Observations at shorter wavelength with smaller stars would be needed to show these variations in ring 5. R i n g et. Unlike rings 6, 5, and 4, the et ring is resolved in postemersion profiles. In the case where the apparent width of a ring is greater than 5 km, the fractional depth of the profile is a function of the apparent optical depth "ca only (i.e., it is not affected by diffraction effects and the finite size of the
460
SICARDY ET AL. TABLE I
Ring
Immersion 15 August 1980 (UT)
Emersion 16 August 1980 (UT)
Duration (sec) i
6 5 4 c~ I~ "q -/ e
22:11 : 16.85 22 : 10 : 21.22 22:09:50.5 22:05:25.28 22:03:27.4 22:00:23.3 21 : 59 : 28.75 21:58:07.25 --
00:45:58.4 00 : 46 : 50.42 00:47:31.32 00:51:51.8 00:53:42.45 00:56:41.75 00 : 57 : 35.5 00:58:55.6 01:04:45.1
0.5 0.5 0.4 0.55 0.8 0.4 0.5 0.5 --
Fractional depth
e
0.4 0.45 0.45 1.2 1.5 0.5 0.6 0.5 8.0
i
0.22 0.35 0.29 0.74 0.53 0.16 0.53 0.70
- 0.02 -+ 0.02 +- 0.015 - 0.005 -+ 0.015 -+ 0.02 -+ 0.015 -+ 0.01 --
Projected width, FWHM e
0.24 0.46 0.35 0.60 0.30 0.25 0.90 0.71 0.97
-+ 0.015 - 0.01 -+ 0.015 -+ 0.001 -+ 0.01 - 0.015 +- 0.005 -+ 0.01 +-- 0.005
(km) i
e
3.7 3.7 2.9 4.0 5.9 2.9 3.7 3.7 --
3.4 3.4 3.4 9.0 11.2 3.7 4.5 3.7 60
N o t e . These times do n o t take into account the time c o n s t a n t of the re c e pt or (0.1 sec).
star). This fractional depth is simply given by 1 - e -~a. We report in Table II the apparent radial width of resolved rings, as well as their normal optical depth ~-,. r. is given by • , = % sin B, B being the inclination of the Earth above the ring plane. Here sin B = 0.90. For postemersion segments of ring a, we obtained an apparent radial width of 10.1 km and "r, = 0.82. Furthermore, one should note that an "irregular" structure is visible in the postemersion profile (Fig. 3) of ring a. This structure was anticipated by Hubbard and Zellner (1980), and is also well identified on postemersion profiles given by Elliot et al. (1981b) and by Nicholson et al. (1982a). This may be due to the presence of a density fluctuation, or more probably to the presence of two ringlets instead of one as T A B L E II Ring
N o r m a l optical depth
Radial width, FWHM (km) i
e
6.6
10.0 12.6 67.5
i
e
0.68 --- 0.03
0.82 -+ 0.03 0.32 -+ 0.01 ->3
previously thought. The distance between the two ringlets, for the segment observed at postemersion, would be 4.2 km. Because of the eccentricity of ring a, this distance would vary along the ring, and the two components would be too close to each other in the preimmersion profile to be separated. Like ring e (Nicholson et al., 1978) and ring 13 (Elliot et al., 1981a), ring oL has a width/radius relation. This relation is well represented by a linear fit for the 13 and e rings, but this fit is not so satisfactory for ring a because the dispersion of points is higher (Nicholson et al., 1982a). The presence of two ringlets in ring a may explain the scattering of widths around a linear fit. As shown by Goldreich and Tremaine (1979), precessing models of elliptical rings, whose widths vary linearly with radius, may be understood in terms of self-gravity in the ring. On the other hand, the "splitting" of ring ot into two components could be explained by the presence of a small satellite (inside the ring) which could have produced a gap. The presence of this satellite might also explain the p o o r e r agreement concerning the linear relation width versus radius in the case of ring or. Ring 13. Just as for ring a, both occulting segments of ring 13 can be resolved. The
15 AUGUST 1980 OCCULTATION BY URANUS apparent radial widths and normal optical depths of these segments are given in Table II. This ring presents a smooth profile, with no significant "irregularities." Ring 0. This ring is not resolved, and is quite similar to rings 6, 5, and 4 described above. On the other hand, one of the most interesting results of the 15 August 1980 occultation was the clear confirmation of a broad component associated with the narrow component of ring -q. This broad component is described below. Ring ~1. The low speed of the ring shadow ( - 8 km/sec) and the signal-to-noise ratio of the observations allowed the unambiguous detection of diffraction peaks caused by the sharp edges of ring ~. The highest peak in the preimmersion profile (Figs. 2 and 3) represents 22% of the total flux, whereas it is reduced to 12% in the postemersion profile. Note also that the postemersion profile is significantly deeper and wider than the preimmersion profile (Fig. 3 and Table I). A postemersion profile has been synthesized by Nicholson et al. (1982a), who described the ring ~/ as an opaque strip with a projected width of 3 km. The first diffraction peaks, which may represent 40% or more of the total flux, are smoothed by the following effects: the finite size of stellar disk (whose diameter was estimated to be 1.8 km) and the time constant of the receptor (0.1 sec). The greater diffraction peaks observed in the preimmersion profiles may be interpreted in several ways: the width of the preimmersion segment may correspond to a particular value for which the peaks are enhanced, or, more likely, the star's diameter has been overestimated so that the smoothing effect is less important than initially thought. In any case, it is quite interesting to note that the ring ~/, which is circular (Elliot et al., 1981b), seems to present azimuthal variations of width and/or optical depth. R i n g 8. Both preimmersion and postemersion profiles are relatively noisy. The
461
fractional depth and the width of ring 8 make it similar to ring -/, apart from the fact that diffraction peaks are not visible. This absence of peaks must be due in part to a broad component located in the inner part of ring 8, with a projected width of about 15 km (Elliot et al., 1981b; Nicholson et al., 1982a). This broad component is not visible on our profiles because of the noise in the data. Ring ~. The widest of Uranus' rings was observed only at postemersion because of the passage of clouds during the preimmersion occultation. The edges of this ring are sharp, as indicated by the diffraction peaks. As pointed out by Nicholson et al. (1978), the width of ring e is a linear function of its radius. The new data from the present occultation confirm this property (Nicholson et al., 1982a). Furthermore, the fine structures of ring • are identical to those shown by Nicholson et al. (1978), relative to 10 March 1977 and to 10 April 1978. This confirms that ring ~ precesses as a whole, with no distortion due to differential precession on a scale of a few years. Note that the deepest part of ring reaches a fractional depth of 97%, indicating the presence of a nearly opaque component. Broad components. Another consequence of the good signal-to-noise ratio was the detection of a broad component associated with the narrow component of ring -q. In preimmersion and postemersion profiles (Fig. 4), the broad ring is delimited at its outer edge by a small feature (with a fractional depth of 10%) located at 56 and 55 km from the narrow component (which is circular), respectively. It is quite interesting to note that the broad component does not seem to have the same shape and the same location relative to the narrow component on preimmersion and postemersion profiles. This should be viewed as only a possibility, considering the higher noise of preimmersion data; further observations are needed to confirm this variation of position and shape of the broad component.
462
SICARDY ET AL.
.9
?
q c
22:11:21.9
22:00:28.3
I
l
? 'I
v!
"6 -
00:56:36.8
00:/..5:53.4 I
FIG. 4. The broad components of ring r I (right). Note the small component (cross) at the edge of the broad component. The latter does not seem to have the same shape and location on the preimmersion and postemersion profiles. On the left, features indicating the possible presence of broad and diffuse components associated with ring 6. Time interval between tick marks is 10 sec.
On the other hand, there seems to be some rapid variation of optical depth in the broad component, on a scale of 100 km or so. The typical optical depth of the broad component as observed from CLCO is 0.03 (Nicholson et al., 1982a) versus 0.07 for ESO observations ( - 3 0 km from CLCO) and 0.1 for CTIO profiles [-135 km from CLCO, see Elliot et al. (1980)]. We suspect the presence of other broad structures close to ring 6 (Fig. 4), but they are not confirmed by other teams and should await further observations. I s o l a t e d events. Apart from the identified ring occultations, we observed isolated events (Bouchet et al., 1980) which are not correlated with isolated events detected at CLCO and CTIO (Elliot, Matthews, private communications). This rules out the possibility of occultations by supplementary rings, or by satellites larger than 100 km. Similar isolated events were observed during previous observations (Millis and Wasserman, 1978; Hubbard and Zellner, 1980). The majority of the events are due to seeing effects. For instance, in our data the signal sometimes decreases on a time scale of about 10 sec, with a drop of 20%, and then
increases again, the minimum exhibiting a sharp and deep drop in signal. Such an event is likely to be due to a rapid decentering of the star caused by scintillation. Although the diaphragm of the photometer had a diameter of 7.5 arcsec, the response of the receptor decreased significantly when the star was moved by about 1.5 arcsec from the center of the aperture. However, for the events listed in Table III the surrounding signal is not noisy, and the drops are sharp and deep (Fig. 5), which makes their interpretation more difficult. These events are interesting in themselves T A B L E III Event
Time 16 August 1980 (UT a)
Duration (sec)
Fractional depth
a b c d e f
00:59:56.1 01:01 : 54.25 01 : 46 : 30.4 02 : 01 : 27.85 02 : 05 : 55.0 02 : 06 : 59.45
0.25 0.3 0.45 1.7 0.4 0.5
0.29 0.30 0.30 0.58 0.27 0.24
a These times do n o t take into account the time constant of the receptor (0.1 sec).
15 AUGUST 1980 OCCULTATION BY URANUS , f , , , , , , , f
....
,,,,,
,,,f,,
......
463
,,f,,,,
F
L
b
a c c 00:59:56.4
01:01:54.6 . . . . . . . . .
~
~,,,
e
f
02:05:55.0
02:06:59.5
d 02:01:27.9
{5
[ .....
.........
I .........
, , , , , , , , , I , , , , , , , , ,
FIG. 5, The profiles of six isolated events, o b s e r v e d during the postemersion part of the occultation (see Table III). The steps on the time axis c o r r e s p o n d s to 1 sec.
because they are not yet explained, and their origin should be clarified to avoid some ambiguities with other " r e a l " events. An observation with two telescopes close to each other (a few hundreds of meters) is now needed to provide a better understanding of their cause. In conclusion, the occultation of the star KM 12 by Uranus' rings was important for a better knowledge of the density profiles of the rings (owing to the good signal-to-noise ratio and the low speed of the star relative to Uranus). In addition, the data of 15/16 August 1980 allowed an improvement in the kinematic model describing the rings as precessing orbits (Elliot et al., 1981b). Three of nine ring profiles were resolved (or, 13, and e). Ring ot presents a double structure which may be caused by the presence of a gap inside the ring, ring 13exhibits a smooth structure, and ring Cs profile confirms the existence of a fixed structure (on a time scale of a few years). These conclusions are valid as long as the features considered are bigger than about 2 km (smaller details are smoothed by diffraction, the finite size of the stellar disk, and the time constant of the detector). The ring ~/occultation profile shows diffraction peaks, indi-
cating a narrow (3 km) opaque ring with very sharp edges. The difference in the height of peaks between preimmersion and postemersion profiles must be investigated. The narrow components contrast with the "broad" (a few tens of kilometers) and faint structures associated with rings -q and (and possibly 6). Other observations are needed to provide a better description of these broad structures, and also to find out the origin of some isolated events whose signature is not clearly different from the rings' signatures.
IV. T H E O C C U L T A T I O N BY T H E P L A N E T A R Y ATMOSPHERE
IV.1. The Occultation Light Curve
The occultation light curve is shown in Fig. 6. It is dominated by numerous spikes which are usually assumed to be due to small density fluctuations in the atmospheric structure. It may be noticed that in the first part of the curve, down to the midoccultation level, the drop of the flux was more rapid in the Dunham et al. (1980) data, considering the differences in the stellar velocity between the two occultations.
464
SICARDY ET AL.
?,
absolute zero f[ux seconds after 2 2 : 3 6 , 1 7 UT 100
200
300
FIc. 6. The light curve during the immersion of the star behind the planet. The flux from Uranus has
not been removed from the curve shown here, so that the absolute zero flux is reached when no signal enters the photometer. Note the presence of numerous narrow and strong "spikes" due to small temperature inhomogeneities in Uranus' atmosphere. In contrast, light curves of the 15 August 1980 occultation recorded simultaneously at Las C a m p a n a s and Cerro Tololo observatories are very similar to the curve we obtained (French et a l . , 1982). So, from this first look, we see that the 15 August 1980 occultation leads to a value of the mean temperature that is higher than the value derived by D u n h a m et al. (1980).
IV.2. The Inversion Method
The inversion of occultation light curves is a well-known procedure. The method used for the present analysis is based upon the integral inversion o f the Abelian equation relating the refraction angle to to both the refractive index Ix and the altitude r0. ~ ( Po) = -
fi
' 2po • dlx
o Ix( r) . dr
[ ( r - Ix(r)) 2 - (r0" Ix(r0))2] -1/2 • dr,
(II.1)
where po is the impact p a r a m e t e r and ro the altitude of closest a p p r o a c h of a given starlight ray. The integral inversion of (II.1) leads to an explicit expression of the refractive index and of the altitude (Abelian integral):
Ix(ro) = exp
~ Jo
ro = po/ix(ro).
(11.2)
This method has already been used for the occultation of 13 Sco by Jupiter. For a detailed discussion the reader is referred to Vapillon et al. (1973) and C o m b e s et al. (1975). V e v e r k a et al. (1974) have used, for various stellar occultations by planets, a similar procedure improved by French et al. (1978). Briefly described, our method consists in using the observational data (i.e., the astrometric position of the star relative to Uranus and the occultation light curve) to derive the refraction angle o~(t) and the impact p a r a m e t e r p ( t ) versus time. This in turn allows Eq. (II.2) to be solved (this is the inversion properly speaking), leading to the determination of the atmospheric refractivity v(h) = Ix(h) - 1 as a function of the altitude h. The origin of the altitude h is usually chosen at the level where the drop of the stellar flux represents half of the full stellar flux ("half-light level"). F r o m the refractivity profile, one can deduce the num-
15 AUGUST 1980 OCCULTATION BY URANUS ber density versus altitude h and finally the vertical temperature profile T(h) through the hydrostatic equation
dT(h) T(h)
-
-
dr(h) v(h)
th g dh k T(h) '
(II.3)
where rh is the mean molecular weight, g the gravity, and k Boltzmann's constant. The inversion requires the knowledge of the initial stellar flux and the zero light level. Furthermore, the horizontal focusing effects of the spherical atmosphere must be taken into account. A set of assumptions have to be made when using the above procedure: 1. The atmosphere is assumed to be spherically symmetric. Otherwise stated, there are no horizontal gradients in the refractive index. 2. The differential refractivity is the major source of stellar light attenuation. In other words, extinction due to scattering and absorption can be neglected. 3. The star is considered to be a point source.
4. The atmosphere is assumed to be a perfect gas in hydrostatic equilibrium. Hydrogen and helium are the major constituents. They are assumed to be well mixed. Table IV gives the values of the different parameters used for the inversion.
IV.3. Baselines and Initial Condition In order to integrate Eq. (11.3) an initial condition is needed. We have imposed T0(h0) at the arbitrary level h0 • To has been fixed (80 < To < 200°K) at the highest altitude where reasonable results are expected T A B L E IV PARAMETERS OF THE INVERSION Perpendicular stellar velocity Molecular weight Gravity Specific refractivity (at 1 b a r and 0°C) A d o p t e d half-light time (UT)
6.790 k m / s e c H2 : 2 g mole-X He : 4 g mole -~ 818 c m sec -2 H 2 : 1 . 3 6 x 10 -4 He : 0.34 × 10 -4 22:38:09.0
465
(h0 - 50 km). Out of the interval (80, 200°K), the values of To lead to clearly unrealistic lapse-rates in the overlying atmosphere. Other authors used a different boundary condition (Wasserman and Veverka, 1973; French et al., 1978) which is equivalent to imposing an isothermal lapse-rate in the overlying atmosphere. What we need in the inversion computation is the normalized flux, that is, F = (~ OOp)/(4~0- ~p), where ~ is the recorded flux, 4ap the flux from the planet, and ~0 the total flux before immersion (due to the full stellar flux plus the planetary flux). The value of ~0 that we derived from the light curve is ~0 = 53,600 -+ 1,000 counts/sec, the error bars indicating the dispersion of the values around the mean level. To derive 6p, we consider the residual flUX ~ r = 750 --- 100 counts/sec. We have ~br = dpp + ~bs, where +s is the flux due to the star, which does not reach zero, even when the star is well behind the planet. This flux is not negligible and corresponds to a maximum refraction angle of about 0.9 arcsec. The minimum value of +s has been computed by Elliot et al. (1977b), who found (16H/3p) ~o, where H is the scale height of the probed atmosphere (H = kT/thg) and p the apparent distance of the star to the center of the planet at half-light time. Thus, +s >- (16H/3p) +0 = 750 --- 50 counts/sec taking T = 150 -+ 10°K. Then +p = dpr - t~s is estimated to 0 -< +p - 150 counts/sec. We report in Fig. 8b the uncertainties in the temperature profiles due to the uncertainties in ~b0 (=53,600 --- 1,000 counts/sec) and in d~p (0 -< ~bp -< 150 counts/sec). In the same way, the upper and lower baselines may be estimated by different methods and in particular (French et al., 1978) by fitting the observed light curve to the light curve obtained for an isothermal atmosphere. It might be noted that these methods, as well as our method, introduce some arbitrary features in the upper and lower parts of the thermal profile. But as discussed be-
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low, significant results cannot be derived outside the altitude range ( H to - 3 H).
IV.4. Significance o f the Results It must be emphasized that the various authors agree on basic conclusions concerning the limits of significance of the results derived from the inversion method (Vapillon et al., 1973; C o m b e s et al., 1975; W a s s e r m a n n and V e v e r k a , 1973; French et al., 1978). The significance of the derived temperature in the outer atmospheric layers is limited due to various effects: - - T h e noise in the light curve induces errors in the refractivity profiles at the highest altitudes. These errors propagate into the calculated t e m p e r a t u r e profile. M o r e o v e r , starting the inversion at a finite level in the atmosphere, since one cannot integrate to infinity, leads to an initial error in the refractivity profile. An inaccurate determination of the stellar flux prior to occultation has a similar effect (Fig. 8).
- - T h e initial condition on T0(h0) or (dT/
dh) also introduces severe limitations on the significance of the results. As the number density increases exponentially, it can be shown that the influence of To(ho) becomes negligible as deeper atmospheric levels are probed (Fig. 7). - - P h o t o n noise and/or photometric uncertainties in the residual flux result as well in uncertainties in the t e m p e r a t u r e profile in the deepest probed atmospheric layers (Fig. 8). The conclusion of such an error analysis is that, while the inversion method is the best usable procedure, significant temperature profiles cannot be inferred f r o m the uppermost part of the light curve. In practice, and quite independently from the choice of the integration starting point and/or the initial condition, one cannot obtain significant temperature information a b o v e the halflight level. The most accurate results are obtained in the atmospheric range correb
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{K}
15 AUGUST 1980 OCCULTATION BY URANUS b
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FIG. 8. Influence of varying the different parameters. (a) Variation of q, the hydrogen fraction by number (q = nn2/(nn~ + nHz)). (b) Variations of the total initial flux ~b0and of the residual flux d~r(see text). (i) ~b0= 53,600 counts/sec, t~r = 75 counts/sec ("nominal"). (ii) d~0= 54,600 cps, d~r= 75 cps. (iii) dp0 = 52,600 CpS, ~br = 75 CpS. (iv) d~0= 53,600 cps, d~r = 150 cps. (v) ~b0= 53,600 cps, ~br = 0 cps.
sponding to a residual stellar flux of 0.1 to 0.3. Indeed the inversion p r o c e d u r e must be stopped when " n e g a t i v e " values of the residual flux are induced by the noise fluctuations. As a c o n s e q u e n c e the p r o b e d atmospheric range is limited to approximately 3 scale heights below the midoccultation level. Usually the t e m p e r a t u r e profiles derived from stellar or radio occultations exhibit small t e m p e r a t u r e fluctuations. Such a fine structure is mainly due to small flux fluctuations at low frequency. High-frequency fluctuations, denoted " s p i k e s , " translate into much smaller t e m p e r a t u r e fluctuations. Figure 7 shows typical t e m p e r a t u r e fluctuations due to low-frequency flux variations and to spikes. As stressed previously, the inversion method can be used only if the atmosphere is assumed to be spherically stratified. Spikes m a y be induced b y atmospheric scintillation in a turbulent atmosphere or by density fluctuations in a hor-
izontally stratified a t m o s p h e r e (therefore spherically symmetric). W a s s e r m a n n and V e v e r k a have shown convincingly that the inversion method is efficient even in the case of a " s p i k y " light curve. N e v e r t h e less, one must k e e p in mind that if the atmospheric structure is far from spherically symmetric, or if severe ray-crossing occurs, the fine structure of the t e m p e r a t u r e profile may be questionable. In contrast, it must be emphasized that if spherical stratification is a correct assumption, the thermal fine structure is more significant than the derived lapse-rate and t e m p e r a t u r e mean value. IV.5. R e s u l t s
The result of the numerical integration of Eq. (II.3), for a set of values of the boundary condition T0(h0), is shown in Fig. 7. As a consequence of the previous conclusions on the validity of the results, the atmospheric range has been limited to the inter-
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SICARDY ET AL.
val from +50 to - 1 50 km. From the inversion procedure and from Eq. (I1.3), one can simultaneously derive the temperature and the number density versus altitude. The corresponding pressure is thus affected in a quite complex way by the various uncertainties in the temperature, density, and altitude. The T ( P ) profile is given in Fig. 7a. It can be seen from Eq. (11.3) that the mean molecular weight of the atmosphere has a direct influence on the retrieved thermal profile. Following Courtin et al. (1978), an estimate of the hydrogen to helium mixing ratio can be obtained from inversion of infrared brightness temperatures of Uranus. A reasonable estimate is q = 0.9 0.1 in the well-mixed atmosphere. Figure 8 shows the influence of varying the H2/He ratio and the full-light or the zero-light levels, assuming the same boundary condition To(ho). It appears that the boundary condition is responsible for the largest uncertainty on the T(h) profile. We shall not present in this paper any results on the small temperature fluctuations of the T ( P ) profile. The observations of the 15 August occultation obtained from Cerro Tololo, ESO, and Las Campanas observatories have been used to compare the atmospheric structure of Uranus at points separated by - 1 0 0 km along the planetary limb. The results will be published in a common paper of the three teams (French et al., 1982). The main result of this comparative study is that the observed correlation of the three light curves is strong. Turbulence does not dominate the structure of the upper atmosphere, which is strongly layered with a horizontal coherence scale of at least several h u n d r e d kilometers. Most (95%) of the refraction effect is produced inside an atmospheric layer, the thickness of which is 2 H (Combes et al., 1971), corresponding to a horizontal coherence length L -~ 4 ~ (R being the planetary radius and H the scale height). Similar conclusions may be derived from French et al. (1978). For Uranus, L - 4000 km. Thus the above conclusion gives confidence in the thermal
profile derived from the inversion method. Comparison of the light curves obtained at ESO, Cerro Tololo, and Las Campanas observatories reveals a large general agreement (French et al., 1982). Nevertheless, our light curve (ESO) shows a loss of signal relative to the other two curves over the interval 40 to 70 sec after the mid-occultation, probably due to a tracking inaccuracy, which results in a lower temperature (by -5°K) from the -80- to -120-km altitude levels. The thermal profile derived by Nicholson et al. (1982b) from Las Campanas observations results in a mean temperature colder by - 2 0 ° K above the 10-2-mbar pressure level. In contrast, the thermal profile derived by French et al. (1982) from Cerro Tololo observations is in good agreement with our result in the upper atmosphere. These differences are due to small but real differences in the observed light curves and to different methods of determining the zero-light and full-light levels. IV.6. Discussion
In view of the various uncertainties in the retrieved temperature profile discussed in Section IV.5, a conservative conclusion may be that the temperature of the stratosphere of Uranus is nearly constant in the 10-3 to 10-2-mbar pressure range with a mean value of 155 - 15°K. Below this the temperature seems to decrease down to 145°K at the 3.10-2-mbar level. From our result and in agreement with similar results from French et al. (1982) and Nicholson et al. (1982b), it may be concluded that the stratospheric temperature of Uranus is, in contrast with previous studies, as high as the stratospheric temperature of Neptune in the 10-2- to 10-3-mbar pressure range. The low value attributed previously to the Uranian stratospheric temperature was based on the Dunham et al. (1980) occultation observations but also to the lack of CH4 and C2H6 emission features at 7.7 and 12 txm, respectively (Gillett and Rieke, 1977). In Fig. 9 we plotted the
15 AUGUST 1980 OCCULTATION BY URANUS "~ 10"/~
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FIG. 9. Comparison between the temperature profiles obtained from the occultation of star SAO 158687 by Uranus on 10 March 1977 (Dunham et al., 1980) and the profiles derived from 15/16 August 1980 occultation (present work). We took three different boundary conditions for these profiles (see Fig. 7) in order to s h o w the clear discrepancy b e t w e e n the 1977 and 1980 results.
profiles obtained by Dunham et al. (1980) and the profiles derived from the present work. Dunham et al. (1980) derived a mean value of the tem_perature of 95°K in the 3.10 -4- to 2.10-2-mbar pressure range as a result of the occultation of SAO 158687 by Uranus on 10 March 1977. It seems almost impossible to relate this large discrepancy to observations uncertainties since the Dunham et al. results were derived from four observations (immersion and emersion recorded at both Cape Town and the KAO), while our result is in agreement with two other independent observations at Las Campanas and Cerro Tololo. Variations in the upper atmosphere of Uranus with time, while unexpected, may be responsible for the observed discrepancy. New observations of stellar occultations are needed to firmly establish such variations effects (Fig. 9). The low stratospheric temperature (95°K) derived by Dunham et al. (1980) was in agreement with the upper limit of the brightness temperature at 8 and 12 I~m obtained by Gillett and Rieke (1977), leading to TB (8 Ixm) < 100°K. It must be examined whether or not our result is in conflict with this upper limit. We have computed the expected emission in the Ch4 v4 band at 8.0 I~m in two cases, which may be considered as limit-cases for the structure of the atmosphere of Uranus (Fig. 10).
1. A CH4 "supersaturated" model similar to the radiative-convective equilibrium model computed by Wallace (1975) with a constant CH4/H2 mixing ratio, with T = BO°K in the stratosphere above the 0.1mbar pressure level. It may be noticed that the related vertical thermal profile is close to the N profile obtained by Courtin et al. (1978) from the inversion of the available infrared brightness temperatures at h > 10 Ixm. Thus it is only necessary to estimate the brightness temperatures resulting from this model at h < 10 Ixm and more especially at 8 Ixm. We obtained TB (8 I~m) close to 110°K, which considerably exceeds the upper limit obtained by Gillett and Rieke (1977). 2. A second model in which CH4 follows its saturation low, similar to Wallace's saturated model (1980) but with a warmer stratosphere (T = 150°K above the 0.1-mbar pressure level). Such a model leads to a thermal profile close to the Courtin et al. profile I (1978) and is also in agreement with ir available data. The discrepancy between I and N profiles is due to divergent observational data at 300 cm -~. So here again only an estimate of TB (8 ~m) is needed. We obtained TB (8 I~m) = 89°K significantly lower than the observational upper limit. So, there is no conflict between Gillett and Rieke's upper limit and the high stratospheric temperature derived from the occultation for a saturated C H 4 distribution.
470
SICARDY ET AL. I
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But in this case (saturated CH4) the stratospheric temperature should be, following Wallace (1975), 125°K at most, and even less if the cooling of the upper atmosphere by C2H6 and C2H2 (not observed but possibly present) is taken into account. Additional heating could be due to non-LTE processes or to the presence of aerosols. Appleby (1980) has computed various nonLTE models for Uranus. From his results non-LTE processes do not seem to be sufficient to explain the observed temperature (Fig. 10). Additional heating could also be due to aerosols. But it may be impossible to maintain an aerosol layer at these altitudes (Dunham et al., 1980). The magnitude of the needed additional heating is not well defined. Indeed, the derived temperature profile depends upon the assumed atmospheric composition. If helium is strongly depleted the temperature profile would shift toward lower temperature by -15°K. From what is known on the
internal structure of the planet and on the lack (or weakness) of the internal energy source on Uranus, such a depletion of helium cannot be excluded. Even if helium is not significantly depleted in the whole planet it may be depleted in the P < 10-2 mbar pressure range due to gravitational separation, which may take place in this range (N - 1014 cm -3) for values of the eddy mixing coefficient of about 105-106 cm 2 sec -~. Such values are plausible by comparison with Jupiter. A detailed aeronomical model of Uranus, including helium depletion but also the photochemistry of C H 4 , C2H6, and C2H2, is needed to explain quantitatively the observational results. This study seems to establish, in contrast with previous studies, that the stratospheric temperatures would be similar in both Uranus and Neptune at P < 10-2 mbar. The lack of CH4 emission at 8 ixm would indicate that the temperature inver-
15 AUGUST 1980 OCCULTATION BY URANUS
sion on Uranus is located at a higher atmospheric level (P < 1 mbar) than on Neptune (P - 10 mbar). New observations at 17.8 and 19.6 I~m by Tokunaga et al. (1982) seem to be in agreement with these qualitative conclusions.
471
COURTIN, R., D. GAUTIER, AND A. LACOMBE (1978). On the thermal structure of Uranus from infrared measurements. Astron. Astrophys. 63, 97-101. DERMOTT, S. F. (1981). The "braided" F-ring of Saturn. Nature 290, 454-457. DUNHAM, E., J. L. ELLIOT, AND P. J. GIERASCH (1980). The upper atmosphere of Uranus: Mean temperature and temperature variations. Astrophys. J. 235, 279-284. CONCLUSION ELLIOT, J. L., E. DUNHAM, AND D. MINK (1977a). The rings of Uranus. Nature 267, 328-330. The mean temperature of the Uranian at- ELLIOT, J. L., R. G. FRENCH, E. DUNHAM, P. J. mosphere in the pressure range between GIERASCH, I. VEVERKA, C. CHURCH, AND C. SA10-3 and 10-2 mbar is about 155 -+ 15°K and GAN (1977b). Occultation of ~ geminorum by Mars. II. The structure and extinction of the Martian upper decreases to 145°K at the 3 x 10-2-mbar atmosphere. Astrophys. J. 217, 661-679. pressure level. This temperature profile ELLIOT, J. L., E. DUNHAM, L. H. WASSERMAN,R. L. would shift toward colder temperature (by MILLIS, AND J. CHURMS (1978). The radii of Ura15°K) if hydrogen is the only atmospheric nian rings ct, 13, ~, 8, e, "q, 4, 5 and 6 from their constituent, due to global depletion of heoccultations of SAO 158687. Astron. J. 83, 980992. lium or to gravitational separation. This high stratospheric temperature is compati- ELLIOT, J. L., J. A. FROGEL, J. H. ELIAS, J. S. GLASS, R. G. FRENCH, D. J. MINK, AND W. LILLER (1981a). ble with the upper limit of the brightness The 20 March 1980 occultation by the Uranian rings. temperature at 8 ~m (Gillett and Rieke, Astron. J. 86, 127-134. 1977) if CH4 follows its saturation law, but a ELLIOT, J. L., R. G. FRENCH, J. A. FROGEL, J. H. ELIAS, D. J. MINK, AND W. LILLER (1981b). Orbits quantitative explanation of such a high of nine Uranian rings. Astron. J. 86, 444-455. stratospheric temperature remains to be ELLIOT, J. L., et al. (1982). In preparation. found. FRENCH, R. G., J. L. ELLIOT, AND P. J. GIERASCH (1978). Analysis of stellar occultation data. Effects ACKNOWLEDGMENTS of photon noise and initial conditions. Icarus 33, 186-202. We thank F. Gutitrrez, at La Silla Observatory FRENCH, R. G., J. L. ELLIOT, B. SICARDY, AND P. (ESO), who promptly wrote a fast acquisition program NICHOLSON (1982). The upper atmosphere of before the observation. We are grateful to J. Appleby Uranus: A critical test of isotropic turbulence and R. French for rereading the text and giving advice, models. Submitted. and also to J. Elliot and P. Nicholson for helpful comGILLETT, F. C., AND G. H. RIEKE (1977). 5--20 micron ments. This work was supported by RCP 544 Anobservations of Uranus and Neptune. Astrophys. J. neaux, by the ATP Planttologie, the Observatoire de 218, L141-LI44. Paris, and the Universit6 de Pads. GOLDREICH, P., AND S. TREMAINE (1979). Towards a theory for the Uranian rings. Nature 277, 97-99. REFERENCES GOLDREICH, P., AND S. TREMAINE (1980). Disk-satelAPPLEBY, J. (1980). Atmospheric Structures o f the lite interactions. Astrophys. J. 241, 425-441. Giant Planets from Radiative-Convective Equilib- HUBBARD, W. B., AND B. H. ZELLNER(1980). Results rium Models. Ph.D. thesis, SUNY, Stony Brook. from the 10 March 1977 occultation of the Uranus BHATTACHARYYA, J. C., AND K. KUPPUSWAMY system. Astron. J. 85, 1663-1669. (1977). A new Satellite of Uranus. Nature 267, 331- KLEMOLA, A. R., AND B. G. MARSDEN (1977). Pre332. dicted occultations by the rings of Uranus, BOUCHET, P., C. PERRIER, AND B. SICARDY (1980). 1977-1980. Astron. J. 82, 849-851. IAU Circular No. 3503. MILLIS, R. L., L. H. WASSERMAN,AND P. V. BIRCH COMBES, M., J. LECACHEUX, AND L. VAPILLON (1977). Detection of rings around Uranus. Nature (1971). First results of the occultation of 13 Sco by 267, 330-331. Jupiter. Astron. Astrophyhs. 15, 235-238. MILLIS, R. L., AND L. H. WASSERMAN (1978). The COMBES, M., L. VAPILLON, AND J. LECACHEUX occultation of BD-15°3969 by the rings of Uranus. (1975). The occultation of 13 Sco by Jupiter. IV. DiAstron. J. 83, 993-998. vergences with other observers in the derived tem- NICHOLSON, P. D., S. E. PERSSON, K. MATTHEWS, P. perature profiles. Astron. Astrophys. 45, 399-403. GOLDREICH, AND G. NEUGEBAUER (1978). The
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rings of Uranus: Results of the 10 April 1978 occultation. Astron. J. 83, 1240-1248. NICHOLSON, P. D., K. MATTHEWS, AND P. GOLDREICH (1981). The Uranus occultation of 10 June 1979. I. The rings. Astron. J. 86, 596-606. NICHOLSON, P. D., K. MATTHEWS, AND P. GOLDREICH (1982a). Radial widths, optical depths, and eccentricities of the Uranian rings. Astrophys. J. 87, 433-447. NICHOLSON, P. D., et al. (1982b). In preparation. TOKUNAGA, A. T., G. S. ORTON, AND J. CALDWELL (1982). New observational constraints on the temperature inversion of Uranus and Neptune. Submitted. VAPILLON, L., M. COMBES, AND J. LECACHEUX
(1973). The 13 Scorpii occultation by Jupiter. II. The temperature and density profiles of the Jovian upper atmosphere. Astron. Astrophys. 29, 135-149. VEVERKA, J., L. H. WASSERMAN, J. L. ELLIOT, AND C. SAGAN (1974). The occultation of 13 Scorpii by Jupiter. I. The structure of the Jovian upper atmosphere. Astron. J. 79, 73-84. WASSERMAN, L., AND J. VEVERKA (1973). On the reduction of occultation light-curve. Icarus 20, 322-345. WALLACE, L. (1975). On the thermal structure of Uranus. Icarus 25, 538-544. WALLACE, L. (1980). The structure of the Uranus atmosphere. Icarus 43, 231-259.