Variations of the stratospheric temperature along the limb of Uranus: Results of the 22 April 1982 stellar occultation

ICARUS 64, 88-- 106 (1985)

Variations of the Stratospheric Temperature along the Limb of Uranus: Results of the 22 April 1982 Stellar Occultation ~ B. SICARDY,*'t M. COMBES,* J. LECACHEUX,* P. BOUCHET,$ A. BRAHIC,*'t P. LAQUES,§ C. PERRIER,$ L. VAPILLON,* AND Y. ZEAU* *Observatoire de Paris, 92190 Meudon, France, t Universit# de Parts 7, France, SEuropean Southern Observatory, La Silla, Chile, and § Observatoire du Pit" du Midi et de Toulouse, 65200 Bagneres de Bigorre. France Received February 3, 1984: revised April 9, 1985 Stratospheric temperature profiles of Uranus were derived from the stellar occultation of 22 April 1982 in the pressure range 5-30 p,bar. The observations were made at the European Southern Observatory, Chile, and at the Observatoire du Pic du Midi et de Toulouse, France with two telescopes in both sites. The study of these profiles confirms that Uranus" stratosphere is warmer than had been expected from radiative models (J. F. Appleby, 1980, Atmospheric' Structures qfthe Giant Planets from Radiative-Convective Equilibrium Models. PhD. Thesis, State University of New York at Stony Brook) and that there has been a general increase of temperature since 1977 (R. G. French, J. L. Elliot, E. W. Dunham, D. A. Allen, J. H. Elias, J. A. Frogel, and W. Liller, 1983, Icarus 53, 399-414). Furthermore, the profiles exhibit a nonisothermal feature with a maximum temperature around the 8-/xbar pressure level. The amplitude of this feature increases linearly with the diurnally averaged insolation (D) up to the observed value (D) -- 0.15. Moreover, the temperature at 8 p,bar, as well as the mean stratospheric temperature, reaches a plateau around the equator of the planet which is far from maximum insolation. For a nominal abundance of methane "0OH4 - 3 × 10 ~ and normal incidence, the UV absorption could compete with the IR methane absorption bands at the pressure level 8/zbar. However, the high temperatures observed even at grazing incidence imply important circulation phenomena to isothermalize distant regions of the planet. Alternatively, the observed profiles may suggest that an optically thin aerosol layer distributed over one scale height is responsible for the temperature maximum at 8 p~bar. The total mass of dust necessary to heat this region up significantly would be a small fraction (6 x 10rag vs 5 × l0 t" g) of the Uranian ring system, which appears then as a possible reservoir of dust. However, a falling rate of - I msec ~ would deplete the rings in a short time (---2 × l0 s yearsl so that a dynamical process is needed to sustain the aerosol layer. ~,, 1985 Academic Press. Inc

1983) already show some trend in the evolution of the mean stratospheric temperature of Uranus (French et al., 1983). In that sense, a continuing survey of such occultations might enlighten "seasonal" variations off Uranus. However, variation vs time may hardly be distinguishable from "geographical" differences. Such differences may be quite interesting in the case of Uranus, in view of its particular obliquity (-98°). During a few years around 1990, the north pole of the planet will roughly face the Sun, probably leading to some complicated meteorology. Different temperature profiles along the

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

The observations of stellar occultations by a planet may provide the thermal profile of its upper stratosphere. So far, five occultations by Uranus have been used to derive the temperature vertical dependence of zones extending between - 2 and -30/xbar (Dunham et al., 1980; French et al., 1982, 1983; Sicardy et al., 1982). These observations, distributed over 5 years (from 1977 to Based on observations collected at the European Southern Observatory, La Silla, Chile, and at the Observatoire du Pic du Midi et de Toulouse, Pic du Midi, France. 88 0019-1035/85 $3.00 Copyright © 1985by Academic Press, Inc. All rightsof reproduction in any form reserved.

URANUS STRATOSPHERIC TEMPERATURE limb of Uranus may then bring some information about the general circulation and the dynamics of its stratosphere. In this paper we shall report simultaneous observations of the same occultation, allowing to probe d i f f e r e n t regions of the planet corresponding to different latitudes and/or insolations at the s a m e time. We shall present the results of the 22 April 1982 occultation by Uranus, observed from two widely separated sites on the Earth (Chile and France, see Section II). The observations are presented in Section II and the reduction method is briefly described in Section III, then the mean stratospheric temperature and the structure of a nonisothermal feature are considered in Section IV. A discussion and some possible interpretations are given in Section V, before the conclusion in Section VI. For comparison, the temperature profile derived from the 15-16 August 1980 (Sicardy e t al., 1982) occultation is also considered in the text. II. O B S E R V A T I O N S

The occulted stars KM 12 and KME 14 corresponding to the phenomena of 15-16 August 1980 and 22 April 1982, respectively, were especially interesting since they were the brightest of the stars mentioned by Klemola and Mardsen (1977) and by Klemola e t al., (1981). Consequently, the good signal-to-noise ratio of the data led to reli-

89

able stratospheric temperature profiles of Uranus. The 1980 occultation was simultaneously recorded at the 2-m telescope of the Cerro Las Campanas Observatory (CLCO, Chile), at the 4-m telescope of the Cerro Tololo Inter-American Observatory (CTIO, Chile), and at the 3.6-m telescope of the European Southern Observatory (ESO, Chile). Detailed descriptions and results are given by French e t al. (1982), Nicholson et al. (1982), and Sicardy e t al. (1982). The 1982 occultation was observed not only from the observatories cited above (CLCO, CTIO, and ESO) but also from the Observatoire du Pic du Midi et de Toulouse (OPMT, France). For the two sets of the 1982 data that we have reduced (ESO and OPMT), two telescopes were used in both sites in order to carefully compare the recordings made at the same location. These comparisons might allow the detection of "isolated events" (i.e., small satellites) or faint material around Uranus. The results of such comparisons will be published elsewhere. The main information about these observations is given in Table I. It should be noted that all the observations were made in the methane absorption bands at 0.9 and 2.2/zm. This allows them to have a small contribution of the planet in the signal, and then to increase the contrast of the occultation. The geometry of Uranus at the time of

TABLE 1

CONDITIONS OF OBSERVATIONS Date

Station

Event o

Telescope

Photometer

Wavelength

15 A u g 1980

ESO

1

3.6 m

h = 2.2 p,m, Ah = 0.5 /zm

22 A p r 1982

ESO

22 A p r 1982

OPMT

I E I E

3.6 m I m 2 m 1m

ESO InSb Photo voltaic Spectrophotometer ESO InSb ESO InSb In Sb As Ga

a 1 = Immersion, E = Emersion.

h h h h

= = = =

2 . 2 / z m , AX = 0.5 /xm 2 . 2 / x m , AX = 0 . 5 / z m 2.2 g m , Ah = 0.5 /~m 0.88 p~m, Ah = 0 . 0 4 / z m

90

SICARDY ET AL. (a) ~(i03 kin) 40

i ~,'

1/ "

,

i: f -":

"

.,oL ~(I03 kln)

80

60

40

20

0

-20

-40

-60

-80

(b)

~/(i03 knl) 40 /

/

20

:\

-20 N

-40

E.._t

"--

80

60

40

20

-

/

0

~(10 3 kin)

-20

.40

-60

.80

FIG. I, Paths of the stars KM 12 and KME 14 relative to Uranus. (a) Occultation of KM 12 on 15-16 August 1980 (b) Occultation of KM 14 on 22 April 1982. Note the effect of parallax between of the observations of ESO (Chile) and OPMT (France) which allows 1o probe different regions oi' Uranus' stratosphere.

the occultations and the paths of the stars KM 12 and K M E 14 relative to the planet are shown in Figs. la and b. The use of two widely separated sites for the 1982 observations (ESO and OPMT) gives four corresponding suboccultation points on Uranus, widely separated as well. The largest distance between two suboccultation points was - 4 5 0 0 0 km whereas the planetary radius is - 2 6 0 0 0 km. The latitude ¢b and the diurnally averaged insolation (D) (in units of the normal-incidence solar constant at

Uranus) of each suboccultation point are listed in Table II. These quantities may be important when modeling the energy budget and the general circulation of the planet's upper stratosphere (see, for instance, French et al., 1983). Also listed in Table 1I are S, the angle between the rotation axis and the subsolar point (S indicates the " s e a s o n " on Uranus) and a, the phase angle of the planet. Since a < 3° at any time, a small fraction of the disk visible from the Earth is in the dark. One of the

URANUS STRATOSPHERIC TEMPERATURE

91

length used for the observation (Elliot et al., 1981a). At h = 2.2/zm, one derives d G E O G R A P H I C A L P A R A M E T E R S FOR T H E 3.5 km and at h = 0.9 /zm, d - 2.2 km. SUBOCCULTATION POINTS Thus, the vertical spatial resolution of our Date Station Event Suboccultation (D) ° Sb ac profiles was at best - 4 km in 1980 and latitude on Uranus - 6 km in 1982. A careful examination of the fine structures (i.e., the spikes) of the 15 Aug 1980 ESO 1 26?5 0.00 23?9 371 immersion and emersion profiles obtained 22 Apr 1982 ESO 1 5?9 0.15 1679 176 ESO E -1572 0.003 1679 176 from the 15-16 August 1980 occultation at OPMT 1 -3?4 0.066 1679 176 CLCO, CTIO, and ESO has shown a strong OPMT E - 1078 0.020 1679 176 correlation between the small details of the a (D) is the diurnally averaged insolation normalized to the normaltemperature profiles (French et al., 1982). incidence solar flux at Uranus. b S is the angle between the subsolar point on Uranus and the rotation This indicates that " l a y e r s " of a few kiloaxis of Uranus (indicates the "season"). meters in thickness, where the temperature Phase angle of the planet. is perturbed by a few degrees, can be maintained in the horizontal direction over a dissuboccultation points, corresponding to the tance as large as - 1 4 0 km. immersion of the 1980 occultation, was in An inversion program using the lightfull darkness ((D) = 0) and the maximum curves presented here yielded temperature value of (/9) that we have probed is (D) profiles of the upper stratosphere of 0.15. Uranus. The inversion method is described by Sicardy et al. (1982) and in more details III. DATA REDUCTION by Vapillon et al. (1973). Important asThe immersion and emersion lightcurves sumptions are made when using this corresponding to the 1980 and 1982 occulta- method: (i) The atmosphere is spherically tions are shown in Figs. 2a-h with a time symmetric, which appears to be valid in resolution of 0.1 sec. The data of 22 April view of the strong layering cited in the pre1982 that we have obtained are somewhat vious paragraph. (ii) The extinction of the less noisy than those of 15-16 August 1980 star is essentially due to differential refracsince the star KME 14 was roughly 20 times tion; absorption and scattering are nebrighter than the star KM 12. (Note that glected. (iii) The atmosphere is a perfect due to a failure in the recording device the gas in hydrostatic equilibrium, mainly com22 April 1982 ESO emersion lightcurve posed of well-mixed hydrogen and helium. from the 3.6-m telescope was lost). Each of Some causes of uncertainties (such as the the lightcurves presents numerous and determination of the separate stellar and strong spikes due to small variations of planetary fluxes in the total recorded signal) temperature (a few degrees) over vertical induce an uncertainty of a few degrees in scales of a few kilometers. The spikes of the temperature profiles. However, the the 1980 lightcurve are higher and narrower main uncertainty comes from the arbitrary than those of the 1982 lightcurves, mainly boundary condition To (temperature at a due to the smaller apparent diameter of the given altitude) necessary to solve the hystar KM 12 at the distance of Uranus ( - 1 . 5 drostatic equilibrium equation. This uncerkm vs - 6 km for the star KME 14). tainty is important in the upper part of the Actually the vertical spatial resolution of profiles, at p - 2 /,bar and may reach the temperature profiles are limited both by -+40°K. However, the uncertainty rapidly the apparent diameter of the star and by decreases as deeper regions are explored, diffraction. The latter smooths any details down to p - 30 /*bar, and represents smaller than d - 2V~--h, where A is the roughly _5°K. Then some uncertainties in Earth-planet distance and h is the wave- the baseline value, i.e., the contribution of TABLE

II

92

SICARDY ET AL.

the planet in the recorded flux, become imTABLE 111 portant. So, we estimate to -+i5°K the unATMOSPHERIC PARAMETERS FOR THE INVERSION certainty in the temperature profiles in the PROGRAMAND DISCUSSION pressure range 5-30 tzbar. For the 1-m tele . . . . . . . . . . . . . . . . . . . . . . . . . . H2: 2 g m o l e i Molecular weight scope of OPMT, the chosen wavelength He: 4 g mole (0.9/xm) was such that the signal-to-noise /).9 A b u n d a n c e of H2 ratio of the data was somewhat worse than 3.7 × 10 24g M e a n molecular weight kt in the other recordings (Figs. 2a-h). In parH2:1.36 × 10 4 Specific refractivity ticular the contribution of the planet was (at 2 . 2 / x m , 1 bar, and 0°C) He: 0.34 × 10 4 then poorly known, leading to important Gravitation 818 cm sec uncertainties in the derived temperature profiles. H o w e v e r , the v a r i a t i o n s of the profiles around a mean value (i,e., the non- by a few parameters: the temperature and isothermal features) are in good agreement pressure at the temperature maximum; the with those derived from the 2-m telescope amplitude of the wavelike structure (well represented by the difference in temperarecording. The different parameters that we have ture between the pressure levels 8 and 13.8 used in the inversion program are listed in /zbar); and the mean temperature in the pressure range 5-30 p~bar. Table III. The maximum temperature at 8 p~bar is IV. R E S U L T S very peaked in the ESO and OPMT immerThe simultaneous observations of the 22 sion profiles and less pronounced in the April 1982 occultation related to widely emersion profiles. This maximum can be separated sites on Uranus give some evi- noted also in profiles derived from previous dence for significant variations of the ther- observations: 10 March 1977 (Dunham et mal profile as a function of the subocculta- al., 1980), 26 April 1981 (French et al., tion point. This is somewhat in opposition 1983), and rather weak although detectable with what is stated in French et al. 11983), in the 15-16 August 1980 immersion profile i.e., that a general circulation in the strato- (Sicardy et al., 1982). In other words the 8sphere is sufficient to isothermalize the up- tzbar maximum has been observed for 5 per atmosphere. Nevertheless, our results years at different locations on Uranus. Fursupport French and colleagues' conclusion thermore, it is well defined in pressure, the that a global secular increase of the strato- dispersion around 8 / z b a r does not exceed 1/zbar. The vertical extent of the associspheric temperature has been observed durated feature is roughly one scale height, ing the past 5 years on Uranus. The structure of the temperature profiles sharply limited from that below. The mean temperature and the maximum shown in Fig. 3 is qualitatively the same: roughly isothermal below the 14-gbar pres- temperature [T(8 tzbar)] have similar behavsure level, then increasing up to a maxi- iors. In Figs. 4a and b T(8 /zbar) has been mum at 8 / z b a r , and then decreasing again plotted vs the diurnally averaged insolation with decreasing pressure. However, the (D) and vs the latitude. T(8 txbar), and also quantitative behavior is quite different from the mean temperature, reaches a plateau one profile to the other, and can be defined close to the equator, i.e., at (D) - 0.08

FIG. 2. Immersion and emersion lightcurves of the 15-16 August 1980 and 22 April 1982 stellar occultations by Uranus. The origin of the flux c o r r e s p o n d s to the zero of the p h o t o m e t e r (no recorded signal). T h e origin of the time axis is as follows for each curve (in UT): (a) 22 h37m00~; (b) 01h58m30.131~; (C) 01h58m30~; (d) 02h35"~0~; (e) 02h06m28.12: (f) 02u17m33.1~: (g) 02h06"~25-09~; (h) 02h17m30 ~. All the c u r v e s have been plotted with a time resolution of 0.1 sec.

-'lux

ia)

Flux

ib)

15 August 1980 Imm ESO 3.6m 2.2 p.m

LO

->2 April 1982 mm ESO 3.6m 2.2 p.m

C > Z C 3.0

> 60

120

180

2/-0

iO

120

0 =: ~o

N

-'lux

d)

Flux

N 22 April. 1982 Imm ES0 lm 2.2 p.m

1.0

22 A p r i l 1983 Em ESO lm 2.2 p.m

m

L

0

Seconds 120

~econds 5'0

120

~

~ _.2

5

3~ c~3

i.J

~o~ ~.0-0

3

3

3

~

~Z o

i

I

L

I

I

n <

o

1>

3~

Q.

~_

i

"IV 1"~1AU~IVJIS

i

J

i

fro

URANUS STRATOSPHERIC TEMPERATURE :

r

(~p,b] I

~Pressure -

I

I

s

1

i

pected to increase from the equator to the pole o f an oblate rotating planet. Considering the atmosphere as isothermal, which is adequate for an error estimate, we have the relation

I

6

\

/

.,~.\\

,

~ "~'~, txg/kT -

,> !, %% /:

1o

,, '_fe ' /

/:.:/'/ I

60

I

100

I

' I

140

Temperature [K : 1

I

180

95

I

220

FIG. 3. T e m p e r a t u r e profiles o b t a i n e d f r o m the light-

curves of Fig. 2. The profiles are labeled (1) 15 August 1980, immersion, 3.6-m ESO; (2) 22 April 1982, emersion, I-m ESO; (3) 22 April 1982, emersion, 2-m OPMT; (4) 22 April 1982, immersion, 2-m OPMT; (5) 22 April 1982, immersion, I-m ESO; (6) 22 April 1982, immersion, 3.6-m ESO. All the 1982 profiles exhibit a wavelike structure with a maximum temperature around the 8-tzbar pressure level. The 1980 profile, corresponding to a suboccultation point in permanent darkness, is essentially isothermal.

which is far from maximum insolation. In contrast the amplitude of this wavelike feature IT(8/zbar)-T(13.8 izbar)] is increasing with increasing diurnally averaged insolation (D) (Figs. 4a and b). Remarkably enough, the immersion profile of the 10 March 1977 occultation ((D) 0.25) exhibits a maximum close to 8 t~bar which is much less p r o n o u n c e d in the immersion profile ((D) - 0.07), following the results reported by Dunham et al. (1980). The same is true for the 26 April 1981 event with a clear maximum at immersion ((D) 0.19) and barely visible at emersion ((/9) 0.004) [see French et al. (1983)]. Moreover, the ESO 1980 immersion profile corresponding to (D) = 0 is essentially isothermal. H o w e v e r , a small effect that we have not so far taken into account could slightly modify the temperature profiles. Namely, we considered that the Uranian gravitational acceleration g was constant all over the surface of Uranus, whereas it is ex-

dz, / v cm -I dz /

(1)

where z is the altitude, v(z) is the refractivity profile (directly derived from the occultation lightcurves),/z is the mean molecular weight, and k is the Boltzmann's constant (Vapillon et al., 1973). Keeping g constant as the latitude increases will thus erroneously u n d e r e s t i m a t e T, the relative error being 8 T / T ~ - 8g/go, where go is the value o f g at the equator and 8g is the variation of g between the equator and latitude ~b. This is exactly the trend observed in Figs. 4a and b, so that this effect should be quantitatively estimated to know whether it biases our conclusion. The Uranian gravitational potential at latitude 4> and distance r from the planet center is U(r, ~b) = - (GMp/r)[l - (R/r)2J2P2(sinqb)] - r 2 cos z ~boJZ/2 erg (2) where G is the gravitational constant, Mp the planet mass, R the equatorial radius, J2 the second coefficient in the zonal harmonic expansion o f the planet field, Pz Legendre's polynomial of order two (higher order terms in J4P4, J 6 P 6. . . . have been neglected), and to the rotation angular velocity of the planet. Furthermore, to first order in f, the geometrical oblateness of Uranus, we have r = R(I - f s i n 2 ~b), and (2) yields, to first order in J2, f , and m =

R3toZ/GMp,

g(~b) = g0[1 + ( 2 f - ~J2 + m) sin 2 ~b] cm sec -2,

(3)

known as Clairaut's theorem. The methods of determination of f , J2, and m are reviewed in Elliot and Nicholson (1984) and examined in more detail in Elliot et al. (1981b) and in Franklin et al. (1980), from which we obtain f = (2.4 -+ 0.3) x

96

SICARDY ET AL. [

i

{a) 180

T

I

i

(b)

T(K} \

160

180

T (8~b)

//

/

"-

/ o/ /

14.0

/

/

// &ILK)

/ /

40

160

•

/ •

ii

/

/ /

AT =T(8 ~bl_'f (13 8 p.b)

/

120

t

/ -

/

)/

20

1~0

0

120

/

/

) 100 L . 0.0

i 0.1

I 02

0.3

i -20

" 1 '°'?°",.

T (81~b)

0

20

Fl•. 4. Ca) Variations of the maximum temperature T(8/×bar) vs the averaged diurnally insolation
10-2, J2 = (3.349 +- 0.005) x 10 3, and m = (3.6 + 0.1) × I0 2. Equation (3) then reads

g(4)) = g0[l + (6.7 + 0.1) x 10 -2 sin 2 ~h] cm sec ~'. (4) At the highest latitude that we have probed (4) = -2675), we thus derive 8g/go 1.3 x 10 -2 so that the correction to all the profiles we have c o m p u t e d should never e x c e e d - 2°K. As a c o n s e q u e n c e , the trend o b s e r v e d in Fig. 4b is little affected by the variations of g. This effect is noticeable only if 4) -- -+ 90°, since then 8g/go - 7 × 10 2 requiring a correction of - 10°K on the t e m p e r a t u r e profiles. N e v e r t h e l e s s , w h a t e v e r the latitude, longitude, or insolation m a y be, the mean stratospheric t e m p e r a t u r e in 1982 is higher than it was during the 1977 occultation (Dunham et at., 1980). This indicates a

global variation of the stratospheric temperature with time as previously suggested by the results of the 1980 occultation (Sicardy et al., 1982). French et al. (1983) have shown that during the last 5 years, the mean t e m p e r a t u r e has increased by tens of degrees. The reported results support their conclusion. M o r e o v e r , as suggested by French et al. (1983), the mean t e m p e r a t u r e variations with time are, in general, larger than the variations with latitude or insolation. So, the d e p e n d e n c e of the thermal profile on these two p a r a m e t e r s is readily visible only with simultaneous observations of the same occulation. Finally, it must be recalled that the observed stratospheric t e m p e r a t u r e s are significantly larger than e x p e c t e d from radiative models, even for e x t r e m e n o n - L T E cases (Appleby, 1980) for which the tern-

URANUS STRATOSPHERIC TEMPERATURE perature may reach at most 125-130°K in the pressure range considered here. Moreover, strong nonisothermal features are not predicted by current radiative models. In conclusion, from the observed stellar occultations within the last 5 years, including those reported in this paper, it was found: 1. The stratospheric temperature of Uranus is higher and less isothermal than predicted by radiative models. 2. A global temperature variation in the stratosphere of tens of degrees has taken place in a very short time. 3. Nevertheless, at a given time, the mean stratospheric temperature reaches a plateau at the equator or, alternatively, at (D) - 0.07 which is far from maximum insolation. 4. At the same time each profile presents a maximum at 8 t~bar and the amplitude of the corresponding wavelike structure (extending over one scale height) seems to be correlated with the insolation. V. DISCUSSION

Before discussing the main conclusions of the previous chapter, it must be emphasized that the inversion procedure basically leads to the variations of T/I~ vs pressure or altitude, where /z is the mean molecular weight of the gas. Thus, as pointed out in Sicardy et al. (1982), the derived temperature profiles depend upon the assumed atmospheric composition. A significant depletion of helium in the stratosphere of Uranus cannot be excluded, either due to gravitational separation possible at this pressure range or to a global deficiency in the whole atmosphere which may be related to the weakness of the internal energy source in Uranus. Such a helium depletion would shift all the temperature profiles toward lower values by an amount -15°K, in better agreement with radiative models. On the other hand, even the large values derived for a nominal atmospheric composition (HE/He = 0.9) do not conflict with infrared brightness temperature measure-

97

ments in the 7.7-/xm CH4 band (Gillet and Rieke, 1977) nor with more recent observations around 20 /xm (Tokunaga et al., 1983). This consistency is valid if CH4 follows its saturation law, but supersaturated scenarios are currently discarded (Sicardy et al., 1982). 1. Major Heating Mechanisms Three types of mechanisms may be invoked for heating the stratosphere of Uranus in the probed pressure range: photochemical radiative equilibrium, aerosol heating, and dissipation of mechanical energy. Dunham et al. (1980) have ruled out the possibility of efficient aerosol heating because even small grains would fall out too quickly. French et al. (1983) have shown that radiative processes are unlikely to be prominent mainly in view of the long radiative time constant in this region of the Uranian atmosphere. Each of these conclusions are reviewed in the following discussion. 2. Dissipation o f Mechanical Energy Wallace (1983) has demonstrated that the seasonal variations of the insolation cause significant changes in the effective temperature of Uranus. This is due to the inclination of the polar axis and to the weakness of the internal energy flux of the planet. Such seasonal changes could reach - 5 ° K at the poles and -0.5°K at the equator along one orbital period. These variations are related to similar local temperature changes in the deep atmosphere (several atmospheres) and might be drives for temperature variations in the stratosphere even if the radiative time constants are strongly different. The detailed mechanisms of such a relation are unknown at the present time. French et al. (1983) have recently published a comprehensive analysis of heating mechanisms by dissipation of waves in the region under study. In particular they have shown that dissipation of short wavelength waves ( - 6 km) of small temperature amplitudes ( - I ° K ) could produce the observed

98

SICARDY ET AL.

heating in the upper stratosphere. This mechanism requires quite a low value of the eddy diffusion coefficient in the probed region (K < 3 x 104 cm 2 sec 1), which is not implausible for a planet with no significant internal energy source. Nevertheless, in the absence of additional data it remains impossible to relate this mechanism with the observed behavior of the temperature profiles (variations with insolation, altitude, latitude, and time).

3. Photochemical Radiative Equilibrium In view of the high absorption coefficients exhibited by H2, He, and CH4 in the UV, we investigate the possibility of heating the atmosphere of Uranus through a UV absorption of solar radiation by this species, in the pressure range considered in this paper ( - 5 - 3 0 gbar). Our goal is then to compare, in order of magnitude, the resulting heating rate with the heating/cooling rate due to the IR absorption/radiation bands of methane. For purposes of simplicity, we consider that the atmosphere is isothermal (temperature T) and that the relative abundances of H2, He, and CH4 are constant. Furthermore, some c o m m o n quantities are used in the French et al. paper (1983) and in ours. W h e n e v e r possible, the same numerical values are used in order to compare more readily their results and ours, in particular in terms o f heating/cooling rates. IR heating. The main contribution of IR heating by methane comes from the v3 (3.3/xm) absorption band, above the 10-/xbar pressure level (see, e.g., Wallace et al., 1974; Appleby, 1980). The amount of incident solar flux absorbed per unit length in the vertical direction (flux divergence) by the species i is (French et al., 1983) (dTrF/dZ)iR = rli(n/no) f~b(D) erg cm ~ sec i

(5)

where ~'F is the normal incident flux (erg cm -2 sec-~), ~/i is the relative abundance of the absorbent, n is the atmospheric number density (cm-3), no is Loschmidt's number,

fx is the incident solar flux per wavelength interval (erg cm -2 sec -~ /xm -~) normal to itself, at the distance of Uranus, b is the band strength (/xm cm i am t), and (D) is the mean diurnal insolation normalized to the solar constant at Uranus. It is important to note that Eq. (5) assumes that the band remains optically thin, which overestimates (dTrF/dZhR, especially in those regions where the solar illumination is grazing. UV heating. Moreover, species like H2, He, and CH4 exhibit strong absorption coefficients in the ultraviolet wavelengths. These coefficients may be found as a function of wavelength in Prinn (1970), and it appears that the main absorbent is He below 500 .A, replaced by H2 between 500 and 1000 A, then by CH4 between 1000 and 1500 ,~. The UV normal optical depth of the species i above the altitude Z is given by • i(Z) = f l ni(u)/nokidu

n i(Z) / nokin

(6)

where ni(Z) is the number density (cm 3) of i at level Z, k~ is the absorption coefficient (cm 1) of i, and H is the scale height (cm). For typical values of kr~e and kn2 ( - 5 0 cm -I am 1) below, respectively, 500 and 1000 ,~, one finds that the optical depth one is reached for each of the species at nno 10 J1 cm -3 and nile -- 10 I1 cm -3 corresponding to pressure levels of - 2 × 10 2 and 2 × 10 -3 /zbar, respectively, i.e., far above the occultation region. The UV photons between 1000 and 1500 h can go further down since the normal optical depth one is reached for CH4 at ncH4 - 8 × 109 cm 3 taking kcH4 -- 500 cm -I a m - t This corresponds to a pressure of p -- 1.6 ×

10 4/'/~CH4/~bar.

(7)

Assuming that the abundance of methane is constrained by its saturation vapor pressure (SVP), one can estimate ricH4 - 3 × 10 -5 (Appleby, 1980) thus p - 5/zbar. H o w e v e r , in view of the very oblique incidence of the solar rays near the limb of

URANUS STRATOSPHERIC TEMPERATURE the planet, it is the slant-path optical depth which must be considered. Thus, the instantaneous solar flux divergence due to UV absorption by species i is given by

(dTrF/dZ)ov = rliki(n/no)f~,2fxdh

exp(-

,'gi/p, )

erg cm -3 sec 1 (8) where hi and h2 give the spectral range over which the absorption takes place a n d / x is the direction cosine of the solar rays relative to the local vertical. The quantity of interest is the diurnally averaged value of (dcrF/dZ)uv that we denote by (drrF/dZ)uv. The term to be averaged in Eq. (4) is the exponential

99

TABLE ADOPTED

PARAMETERS

S o l a r c o n s t a n t at Uranus Parameters for the blackbody radiation of the Sun ~ Abundance of methane U V a b s o r p t i o n coefficients

Cp b (v3 C H 4 b a n d ) T H " Assumed

IV

FOR HEATING

f N C2 To rtcn4

-

kn 2 krt c = kcH4 = 1.17 × 0.3 tim 140°K 65 k m

3.70 x 2.38 × 1.43883 5770°K 3 x 10

PROCESSES

103 e r g c m z s e c i 10 ~2 e r g cm'- s e c cm °K ~

50cm 'am ' 50cm 'am a 500 cm ' am ' lOSergg I°K t cm ' am t

to r a d i a t e l i k e a b l a c k b o d y .

In all the calculations above, we did not take into account the Rayleigh scattering optical depth Ts of H2 and He. The following where P = 2~-/~0 is the rotation period of the order of magnitude computation shows that planet and where ~ is given by tx = sin 4~ ~-s remain actually negligible. The Rayleigh cos S + cos 4~ sin S sin tot. (Note that absorption coefficient o-~ may be found in with these notations, we have (D) = Allen (1973): o-~ - 3.31 x 10 '8 v~/no (n/no)/ 1 h4m c m -1, where v0 is the refractivity at L,., .o ixdt. STP, n is the total number density of the To compute the integral in Eq. (8), we gas, and k is the wavelength. Table III gives assumed that the Sun radiates like a black- v0 - 1.26 x 10 -4 so that ~'s (between infinity body at temperature To: fx = (N/h 5) exp(C2/ and pressure level p) is - 5 . 3 5 x 10 -13 (Ptzbar 4 hTo - l) where C2 is a constant and N a Hcm)/(h~,mT). At P = 10/zm and T - 140°K, w i t h H - 6.5 x 106cmand h = 0.1/xm, one normalizing factor chosen so that f~fxdh is obtains zs - 2 x 10 -3 , which can be nethe solar constant at Uranus. The methane glected in view of the results provided by abundance was set at 3 x 10 -5 and the other Eqs. (6) and (7). This approximation renumerical values we used are in Table IV. mains valid at any incidence angle since On the other hand, the integral in Eq. (9) both optical depths are multipled by l//x was computed numerically for different lat- when the solar rays are inclined with reitudes on Uranus. The results are displayed spect to the local vertical. in Fig. 5 where both (dTrF/dZ)m and (d~rF/ Interestingly enough, the pressure level dZ)uv have been plotted against pressure. at which the UV absorption overcomes the It appears that close to the pole, where IR absorption for normal incident solar flux the solar rays are nearly vertical, the lies close to the maximum temperature obamount of energy absorbed in the UV served on the profiles displayed in Fig. 3. would o v e r c o m e the IR absorption around H o w e v e r , the corresponding suboccultathe 10-~bar level. This situation varies tion points on Uranus would have received slowly until the latitude - 2 0 ° is reached. a relatively small amount of energy through Then, the energies absorbed both in the IR IR and IV absorptions on the date they and the UV drop sharply as the diurnally were observed. Thus the thermal structures averaged insolation (D) and the UV slant- exhibited in Fig. 3 could be remnants from path optical depth ~-i//xtend to 0 and infinity, the time when these regions were more direspectively. rectly lit by the Sun. Another alternative is ( e x p ( - ~'i/Ix)) = ~

.,-0 e x p ( -

~i/l~)dt

(9)

100

SICARDY ET AL. ;

i

i

i

Pressure (#b)

i

1~

22APRIL1982

/

~CH4=3xI0-5

+

z5 °

' / ~,,

f.j~j/J"

20

30

~

+

,

-

,

FLux divergence (erg,cm -3 s -1) I 10-13

I 10-12

i01 11

l

10-10

I 10-9

I 10-8

--

FiG. 5. Solar flux divergences due to UV absorption by m e t h a n e (solid curves), and to IR absorption by m e t h a n e (dashed curves) as a function of pressure [see Eqs. (5) and (8), respectively]. T h e curves have been c o m p u t e d for various latitudes on U r a n u s (see labels) and correspond to the configuration of the planet of April 1982. T h e m e t h a n e a b u n d a n c e was a s s u m e d to be ~cH+ = 3 × 10 ~.

that important p h e n o m e n a of circulation are able to r e p r o d u c e close to the equator t e m p e r a t u r e profiles existing in other more illuminated regions. A possible test of such h y p o t h e s e s is to evaluate the heating/cooling rates due to the different absorptions and radiations and c o m p a r e the results with the observations. The total heating rate (i.e., in the IR and the UV) due to m e t h a n e m a y be approxim a t e d by (French et al., 1983) (dT/dt)h ~ ( d ~ F / d Z ) h / ~ c v n °K sec ~ (10)

where (dlrF/dZ)h = (dTrF/dZ)m + ( d ~ F / dZ)uv and cp is the specific heat per gram at constant pressure. We c o m p u t e d (&rF/dZ)h as a function of latitude for different years (from 1974 to 1982) at the fixed pressure level of p = 8 ~bar. Then the heating rate given in (I0) m a y be written as (dT/dt)h ~ O. 18

10 - 9

(d~r F/dZ)h erg cm 3 sec

°K y e a r i.

(11)

The cooling rate d u e to the ~'4 (7.7-~m) m e t h a n e emission band is also found in F r e n c h et al. (1983). Taking again ~/cu4 = 3

× 10 -5 and T = 140°K, one finds a cooling rate of (dT/dt)~ ~ 10°K year ~

(12)

at p - 8/~bar. Figure 6 shows that the cooling would be largely dominant in all the regions that we have probed since we get (dT/dt)h ~ 0.2°K year ~ for all the suboccultation points. One can see that the regions illuminated under grazing incidence would not have received a significant a m o u n t of energy for quite a long time. For instance, the point at latitude ~b = -15°2 would not have received in April 1982 the energy a b s o r b e d at the same date at 4~ =- 5 °9 for 6 years or so. This interval of time reaches 7 years for the 15 August 1980 ESO immersion profile. Although Fig. 4 shows a decrease of t e m p e r a t u r e as one probes lower and lower latitudes, the drop of temperature is still slow in view of the cooling rate of 10°K y e a r -t estimated in (12). The 15 August 1980 profile is an e x t r e m e case since it exhibits a m e a n t e m p e r a t u r e as high as - 1 5 0 ° K although it would not have absorbed in the IR and the UV for several years. U n d e r such circumstances, circulation p h e n o m e n a are needed in order to

URANUS STRATOSPHERIC TEMPERATURE

101

10-8

dance o f - 3 x 10-5? If not, as it seems to be the case, is it possible to infer some quantitative conclusions as to the importance of circulation in the Uranian upper atmosphere?

10-9

4. Aerosol Heating

i

i

FLux divergence (erg.cm -3. s -1 )

p = 10-10

8pb

T/CH4 = 3 x 1 0 - 5

10-11

10 -12

10-13 Latitude (*)

-6'0.

_3'00

60

3'0.

6'00

9'o"

FIG. 6. Solar flux divergence due to U V and IR absorption by m e t h a n e at p = 8/zbar, as a function o f latitude on U r a n u s , for different years (see labels). The dots indicate the points probed during the 22 April 1982 occultation. The flux divergence m a y be directly translated in heating rate t h a n k s to Eq. (11). T h e methane a b u n d a n c e w a s a s s u m e d to be "0CH4 = 3 × 10 -5.

isothermalize the upper atmosphere of the planet. Our model remains clearly too crude for further conclusions. However, we believe that UV absorption should be taken into account in radiative transfer models dealing with pressures as low as -10/zbar. The following points would be worth investigating: (i) Is the UV absorption by methane sufficient to heat up the upper atmosphere as high as -160-170°K around the 8-/zbar level? As long as we can estimate, Eq. (1 I) would give a heating rate of - 3 ° K year ' near the pole of the planet, comparable to -10°K year -~ from Eq. (12), but not yet sufficient to balance the cooling rate for many years. (ii) Is the decrease of temperature observed close to the limb of the planet (Fig. 4) consistent with a methane abun-

We now consider the effect of dust on the thermal balance of the atmosphere. There is some observational evidence for dust in planetary atmospheres [see, for instance, the review by Appleby (1980)]. Thermal implications of absorption by dust have been investigated by Wallace et al. (1974). These authors find that, if distributed above the 100-/xbar level and if it absorbs -15% of the incident solar flux, a dust layer may heat up the surrounding atmosphere 10 times more efficiently than methane in the IRo This would increase, for instance, the stratospheric temperature of Jupiter from 170 to -250°K in the pressure range 1-100/xbar. However, some points should be explicited such as the possible mechanisms to transfer energy from a grain to the gas and the possible origin of dust in the atmosphere. This discussion proceeds in two steps: first, we consider the effect of dust on the energy balance of the gas and second, we estimate the quantity of aerosols necessary to significantly heat up the atmosphere; we then discuss a possible scenario of replenishment of such aerosols. As in Section IV.3, we deal with orders of magnitude and we consider the simplest possible model of dust layer. Namely, we investigate the effect of a homogeneous dust layer distributed over one scale height between the pressure levels 15 and 1.5/.tbar and composed of identical spherical grains of radius a. The adjustable parameter is then the total vertical optical depth, r0, of the layer. This model is clearly ad hoc, but our main goal is to estimate such simple quantities as z0, the number density of particles, and the total mass of the layer, and to see whether significant heating by dust requires realistic values of these quantities. For simplicity, we set the origin of alti-

102

SICARDY ET AL.

tudes Z at p = 15 ~bar. The incident solar flux normal to itself at level Z isf~ exp - (rd /~)(1 - Z/H), and we denote the diurnally averaged value of this quantity @,). At equilibrium the energy balance tbr one particle reads ,B.a 2

fx Qx(fx)dh + 4"n'a2 fx [ F x ( T g ) - F~(Tp)] Qxdh + 41raZC(Tp, Tg) = 0

(13)

where Qx is the absorption efficiency factor, Fx is the b l a c k b o d y emittance at wavelength X, and C (Tp, Tg) is the flux of collisional energy (erg cm -2 sec 1) transferred from the gas at t e m p e r a t u r e Tg to the particle at t e m p e r a t u r e Tp. We consider a typical radius of particles a ~ 0.1 /zm. Perfectly spherical and homogeneous grains are not e x p e c t e d to absorb and radiate if the characteristic quantity x = 2rca/h is less than unity. So Qx is equal to ~1 for h < 0.6 ~ m and to ~ 0 for h > 0.6/xm. As a c o n s e q u e n c e , the grains are able to a b s o r b a significant part of the solar spectrum but remain unable to radiate efficiently this energy in the infrared. Thus, the grains are heated up to a t e m p e r a t u r e somewhat higher than the b l a c k b o d y t e m p e r a t u r e at the distance of Uranus (~60°K) and the energy a b s o r b e d by the particles must be released through direct interactions between the grains and the surrounding gas molecules [see last t e r m of Eq. (13)]. We estimate the third term C (Tp, Tg) by assuming that during a collision p a r t i c l e molecule, the gas molecule is actually absorbed for a short while and then released at " t e m p e r a t u r e " Tp. The energy transferred at each collision is then on an average ~ k (lg - Tp), where k is B o l t z m a n n ' s constant. The thermal collision rate can be calculated in a purely kinematic approach since the molecular m e a n - f l e e path (~5 cm at p ~ 10 /xbar) is m u c h larger than the particle radii (assumed smaller than ~1 Ixm). This collisional rate is given by 41rr2vgn/6 w h e r e Vg is the mean velocity of molecules in the Boltzmann distribution (Vg

It immediately follows that

= (8kTg/~l,~)l/2).

C( Tp, Tg) = Vgp( Tg - Tp)/6 Tg erg cm : s e c - ' .

(14)

With Tg - 140°K a n d p = 8 p~bar, one obtains C(Tp, Tg) - 103 (Tg - Tp) erg cm 2 sec--l. F u r t h e r m o r e , expecting Tp - Tg, we can write

f o~,., [F~(Tg) ) - F~(To)ldX - 2 × 10 73(T4g - T 4) e r g c m 2 s e c i.

(15)

This shows that the collisional term actually o v e r w h e l m s the b l a c k b o d y r a d i a t i o n absorption term in Eq. (13). Furthermore, (0.6,~m

with typical values of Jo

Qx(j~)dx ( < 4 x

103 erg cm -2 sec-~), one can see from Eq. (14) that Tp - Tg remains of the order of a fraction of a degree, thus validating the assumption Tp - - Tg. Thus, in such a model, all the solar energy a b s o r b e d by the grains is provided to the surrounding gas, so that the solar flux divergence due to the dust at level Z is given by

f

( J , 6 , u m

(dTrF/dZ)~ = ~o

Q~(f~)dX

(To~H) e x p [ - (%/H)(I - Z/H)] erg cm 3 sec-~.

(16)

We h a v e c o m p u t e d numerically the diurnally a v e r a g e d value (dTrF/dZ)a at the level corresponding to p = 8 /~bar. The results are displayed in Fig. 7 where (d~F/dZ)~ is plotted against latitude for different years. This figure is thus the equivalent of Fig. 6. We have chosen an optical depth ~'0 of 7 x 10 -5 so that the flux divergence at high latitudes is the same in the two figures. Otherwise stated, this value of r0 corresponds to the limit a b o v e which heating by dust and by IR + U V methane absorption are competing. Owing to the very small value of the argument of the exponential in Eq. (16), the curves corresponding to other values of ~'0

URANUS STRATOSPHERIC TEMPERATURE

10-8

103

tent with the t e m p e r a t u r e profiles displayed in Fig. 3 w h e r e the 1980 profile is not clearly cooler than the other 1982 profiles. We n o w estimate the other physical characteristics o f this possible dust layer. First, the numerical density na of the grains is given by

FLux divergence (erg cm

~

q 10-9

na -- T0/(TrHa 2) particle c m - L

(17)

p=gpb

10-lo

And the corresponding aerosol density in the a t m o s p h e r e would be

T/CH4= 3x10 -5

Pa = ~Trppa3na g cm -3

(18)

10-11

10-12

~el ~=

=~

10-13 Lotitude (*)

-60.

-3'0.

;*

3'00

6~

~'0,

FIG. 7. Solar flux divergence at p = 8/zbar due to an aerosol layer of optical depth 7 x 10-5 (see text), as a function of latitude on Uranus, for different years (see labels). Otherwise equivalent to Fig. 6. are easily obtained by translation along the logarithmic scale of Fig. 7. The curves of Figs. 6 and 7 exhibit the same qualitative behaviors, but rather different q u a n t i t a t i v e behaviors: (dTrF/dZ)a remains essentially constant f r o m ~b = 90 ° until a latitude v e r y close to the value corresponding to p e r m a n e n t darkness (i.e., - S ; cf. Table II), then drops to zero rapidly. This is due to the low optical depth of the layer considered here. An important c o n s e q u e n c e of this b e h a v i o r is that regions illuminated u n d e r very grazing incidence can still be significantly heated up by the layer. F o r instance, the 15 August 1980 E S O i m m e r s i o n suboccultation point (~b = -26°5) would h a v e received less than one y e a r before it was o b s e r v e d , as m u c h energy as the 22 April 1982 E S O emersion suboccultation point (th = -15°2) at the date w h e n it was o b s e r v e d . In view of a cooling rate of - 1 0 ° K y e a r -l, this is consis-

where pp is the density of the material constituting the particles. With r0 = 7 × 10 -5 a n d p p = 3 g cm -3, one obtains na - 3 × 10 -2 particle c m -3 and pa - 4 × 10 16 g cm-3. Figure 4 shows that this dust layer should extend at least f r o m latitude - 1 0 ° to latitude + 10 °, which c o r r e s p o n d s to a strip of width - 1 0 , 0 0 0 k m on Uranus. The minim u m total m a s s of aerosol involved is thus ma ~ 27rRWHpa g

(19)

w h e r e R - 26,000 k m is the planetary radius. F r o m Eqs. (18) and (19), one obtains a minimal m a s s ma of - 4 × 10 l° g. T h e question is of course to k n o w what might be the origin of such aerosols. Phen o m e n a such as polymerization of molecules or c o n d e n s a t i o n o f droplets cannot be investigated at the present time, since very little is k n o w n about the presence and a b u n d a n c e of minor constituents in the upper a t m o s p h e r e of Uranus. We consider the possibility o f replenishing such a layer f r o m the outside, i.e., with particles of the envir o n m e n t of the planet, spiraling inward through P o y n t i n g - R o b e r t s o n and p l a s m a drags. A possible reservoir for such particles could be the ring s y s t e m of Uranus, since halos o f dust h a v e already been associated with Jupiter and Saturn rings [see the review b y Burns et al. (1984)]. The currently estimated m a s s of Uranus rings, m -- 5 × 1018 g (Goldreich and Tremaine, 1979), would largely o v e r c o m e the m i n i m u m m a s s of aerosols required to significantly heat the a t m o s p h e r e in the pres-

104

SICARDY ET AL.

sure range 1.5-15 /xbar. H o w e v e r , in the absence of any other m e c h a n i s m , the particles will fall d o w n so that the dust layer should be p e r m a n e n t l y replenished. The particles will reach a terminal velocity Vp under the action of gravity and viscous drag f r o m the gas. As we shall see, Up is much smaller than the m e a n thermal velocity of the molecules Vg so that we are dealing with Epstein drag. A spherical grain undergoes in such a case a net viscous force 47r Fv ~ ~-- pgr2VgVp dyn

(20)

where pg is the local density of gas (g cm 3). This formula leads to a terminal velocity of Vp - (pp/pg)(r/og)g cm sec i

(21)

which yields v o - 140 cm sec ~ at p ~- 8 /zbar with Pp - 3 g c m -3 and a - 0. I /xm. F o r icy grains, Vg - 30 cm sec ~. This velocity is quite smaller than the mean thermal velocity of molecules, Ug "~ 1 0 0 T I/2 "~ 1200 m s e c - ~. Previous estimations by D u n h a m et al. (1980) gave a m u c h larger terminal velocity ( - 7 5 m sec 1). H o w e v e r , the formula they used Up - (2 rg pp/3 pg)l/2 is valid only if Up Vg, which is not the case here. Such a terminal velocity would give a mass flux integrated o v e r all the layer of M~ = 2rrRWpavp g s e c i

(22)

and numerically, Ma - 9 x 105 g sec ~. This flux would deplete the rings in ~2 x 105 years, which is unreasonably short compared to the age of the Solar System. Even a meteoritic flux c o m p a r a b l e to that received on the Earth ( - - 1 0 -16 g c m 2 sec i: Hughes, 1978) would provide an incoming mass of only ~ 3 x 10 3 g sec i in the layer considered here. Thus, although the quantity of dust necessary to significantly heat up the stratosphere of U r a n u s is v e r y small c o m p a r e d to the m a s s of the rings, dynamical mechanism is still needed to sustain the aerosol layer. On the other hand, sustaining such an

aerosol layer would require typical velocities in the gas o f - 1 m sec -1. At the present time, such p a r a m e t e r s as the eddy diffusion coefficient K are poorly k n o w n and furthermore, no physical m e c h a n i s m which could account for such vertical velocities can be proposed. vI. CONCLUSION The o b s e r v a t i o n of the 22 April 1982 stellar occultation by Uranus allowed us to probe at the same time four widely separated points in the upper stratosphere of the planet. The corresponding temperature profiles h a v e been derived and yield the following main conclusions: I. As established from previous stellar occultations, the stratosphere of Uranus a p p e a r s to be w a r m e r than expected from radiative models in the pressure range 5-30 /xbar (cf. A p p l e b y , 1980). 2. We confirm the general increase of t e m p e r a t u r e noted by French et al. (1983), f r o m 1977 to 1981. 3. S u r i m p o s e d to this general trend is a variation of t e m p e r a t u r e with the geographical position of the probed region. The m e a n t e m p e r a t u r e first increases with diurnally a v e r a g e d insolation at negative latitudes and then reaches a plateau after the equator which is far from m a x i m u m insolation. F u r t h e r m o r e , the profiles exhibit a nonisothermal feature with a m a x i m u m temperature around the 8-/xbar pressure level. This m a x i m u m has the same behavior as that described a b o v e for the mean temperature. H o w e v e r , the amplitude of this wavelike feature seems to increase with diurnally averaged insolation; this property is confirmed by the immersion profile of the 1980 occultation, corresponding to permanent darkness, which is essentially isothermal. S o m e order of magnitude calculations have been made in this p a p e r to test some possible heating mechanisms: 4. We have found that the strong UV absorption b y m e t h a n e can c o m p e t e with the

URANUS STRATOSPHERIC TEMPERATURE IR methane bands in the atmospheric thermal balance around the pressure range 1-10 /zbar, assuming a relative abundance of "0CH4= 3 X 10 -5. It should be interesting to include this effect in more sophisticated radiative transfer models to see whether or not such an absorption could account for a maximum temperature as high as 160170°K. However, the observed temperature profiles correspond to regions of grazing incidence with important slant-path UV optical depth and thus small absorption. Thus, if due to UV heating, the shape and mean temperature of the profiles would require important circulation phenomena in order to "transport" high temperatures from well-illuminated regions to the limb of the planet. 5. Such circulation phenomena are not required if we assume that the heating is due to an optically thin layer absorbing a significant part of the solar spectrum, because an important absorption would still occur at very grazing incidence. We have supposed that this layer is composed of dust particles (radius: 0.1 gm) which can absorb or emit significantly energy only at wavelengths h < 0.6 p.m. The resulting heating can compete with IR and UV absorptions by methane if the optical depth of the layer exceeds - 7 × 10 -5, requiring a minimum total mass of dust of - 4 × 101° g. A possible origin for such aerosols could be dust associated with the Uranian ring system. However, a mechanism would be needed to sustain such an aerosol layer since the falling rate of the particles ( - 1 m sec -l) would require a permanent replenishment which would rapidly deplete the rings. In any case, it appears that simultaneous observations of a stellar occultation from widely separated sites on the Earth give some relevant information about the geographical variations of temperature on the planet under study. More specifically, we have shown the existence of a hot layer in the upper atmosphere of Uranus. The properties and behavior of this layer will be bet-

ter known as future observations achieved.

105 are

ACKNOWLEDGMENTS We thank D. Carriole, M. L. Chanin, R. Courtin, D. Gautier, C. Parisot, and Ph. Waldteufel for many helpful comments and discussions concerning Section V of this paper. We are grateful to two anonymous referees for constructive criticism and for several suggestions to improve the paper. REFERENCES ALLEN, C. W. (1973). Astrophysical Quantities, p. 93. Oxford Univ. Press (Athlone), London/New York. APPLEBY, J. F. (1980). Atmospheric Structures of the Giant Planets from Radiative-Convective Equilibrium Models. PhD. Thesis, State University of New York at Stony Brook. ATREYA, A. K., T. M. DONAHUE, AND M. C. FESTOU (1981). Jupiter: Structure and composition of the upper stratosphere. Astrophys. J. 247, L43-L47. BURNS, J. k . , M. R. SHOWALTER, AND G. MORFILL (1984). Ethereal rings: Jupiter's and others. In Planetary Rings (R. Greenberg and A. Brahic, Eds.). Univ. of Arizona Press, Tucson. CARLSON, R. W., AND D. L. JUDGE (1976). Pioneer to ultraviolet photometry observations of Jupiter: The helium to hydrogen ratios. In Jupiter (T. Gehrels, Ed.), pp. 418-440. Univ. of Arizona Press, Tucson. DUNHAM, E. W., J. L. ELLIOT, AND P. J. GIERASCH (1980). The upper atmosphere of Uranus: Mean temperature and temperature variations. Astrophys. J. 235, 274-284. ELLIOT, J. L., J. A. FROGEL, J. H. ELIAS, I. S. GLASS, R. G. FRENCH, D. J. MINK, AND W. L1LLER(1981a). The 20 March 1980 occultation by the Uranian rings. Astron. J. 86, 127-134. ELLIOT, J. L., R. G. FRENCH, J. A. FROGEL, J. H. ELIAS, D. J. MINK, AND W. LILLER (1981b). Orbits of nine Uranian rings. Astron. J. 86, 444-455. ELLIOT, J. L., AND P. D. NICHOLSON (1984). The rings of Uranus. In Planetary Rings (R. Greenberg and A. Brahic, Eds.). Univ. of Arizona Press, Tucson. FRANKLIN, F. A., C. C. AvIs, G. COLUMBO, AND I. I. SHAPIRO (1980). The geometric oblateness of Uranus. Astrophys. J. 236, 1031-1034. FRENCH, R. G., J. L. ELLIOT, E. W. DUNHAM, D. A. ALLEN, J. H. ELIAS, J. A. FROGEL, AND W. LILLER (1983). The thermal structure and energy balance of the Uranian upper atmosphere. Icarus 53, 399-414. FRENCH, R. G., J. L. ELLIOT, B. SICARDY, P. D. NICHOLSON, AND K. MATTHEWS (1982). The upper atmosphere of Uranus: A Critical test of isotropic turbulence models. Icarus 51, 491-508. GILLET, F. C., AND G. H. RIEKE (1977). 5--20 Micron observations of Uranus and Neptune. Astrophys. J. 218, LI41-L144.

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