Atmospheric and cloud structures of the Jovian planets

ICARUS 20, 465--476 (1973)

Atmospheric and Cloud Structures of the Jovian Planets S. J. WEIDENSCHILLING Department of Earth and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 AND

J. S. L E W I S Planetary Astronomy Laboratory, Department of Earth and Planetary Sciences, and Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 R e c e i v e d A u g u s t 6, 1973 W e t a d i a b a t i c a t m o s p h e r i c m o d e l s are c o m p u t e d for t h e four J o v i a n p l a n e t s . Possible c l o u d - f o r m i n g c o n d e n s a t e s c o n s i d e r e d are HzO ice, a q u e o u s N H a solution, N H 4 S t t , a n d solid N H a , C H , , a n d Ar. Some t e c h n i q u e s for c o m p u t e r c a l c u l a t i o n of c o n d e n s a t i o n i n a m u l t i p h a s e s y s t e m of v a r i a b l e c o m p o s i t i o n are discussed. N o m i n a l m o d e l s are c o m p u t e d for all four p l a n e t s , a n d t h e effects of v a r i a t i o n s in c o m p o s i t i o n a n d different p r e s s u r e - t e m p e r a t u r e regimes are i n v e s t i g a t e d i n d e t a i l for J u p i t e r . T h e m e a n i n g of t h e c a l c u l a t e d cloud d e n s i t i e s a n d t h e i r r e l a t i o n to t h e a c t u a l d e n s i t i e s are discussed. T h e c o m p u t e d a t m o s p h e r i c profiles r e p r e s e n t a v e r a g e c o n d i t i o n s , s u b j e c t t o c o n s i d e r a b l e local v a r i a t i o n s . I . INTRODUCTIOI~

Tile major planets show no visible solid surfaces, only cloudy atmospheres of great apparent depth. Indeed, present models of the interiors of Jupiter and Saturn (Hubbard, 1970, 1973) do not even establish the existence of any distinct "surface." Only very approximate internal models have been published for Uranus and Neptune (Reynolds, 1973, private comm. ; Makalkin, 1973) b u t deep, massive atmospheres, extending well below the visible cloud tops, seem to be required to account for the low bulk densities of these planets. Only the outer layers of the atmospheres of the Jovian planets can be probed b y visible or infrared observations, either from Earth or from spacecraft. Atmospheric deepentry probes will ultimately be needed to determine the compositions and structures of their lower atmospheres. Within the formal assumptions of thermodynamic and hydrostatic equilibrium, it is possible to compute the cloud structure for any condensate in an atmos: Copyright © 1973by AcademicPress, Inc. All rights of reproduction in any form reserved, Printed in Great Britain

465

phere of arbitrary composition. Lasker (1963) investigated the dependence of cloud structure on ammonia gas abundance in the atmosphere of Jupiter, considering liquid and solid ammonia as possible condensates, Lewis (1969a) considered a cosmic-abundance mixture of hydrogen, helium, H 2 0 , NH3, H2S , CH4, and neon, and showed that an aqueous ammonia solution would be present instead of liquid ammonia. Also, following a suggestion b y Wildt (1937), he showed that ammonium hydrosulfide (NH4SH) would also form a cloud layer, and computed the cloud structures resulting from several assumed atmospheric compositions. Lewis (1969b) also showed that a complex multilayered cloud structure should exist in the atmospheres of all the major planets. The details of the structure would depend on the abundances of the condensable gases and the atmospheric pressure-temperature profile. Cook ( 1972 ) applied Lewis's method to nominal atmospheric models of all the major planets, but did not consider formation of NH4SH, or condensation of CH 4

466

WEIDENSCHILLING AND LEWIS

- 60

-[

~95

\

_= x , / y -"

-6

-5

90

,

;

0

0

80

,

,

,,~

0

0

O

_

1', T,T

-4

3)

-3

-2

,

"

r~

0 /

-I

0

£

o -

~

m

o

o

III, I , I I

/

/

2

S

lOglo PH20(TORR) FIG. l. A r e p r e s e n t a t i o n of t h e p h a s e d i a g r a m of t h e N H 3 - H 2 0 s y s t e m o n t h e Iog'PNH 3 -- lOgPH2 o p l a n e . T h e scalloped line r u n n i n g f r o m far left t o b o t t o m r i g h t is t h e freezing line of a q u e o u s solutions. T h e d i a g o n a l s t r a i g h t lines are s o l u t i o n i s o p l e t h s w i t h c o n c e n t r a t i o n s g i v e n in mole p e r c e n t NI-I 3. T h e f a m i l y of c u r v e s i n t e r s e c t i n g t h e i s o p l e t h s is a set of i s o t h e r m s , w i t h t e m p e r a t u r e s in degrees C. T h e d i a g o n a l d a s h e d line a t t h e r i g h t r e p r e s e n t s t h e b u l k N H 3 : H 2 0 r a t i o in a s o l a r - c o m p o s i t i o n a t m o s p h e r e . T h e d a s h e d lines l a b e l e d A t h r o u g h F are, r e s p e c t i v e l y , cloud comp o s i t i o n t r a c k s for solar c o m p o s i t i o n J u p i t e r , S a t u r n , U r a n u s , a n d N e p t u n e m o d e l a t m o s p h e r e s , a n d U r a n u s a n d N e p t u n e a t m o s p h e r e s e n r i c h e d in b o t h N H 3 a n d H 2 0 b y a f a c t o r of t e n . T h e × o n e a c h t r a c k m a r k s t h e b e g i n n i n g of N H ¢ S H f o r m a t i o n . T h e p h a s e d i a g r a m is r e v i s e d f r o m t h a t g i v e n b y Lewis (1969a), w h o d e s c r i b e d its c o n s t r u c t i o n in detail.

or Ar. His results, therefore, are at best very incomplete. Previous calculations of this type were done manually, using diagrams such as Fig. 1 in order to keep track of the varying concentration of the aqueous ammonia condensate. We report here the results of a computer program which has enabled us to study the effects of temperature, pressure, and composition in cloud structure for a large ensemble of model arm ospheres for all of the major planets. II. COMPUTATIONAL METHODS AND ASSUMPTIONS

The derivation of the wet adiabatic lapse rate and the calculation of cloud structure has been described in detail by Lewis (1969a), and will not be repeated here. We shall describe in detail only the additions which we have made to Lewis's treatment. The equation of hydrostatic equilibrium is dP P

Fg d Z RT

(1)

when F is the mean molecular weight of the atmosphere, g is the local gravitational

acceleration, R is the gas constant, and is the average temperature over the height increment d Z . The wet adiabatic lapse rate can be derived in a straightforward manner. For 1 mole of gas undergoing an adiabatic expansion, conservation of energy requires that (2t, d T - - v d P + Z A,~dX,, = O,

(2)

K

where Cp is the mean molar heat capacity of the gas at constant pressure, v is the molar volume, A~ is the molar enthalpy of condensation of the K t h component gas, and dX,¢ is a differential change in the number of moles of the gas present, which is equal to the change in the mole fraction of gas K. For an ideal gas mixture, we have X~ = P,,/P

(3)

Pv = RT,

(4)

and where P~ is the partial pressure of gas K. Then d X ~ - dP~ p

P,~ p2 dP.

(5)

For the vapor in equilibrium with the

ATMOSPHERIC MODELS OF JOVIAN PLANETS

condensed phase, the Clausius-Clapeyron equation gives

467

between the partial pressure and vapor pressure is a measure of the amount of condensate which has formed in t h a t dP~ ~ d T P RT " (6) altitude increment. The partial pressure is then set equal to the vapor pressure, and Making the appropriate substitutions from the next increment is computed using the Eqs. (1), (a), (4), (5), and (6), Eq. (2) can be wet adiabatic lapse rate. For the case where NH 3 solution of variable composition rewritten as is condensing, the procedure is more complicated. For use with a computer, we need a numerical counterpart to the phase diagram of Fig. 1. In principal, the phase -~ ~ X"A"2dT=2OR.T (7) boundaries are simple to establish; if a component can enter more than one phase Which give the wet adiabatic lapse rate (e.g., water as ice or in solution), the phase with the lower partial vapor pressure of t h a t component is the stable phase. Accurate empirical expressions for the (8) vapor pressures of the pure components For condensation of aqueous NH 3 solution are available from the International Critical at concentration C, for every mole of Tables (1928) and other sources. We still solution, C moles o f N H 3 and (1 - C) moles require expressions for the partial vapor of H20 condense. The change in number of pressures of NH 3 and H20 in equilibrium with solution at arbitrary concentration moles of solution is and temperature (the solution deviates 1 greatly from ideality). Haudenschild (1970) dXs = 1 - C dXH2°" (9) derived such expressions which retained I f we let ;~ be the heat of vaporization of the form of the Clausius-Clapeyron depenthe bulk solution at this concentration, the dence, but Cook (1972) found t h a t they did analogous expression for the lapse rate in not define the phase boundaries with sufficient accuracy. Our approach was less a region of condensing solution is elegant but more accurate. The partial vapor pressure of either NH 3 or H:O in solution at any temperature and concentration was expressed as the product of the /H20 vapor pressure of the pure liquid phase at t h a t temperature and a fifth-order polyFor a condensate of constant composi- nomial in the concentration. The cotion, calculation of the wet adiabat is efficients of the polynomial were chosen to straightforward. We specify an atmos- meet the conditions of g a o u l t ' s and pheric composition and some reference Henry's laws at either end of the concentrapressure and temperature at which none tion range. Since the Henry's law coof the possible condensables is saturated. efficient is itself temperature-dependent, For some altitude increment (usually lkm), the polynomial coefficients are themselves we compute the pressure and temperature functions of temperature. This rather changes from the hydrostatic equilibrium tedious procedure produced an excellent condition and the dry adiabatic lapse rate fit to the ice freezing curve, and to the (-i~g/Cp). The vapor pressures of possible partial pressure data tabulated by Wilson condensates at t h a t temperature are com- (1925), Linke (1965), and the International pared with the partial pressures of the Critical Tables. condensable gases. I f the partial pressure The equilibrium concentration, C, of of a species exceeds the vapor pressure, the aqueous NH 3 solution is variable, but condensation must occur. The difference it can be seen from Fig. 1 t h a t it is uniquely

-..gr,

18

]/[

468

WEIDENSCttlLLING AND LEWIS

determined by the partial pressures of NH 3 and H20. The partial pressures in turn are functions of C. We can escape from this seemingly circular reasoning by the following method: Imagine a closed system containing solution at concentration C in equilibrium with a gas at temperature T and total pressure P. The mole fractions o f N H 3 and H20 in the gas are X a and Xw, respectively. The partial pressures of NH 3 and H20 are equal to their vapor pressures : P A = X a" P and Pw = Xw" P. Suppose we expand this system adiabatically by an infinitesimal amount, so t h a t pressure and temperature change by amounts dP and dT. Some condensation will occur, at concentration C + dC, and X A and X w will change accordingly. Since C is defined as the mole fraction of NH 3, we have, to first order in C

C

dXA

(11)

dXA + dXw and C dXA -- (1 --~) dXw"

(12)

Also, for ideal gases dP A = P d X A + X a d P

(13)

dPw = P d X w + X w d P .

(14)

But PA and Pw arc also the vapor pressures at equilibrium, and may be expressed as PA = PA(C, T) and Pw = Pw(C, T), with expressions of the sort described above. We then have OPA OPA clPa = ~ o - d C + ~ - d T (15) dPw=~dC~dT.

(16)

Eqs. (12), (13), (14), (15), and (16) may be combined and solved for dC in terms of dP and dT, giving

de=

[~ -FCV,

(1-C/

dT

(17)

The high pressures in the lower atmospheres of Uranus and Neptune necessitate a correction to the vapor pressure due to the total pressure. This introduces additional terms in the expression for dC, but the derivation is identical. I f we know P, T, C, and composition for a single point in the atmosphere, we can integrate Eqs. (1), (15) and (17) to find the wet adiabatic profile and composition of the cloud at any other altitude. At the base of the cloud, these quantities are known; C is found by trial and error, with the requirement t h a t NH 3 and H20 saturate simultaneously. In our calculations, we have ignored the presence of the two hydrates of ammonia, N H j . H a O , and 2NH3-H20. Instead, the vapor pressure equations for the solution are extrapolated into the hydrate stability fields. In effect, the phase diagram of Fig. 1 has the phase boundaries of ice and solid NH 3 extrapolated to a single metastable eutectic in the neighborhood of C = 0.45, T = 160°C. There are two justifications for this procedure, aside from the obvious saving of computer time. First, Lewis (1969a) has shown t h a t under equilibrium conditions, the masses of any hydrate clouds are very small and have a negligible effect on the tropospheric structure. Second, there are ample grounds to expect the presence of metastable liquid rather than hydrates under cloud-forming conditions. Supercooling of HzO is by no means uncommon in terrestrial clouds, due to the lack of crystal nucleation sites in isolated droplets. At the low temperatures encountered in the NH3-HzO system, the rate of crystal nucleation is very slow. Even with macroscopic laboratory apparatus, in which nucleation sites are presumably abundant, investigators have commonly encountered marked supercooling (Elliott, 1924). The presence of any distinct cloud layer, however tenuous, composed chiefly of ammonia hydrates, is therefore extremely unlikely in any atmosphere t h a t is not essentially stagnant. Some hydrate crystals will, of course, be present as minor constituents of the clouds of solution and solid ammonia, indeed, Lewis (1969a) estimated 30 ppb of 2NH3.H20 in the solid ammonia clouds. Further implica-

ATMOSPHERIC MODELS OF JOVIAN PLANETS

tions of supercooling will be discussed in Section IV, below. Lewis (1969a) and Lewis and Prinn (1970) showed t h a t the failure to detect H2S spectroscopically in the atmosphere of Jupiter could be explained by the reaction of H~S with NH 3 to form solid NH4SH. A distinct cloud layer was predicted near the 230°K level. To establish an upper limit on the H2S abundance above this cloud layer, he neglected the solubility of H2S in aqueous NH 3 solution clouds. However, the weak acid H,S is soluble in any basic solution. Any detailed calculation of the cloud structure must take effect into account. We have used an empirical expression developed by Leyko (1964) for the solubility of H2S as a function of NH 3 concentration and temperature, extrapolated to lower temperatures. In the most extreme model atmospheres for Uranus and Neptune, containing massive solution cloud layers, the mass of NH~SH clouds is decreased by about 30% by consideration of H2S dissolution. The computed cloud density in any interval of altitude is proportional to the difference in weight fraction in the gas phase at the bottom and top of the interval. The mass per unit area, M j, of a hydrostatic atmosphere above a point J is equal to the pressure at t h a t point divided by the local gravity.

M~ = Pj/ff.

(18)

The mass per unit area of a single component above point J is mj M~, where mj is the weight fraction of t h a t component. I t follows t h a t the average cloud density in the interval of altitude A from I to J is

469

condensate. This formula has the intuitive advantage of giving a cloud density t h a t is independent of the step size, and dependent only on the changing composition of the atmosphere with altitude. The cloud densities computed by Lewis (1969a), though similar in magnitude, depended explicitly on the size of the altitude increment, and cannot be compared quantitatively with the results reported below. I t is important to stress t h a t the relationship of any computed density to t h a t actually present in a dynamically formed cloud is unclear. Some implications of this question will be discussed in Section IV. We must justify our choice of atmospheric models. For Jupiter and Saturn, the planetary bulk densities and spectroscopic abundances are consistent with solar composition. Uranus and Neptune are too dense to be of solar composition, and the atmosphere of Uranus is enriched in CH 4 relative to solar material (Prinn and Lewis, 1973). Table I defines an atmosphere containing solar proportion of H, He, O, C, N, S, and Ar. The heavier reactive elements are assumed segregated in the planetary interior. The noble gases other than He and Ar have a negligible effect on the atmosphere structure. The greatest uncertainty is the He abundance. However, varying the amount of He will only change the vertical scale of the atmosphere and not the qualitative results. The solar composition defined here is consistent with Hubbard's (1970) model for the interior of Jupiter. We assume an identical H : H e TABLE I SOLAR COMPOSITIONATI~OSPHERE

D = (m' ~ mJ).l~

(19)

or for more than one component condensing,

D = ,~ [p,,(XKx -- X~j)] P. ~gA

(20)

This formula is due basically to Cook ( 1972), except for a confusion of molar and weight fractions in his derivation which eliminated the dependence on molecular weight of the

Species

Number fraction

H2 He tt20 CH4 )~I-I3 H2S Ar

0.886 0.112 1.05 x 10-a 6.30 × 10-4 1.52 × 10-4 2.90 x 10-s 9.50 × 10-6

Mean molecular weight = 2.25.

470

WEIDENSCHILLING AND LEWIS

N

~ U

~:

50

i

- - Ar ~'~

~

~

H

4

w

" 200

_ _ N- 2 ~ . . . . . . . . . -

,,,

. . . .

500

.-

.--

- -~=~-T_

NH 3 Hz0

.-------

=NH.S

H20+--

~,_____ ~,

,OO, oo_ 6005.01

I

I

I

I

.I

I

10

I0 z

TOTAL

-

103

PRESSURE (BARS)

FIG. 2. Nominal atmospheric models for Jupiter, Saturn, Uranus, and Neptune (solid lines), and condensation thresholds of cloud-forming gases for solar composition {dashed lines). Increasing the relative abundance of a condensable gas shifts its condensation line to the left. The H~O curve which is closed at the right is the ice phase boundary.

ratio for all four planets, following the suggestion of Cameron (1973) t h a t their density differences are due to variations not in He content, but in the amount of involatile rock- and ice-forming elements. I t is of interest t h a t Veverka et al. (1973) concluded from an analysis of data from a stellar occultation t h a t Neptune's upper atmosphere was predominantly hydrogen, and therefore would be consistent with a solar H : H e ratio. Different condensable and compound-forming elements will be enriched by different amounts, depending on the temperature and conditions of accretion. Lewis (1973) gave a detailed account of the condensation sequence. For our purposes, it suffices to say t h a t condensation in a cooling solar nebula enriches the solid matter successively in

S, 0, N, C, and Ar. An atmosphere t h a t is enriched in Ctt 4 will almost certainly also be enriched in NH 3, but the converse need not be true. III. RESULTS The nominal atmospheric P-T profiles are shown in Fig. 2, along with condensation thresholds for the various cloud-forming compounds if present in order of abundance. To first order, the effect of an increase in amount of any compound can be seen by shifting its condensation threshold line to the left by the factor of enrichment (condensation will alter the shape of the P-T curve somewhat). The parameters of the nominal model atmospheres are given in Table II. Since the

TABLE II PARAMETERS OF NOMII~AI, PLANETARY ATMOSPHERES

Initial P (bars) Initial if' (°K) Stratospheric T (°K) Gravity (cm/sec 2)

J

S

25 400 90 2400

60 400 70 1000

The zero of altitude is set at the initial P, T point.

U 250 450 50 900

N 900 500 35 1100

ATMOSPHERIC

MODELS

OF JOVIAN

ing aqueous NH 3 solution clouds to form at the lowest level. The cloud base is lowered, but as long as a cloud layer remains optically thick, its appearance from above is unchanged. Figure 3 also shows the integrated amounts of each gas present in a vertical column above any altitude. These cannot be directly related to spectroscopically observed amounts of H 2, NH 3, and CH 4 without a detailed scattering model, as discussed by H u n t (1973). We note incidentally t h a t H u n t used Divine's (1970) model atmosphere for Jupiter, which did not consider the formation of NH4SH. A recalculation of Divine's model with H~_Sadded in solar proportions shows a NH4SH layer with its base near the 200°K level. This layer is only slightly more dense than the NIt 3 cloud layer, and may be optically thin, in which case H u n t ' s results will not be changed greatly. This model bears a close resemblance to t h a t labeled A in Fig. 4. All condensable gases need not be present in solar proportions, even for Jupiter. Figure 5 shows the result of enrichment of all condensables by a factor of five. The cloud bases are lowered, and the maximum

actual range of possible atmospheres is quite wide for each planet, we will first consider the nominal model for Jupiter, then see how the cloud structure is affected by changes in composition and pressure. The results can easily be extended to the other planets by analogy with Jupiter. Figure 3 shows the atmospheric profile for the nominal model of Jupiter. The principal cloud layers are ice, NH4SH, and NH 3. The choice of 400°K, 25 bars for the reference level gives the NH 3 cloud base a pressure of precisely 1 bar. The cloud base is just below the stability threshold of aqueous NH 3 solution. This result is quite different from t h a t of Lewis (1969a), who found ice to be a relatively unimportant cloud constituent for Jupiter. The difference is due mainly to our assumption of lower total pressure at any temperature level than in his model. Lowering the total pressure causes condensation to occur at lower temperatures. In the phase diagram of Fig. 1, the cloud composition track is lowered and enters into the ice region more deeply. Figure 4 shows the effect of varying the assumed pressure at the initial temperature level. Increasing the pressure causes saturation at a higher temperature, allow0

I

471

PLANETS

LOG GAB ABUNDANCE, CM. AMAGAT 3 4

2

160

S

\ \

XN\

i \

• ~

\

\\\\\

i 140

.J , ~ x L ~ NH45H

~.

\

\

\\

k

0.5-- _ 120 k

k

\

I--

\ CH4

-

140 160 180 o

zoo

\\

220 ~

u.

fCE

h 60

~

/ / SOLUTION

~

\

\\

240

6-7-B-9-I0--

\

- ~o N 280 500

4O -5

I -4

[

-3

I

[

-2 -I LOG CLOUD DENSITY (g/£)

Fro. 3. ~ o m i n a l atmospheric profile for solar-composition J u p i t e r . Solid lines show c o m p u t e d cloud densities ; dashed lines are i n t e g r a t e d a m o u n t s of spectroscopically active c o m p o u n d s in t h e gas phase present in a vertical column a b o v e a n y altitude, in cm a m a g a t . The zero of a l t i t u d e is at the 400°K level. Most of the H 2 0 forms ice clouds ; aqueous N H 3 solution is present only m a r g i n a l l y if supercooling is not assumed.

472

WEIDENSCHILLING AND LEWIS 1

~

l PRESSURE, BARS A B C -0.2-

140

.~

. __,._*.

NH3

-J 1 2 0 o~ 0 0

I00

--

IO0

-0.5-

- I . 0 - --

- 1.0-

-2.0-

12o 14Q

-0.5-

180

-2X)-

~ , , . . . . . , ~

-LO-

NH4S H .--~_.~

-50-

--

200 ~_ 220

o =

240

8o

~,

-2.0-

-5,0-

-IO.O-

u.I

280

-&O-

6o

,~

260 IT

-I0.0-

-2QO-

500

40

I

I

I

-5

-2

-I

LOG CLOUD DENSITY (g/~,)

FIG. 4. Cloud profiles for three assumed P - T profiles for a solar-composition Jupiter. Pressures at 400°K are: Model A (dotted line), 10 bars; Model B (solid line), 25 bars; Model C (dashed line), 50 bars. Temperatures are nearly the same for all three models. densities are increased b y a b o u t the factor of enrichment. There are minor differences in cloud structure due to changes in the lapse rate a n d the a m o u n t of solution, b u t to a good a p p r o x i m a t i o n , each cloud layer can be t r e a t e d i n d e p e n d e n t l y when v a r y i n g a b u n d a n c e s in the same proportion, or if the elements varied do n o t react chemically.

1

I f the a b u n d a n c e ratio of two interacting elements is varied, there can be a m u c h greater effect. Figure 6 shows the effect of v a r y i n g the S : N ratio. I n solar material, the S : N ratio is a b o u t 0.2, a n d f o r m a t i o n of N H 4 S H exhausts H2S. A n y increase in H2S adds to the a m o u n t of N H 4 S H cloud a n d depletes the solid N H 3 cloud b y the

]

I

140

.J 120

~I00

8o 60

--

ICE

%

SOLUTION

%

%

_x

40 [

I

-3

-2

I -I

LQG CLOUD D E N S I T Y (g/~.)

Fro. 5. Effect of varying absolute abundances for Jupiter models with P = 25 bars at T = 400°K. Solid line : solar composition. Dashed line : enriched five times in H20, NH3, and H2S.

473

ATMOSPHERIC MODELS OF JOVIAN PLANETS I

I

140 ~c

_T LLI

NH 3

,,>, 120 J 0 0 .,¢,.

I00

5:

0

80

--

ICE

~

,

-

""%

--

I---

60--

SOLUTION

/

40--

I

I

-3

--4

-2

LOG CLOUD DENSITY (q/.~)

F z G . 6. Effect o f v a r y i n g S:N" ratio. Solid line: S :1~ = 0 . 2 (solar ratio). D a s h e d line: S : N

same amount. If the S : N ratio exceeded unity, NH 3 would be exhausted and would form no cloud layer. Figures 7, 8, and 9 show the nominal atmospheric structures for Saturn, Uranus, and Neptune. The cloud layers are much

deeper than for Jupiter (note the change in vertical scale), since the lower gravity increases the scale height, and Uranus and Neptune are assumed to have greater amounts of condensables. If Uranus and Neptune are enriched several times in NH 3

I

t

350

I00

--I

140

w

> 300 w J

(/3 rr"

--5

~o 25o 0 o

n,, 1.1_ LIJ

200

<

< m

180 oI.~

n,, =)

2 2 0 ,~ ec

,i.u r,," (3.

150 -- SOLUTION

5

m20

rr"

260 t.-

300

I00

I -3

I

= 0.8.

I

-2 -I LOG CLOUD DENSITY (g/Z)

E 0

F I G . 7. N o m i n a l Saturn model, solar c o m p o s i t i o n . N o t e c h a n g e in vertical scale.

474

WEIDENSCHILLING i

LEWIS

AND

~

]

500

60

- -

--I

--80 -- I00

=~ 45o --5

~400

150

,,>, .J 350

--

200 z

o

Q: -- 2 0

300

o

¢n

o a~ 250 LL

250

300

50

F-

D 200 NH 3 - H20

SOL

< 150

~

I00 ~ I

-4

--

[

I

-2

-3

LOG CLOUD

150

[

-I

350

- - IO0

--

400

0

DENSITY (g/t,)

FIG. 8. Nominal Uranus model, ten times solar a m o u n t s of H20, NH3, H2S , and CH 4.

and H 2 0 with respect to solar abundances, then ice is not present at any level. Uranus and Neptune have thick CH 4 clouds. Spectroscopic data for Uranus appear to be more consistent with a thin CH 4 haze (Prinn and Lewis, 1973), which might

I

indicate less enrichment in CH 4 or a warmer atmosphere than assumed here. The result, however, is sensitive to the assumed scattering model. Neptune also possesses a layer of Ar haze above the CH 4 clouds. This haze is present even if Ar is

I

I

I

Ar

500 ~

--0.I ~J'~-~..__._.....~

CH 4

-- 40 =

-- I

450 ~ >

--%%.%

N 400

\

--

~

u~

o 300-=~

--30

\

L6 - -

~

IOO"

-- 10 ~.

200 °

3oo 250

O. . . . . . . . . . . .

--[oo

o_ _

~ 200 150

NH 3 - H 2 0 SOLUTI

I00

400 °

%

[ -4

3o0 °

-3

l

E

% %

-2 -I LOG CLOUD DENSITY [g/e)

--500 l 0

FIG. 9. Nominal Neptune model, ten times solar a m o u n t s of H20, NH3, H2S, CH4, and Ar. Solid lines are computed cloud densities. Curved dashed line at right is m a x i m u m cloud density, if proportional to a t m o s p h e r i c d e n s i t y , and set at 1 0 - 3 g / l i t e r at standard density. H o r i z o n t a l d a s h e d lines s h o w s c h e m a t i c a l l y the lowering of cloud bases by precipitation.

A T M O S P H E R I C M O D E L S OF J O V I A N P L A N E T S

not enriched with respect to solar abundance, if the stratospheric temperature is below 40°K. IV. DISCUSSION The question naturally arises: how well do these idealized cloud profiles correspond to real cloud structures? I t is helpful to consider an analogous treatment of the Earth's atmosphere. Presumably, we would predict a uniform layer of ice and/or water clouds, their mass depending on the assumed water content of the atmosphere. Local variations, from clear days to thunderstorms, would simply not be predicted. We can expect our cloud profiles to bear a similar relationship to the actual conditions. At best, if we know the atmospheric composition and P - T profile, the cloud profiles will represent a space- and time-average over the entire planet, with some additional idealizations discussed below. The belts and zones of Jupiter are a fine example of large-scale deviations from the planetwide average; presumably there are more local variations as well, since different parcels of rising and falling atmosphere will have different histories of condensation. Wide-area scanning may produce a truer picture of an atmosphere, in some ways, than an actual entry probe. Another limitation in this analysis is the assumption of thermodynamic equilibrium. ~.¥e have mentioned supercooling in reference to the formation of ammonia hydrates. Jupiter and Saturn have levels where water ice is stable with respect to solution, but supercooled solution may well occur there. The prospect exists of an entry probe "icing u p " is it descends through the region. A more likely occurrence is supersaturation. We have assumed t h a t condensation takes place as soon as saturation occurs. However, if the major planets lack solid surfaces, condensation nuclei such as dust particles may be lacking. Particles from a lower cloud level may be swept upward to nucleate the next layer, nucleation sites may be provided by ions made by electrical discharges or cosmic rays, or a considerable degree of supersaturation may be required to begin condensation. In t h a t

475

case, the actual cloud bases would be higher than predicted (Stauffer and Kiang, 1973). The calculation of cloud density involves the implicit assumption t h a t the condensate remains precisely at the altitude of its condensation. Actually we can expect it to be carried for some distance with the rising parcel of atmosphere. The effect will be to alter the calculated cloud profiles; the density will be less strongly peaked at the base, and will fall off more slowly with altitude (Sorokina et al., 1973). In the Earth's atmosphere, measured cloud densities seldom agree with the predictions of this type of "rising-parcel" adiabatic condensation theory. Local densities are affected by many factors, including the presence of condensation nuclei, speed of ascent, droplet size distribution, and mixing with air parcels of different composition (i.e., humidity). Their effects are described in detail by Mason (1971, Chap. 3) ; in general the actual densities are lower than predicted. Even so, the indicated cloud densities for the major planets are very high. Nonpreeipitating clouds in the Earth's atmosphere seldom attain densities greater than 10-3 grams per liter. This density is exceeded by two or three orders of magnitude for Uranus and Neptune. Even if we allow the maximum cloud density to scale as the atmospheric density, as in Fig. 9, the computed cloud densities are too great. We must conclude t h a t precipitation occurs; indeed, it appears t h a t a rising parcel of atmosphere may produce a "rain" or "snow" of aqueous NH 3 solution, NH4SH, and solid NH 3 and CH 4 at different levels. Precipitation will decrease the magnitude of the lapse rate, and increase the amount of condensable gas below the predicted cloud base. The cloud bases will be lowered somewhat, as shown in Fig. 9.

V. CONCLUSIONS The details of the cloud structures presented here are dependent on the assumed atmospheric compositions and pressure-temperature profiles. However,

476

WEIDENSCHILLING A N D L E W I S

some general conclusions can be drawn which are not very sensitive to these a s s u m p t i o n s . I c e is l i k e l y t o b e t h e m o s t important cloud constituent on Jupiter, w i t h h i g h e r , less m a s s i v e l a y e r s o f N H 4 S H a n d s o l i d N H 3. B o t h ice a n d a q u e o u s N H 3 solution layers may be present on Saturn. Uranus and Neptune have very deep and m a s s i v e s o l u t i o n c l o u d l a y e r s ; H 2 0 ice is insignificant as a cloud constituent will not be present at any level if their atmospheres are significantly enriched in both NH 3 and H20. Neptune probably has a thin Ar haze above or mixed with the CH 4 cloud layer. Precipitation probably accompanies cloud f o r m a t i o n i n m a n y cases, a n d a l t e r s t h e cloud profiles from those computed. The properties of the cloud tops are insensitive to variations in bulk atmospheric composition. All computed cloud structures represent planetwide average conditions; entry probes may encounter very different local conditions.

J~CKNOWLEDGMENTS

We gratefully acknowledge the programming assistance of Philip Schaller. We thank Dr. D. Stauffer and Dr. C. S. Kiang for helpful discussions. This work was supported under NASA Grant NGL-22-009-521. One of us (S.J.W.) was supported by a National Science Foundation fellowship at the time of this work. This is contribution no. 88 of the M.I.T. P l a n e t a r y Astronomy Laboratory.

REFERENCES CAMERON, A. G. W. (1973). Formation of the outer planets. Space Sci. Rev. 14, 383. COOK, W. S. (1972). N H a - H 2 0 cloud models for the outer planets. Martin Marietta Corp. Report No. D-72-48740-005. DIVINE, N. (1970). The planet Jupiter. NASASP-8069. ELLIOTT, L. D. (1924). The freezing point curve of the system water-ammonia. J. Phys. Chem. 28, 887. I-~AUDENSCHILD,C. ( 1970 ). Multi-phase ammonia water system. J P L Space Programs Summary 37-64, Vol. I I I , 4.

HUBBARD, W. B. (1970). Structure of J u p i t e r :

chemical composition, contraction, and rotation. Astrophys. J. 162, 687. HUBBARD, W. B. (1973). Interior of J u p i t e r and Saturn. Ann. Rev. Earth Planet Sci. 1, 85. HUNT, G. E. (1973). Formation of spectral lines in planetary atmospheres IV. Theoretical evidence for structure of Jovian clouds from spectroscopic observation of methane and hydrogen quadrupole lines. Icarus 18, 637. INTERNATIONAL CRITICAL TABLES (1928). McGraw-Hill Book Co., Inc., New York. LASKER, B. M. (1963). W e t adiabatic model atmospheres for Jupiter. Astrophys. J. 138,709. LEwis, J. S. (1969a). The clouds of J u p i t e r and the N H a - H 2 0 and NHa-H2S systems. Icarus 10, 365. LEWIS, J. S. (1969b). Observability of spectroscopically active compounds in the atmosphere of Jupiter. Icarus 16, 393. LEWIS, J. S. (1973). Chemistry of the outer solar system. Space Sei. Rev. 14, 40I. LEWIS, J. S., AND PRINN, R. G. (1970). J u p i t e r ' s clouds; structure and composition. Science 169, 472. LEYKO, J. (1964). Equilibrium studies on the H 2 S - N H a - H 2 0 system. I. Bull. Acad. Polon. Sci. Ser. Chim. 12, 275. LINKE, W. F. (1965). "Solubilities of Inorganic and Metal-organic Compounds," 4th ed. American Chemical Society, Washington, D.C. MAKALKIN, A. B. (1973). The structure of models of Neptune. SolarSyst. Res. 6, 153. MASON, B. J. (1971). "The Physics of Clouds," 2nd ed. Oxford Univ. Press, London. PRINN, R. G., AND LEWIS, J. S. (1973). Uranus atmosphere: structure and composition. Astrophys. J. 179, 333. SOROKINA,L. P., TEIFEL, V. G., ANDUSOL'TSEVA, L. A. (1973). Optical characteristics and structure of the Jovian atmosphere V. Probable structure of the ammonia aerosol layer. Solar. Syst. Res. 6, 68. STAUFFER, D., AND KIANG, C. S. (1973). Cloud base levels for Jupiter and Venus and the heretomolecular nucleation theory. Icarus (submitted). VEVERKA, J., WASSERMAN, L., AND SAGAN, C. (1973). On the upper atmosphere of Neptune. Cornell U. Center for Radiophys. and Space Res., Report 543. WILDT, R. (1937). Photochemistry of planetary atmospheres. Astrophys. J. 86, 321. WILSON, J. A. (1925). The total and partial vapor pressures of aqueous ammonia solutions. U. lU. Eng. Exp. Sta. Bull. 146.