The Jupiter greenhouse

ICARUS 16, 397 400 (1972)

The Jupiter Greenhouse CARL SAGAN AND GEORGE MULLEN 1 Laboratory for Planetary Stuzlies, Cornell University, Ithaca, New York 14850 R e c e i v e d N o v e m b e r 5, 1971 ; revised J a n u a r y 8, 1972 A step f u n c t i o n n o n g r a y a p p r o x i m a t i o n t o i n f r a r e d a b s o r p t i o n b y H2, NH3, a n d CH4 o n J u p i t e r implies a t e m p e r a t u r e a t t h e lower clouds of 270 to 340°K. S u c h clouds are c o n j e c t u r e d to b e a q u e o u s . No c o n t r a d i c t i o n is i m p l i e d b y r e p o r t e d lower r o t a t i o n a l t e m p e r a t u r e s .

Present estimates of the composition of the atmosphere of Jupiter, as well as the other Jovian planets, give molecular hydrogen as the primary constituent with ~10 -'~ methane and ammonia. From the estimated near-infrared H2 abundances, as well as the pressure broadening of individual rotational lines, effective pressures ~ several bars have been calculated (see, e.g., McElroy, 1969; Farmer, 1969). Even with the presence of substantial quantities of chromophores in the Jovian atmosphere and Rayleigh scattering, a significant fraction of incident sunlight should arrive at this pressure level. However, permitted dipole transitions of methane and ammonia, as well as permitted quadrupole and pressure-induced dipole transitions of H,~, should provide a very substantial infrared opacity above this level. We are interested in calculating the resulting greenhouse effect, above the level at temperature T~ which, in the simple reflecting layer formalism, characterizes the infrared abundances. By analogy with Venus (Sagan and Pollack, 1969), we believe this formalism to be adequate for the problem. We use a simple two-layer emission model with square-wave absorption bands. The condition of energy balance is 1S(1 - A ) = ~ B ~ ( T ~ ) zJ~i

i

4- ~ B,~j(2 -1/4 Te)/I,~j,

(1)

J 1 P e r m a n e n t a d d r e s s : D e p a r t m e n t of Physics, Mansfield S t a t e College, Mansfield, P e n n s y l v a n i a 16933. 397 © 1972by AcademicPress, Inc.

where S is the solar constant at Jupiter, is the Jovian bolometric Russell-Bond albedo, the B~ (T) are the Planck specific intensities in wavelength space, the/12 are the selected wavelength intervals, and Te is the effective planetary temperature. We have used the Eddington approximation for the planetary skin temperature, and have assumed that emission to space in strong absorption features occurs at the skin temperature, and in windows occurs at the bottom of the absorbing layer. Equation (1) is solved iteratively for the temperature at the bottom. A similar protocol for the Earth (Sagan and Mullen, 1971) gives quite satisfactory global temperatures. Small variations in the precise step function assignments are found to have little effect on the derived temperatures. The assumed step function absorption for the gases in question are shown in Fig. l, derived from laboratory absorption spectra kindly obtained with a Perkin-Elmer Model 621 double beam spectrophotometer for us by Dr. B. N. Khaxe; and calculated spectra kindly provided by Dr. L. D. G. Young. Jupiter's .4 is imperfectly known, in part because the phase integral cannot be evaluated properly until spacecraft fly by the planet. All published estimates, however, appear to lie in the range 0.4 to 0.6, corresponding to a range of effective temperature from 98 to 108°K. The resulting calculations for various combinations of the foregoing gases axe displayed in Fig. 2. Methane, ammonia, and hydrogen together provide an atmosphere which is almost entirely opaque

398

CARL SAGAN AND GEORGE MULLEN

T

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II

5.5

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7.2 8D

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0 J 142 170 2.20- 244

1 "3

16

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35

CH4

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8.6

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150

C 1-14-I- NI-13+ I-I2

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IJ2 La6 U ~ L7 Lq 2.628 41

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Fro'. 1. Step f u n c t i o n a p p r o x i m a t i o n to t h e transmissior~ s p e c t r a of CH4, NH3, H 2 0 . a n d H2. based on l a b o r a t o r y s p e c t r a {courtesy of Dr. B. N. K h a r e ) a n d t h e o r e t i c a l c a l c u l a t i o n s (courtesy of Dr. L. D. G. Y o u n g ) for p a t h s a n d p r e s s u r e b r o a d e n i n g a p p r o p r i a t e for J u p i t e r . Various c o m b i n e d s p e c t r a are also shown. T is t h e t r a n s m i s s i v i t y .

longward of 5.5t~. The resulting temperature at the "effective reflecting level" is calculated to be 270=~ 5°K, depending upon the bolometric albedo (Fig. 2). If Jupiter emits 2.7 times its absorbed solar flux to space, due to internal energy sources (Aumann, et al., 1969), the derived value of T~ is in creased by a factor <(2.7) 1/4. Thus, we estimate 270°K < T~ < 340°K. Temperatures ~>300°K are reported by Westphal (1969) for the North Equatorial Belt in the 5/~ window, the longest wavelength window in which, according to these calculations, it is possible to look to the effective reflecting level in the near infrared (cf. Hogan et al., 1969). The question of what is the 300°K reflector arises, and an answer equally naturally

suggests itself: water, its compounds, and solutions are the only plausible cosmically abundant material to provide a 300°K cloud deck on Jupiter. This result confirms a previous conclusion that the opacity of" NH3, CH4, and H2 on Jupiter is too great for the effective reflecting level to be NH;~ : water clouds were also suggested then (Sagan, 1966). Because of ammonia in the Jovian atmosphere, this water is likely to be present in the form of ammonium hydroxide (Lewis, 1969). Laboratory simulations (e.g. Sagan and Khare, 1971), suggest that there is substantial organic chemistry occurring in the vicinity of these aqueous clouds. Our result has interesting implications for rotational temperatures determined

399

THE JUPITER GREENHOUSE

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~

CH4+NH3+H2+ H20

280

~ C H 4 +

NH3+H~,

260

240

= 220 c

® 200 0

E 180

ACKNO~LEDGMENT

160 140 120 I00 0.3

b r o k e n a m m o n i a cirrus at 120°K a n d a dense w a t e r cumulus at 270 to 340°K. I f the clouds are aqueous there will be an equilibrium v a p o r pressure of w a t e r a b o v e them. The assumed absorption spectrum for this w a t e r v a p o r is shown in Fig. 1 a n d the resulting 26 ° greenhouse i n c r e m e n t is shown in Fig. 2. Because of b a n d s a t u r a t i o n , v e r y considerable increases in t h e a m o u n t s of c o n s t i t u e n t gases will not alter these conclusions in a m a j o r way. Similar conclusions a p p l y to the o t h e r J o v i a n planets. P r e l i m i n a r y a r g u m e n t s f r o m m i c r o w a v e s p e c t r a for dense aqueous clouds on J u p i t e r and S a t u r n will be discussed elsewhere.

~ N H ~ C H 4 0.4

0.5

3 (andNH3+CH4 ) j 06

W e are g r a t e f u l to B. N. K h a r e for t h e l a b o r a t o r y i n f r a r e d s p e c t r a ; to L. D. G. Y o u n g for t h e c a l c u l a t e d H2 s p e c t r a ; a n d to M. J . S. B e l t o n , P. Silvaggio, A. T. a n d L. D. G. Y o u n g , a n d N. J. W o o l f for c o m m e n t s o n t h e m a n u s c r i p t . T h i s r e s e a r c h was s u p p o r t e d b y t h e A t m o s p h e r i c Sciences Section, N a t i o n a l Science F o u n d a t i o n , u n d e r G r a n t GA 23945.

0.7

Albedo(~,)

FI(;. 2. C a l c u l a t e d t e m p e r a t u r e a t b o t t o m of "effective reflecting l a y e r " for g r e e n h o u s e effects d u e to v a r i o u s c o m b i n a t i o n s of J o v i a n gases. T h e effect of a d d i n g c o m p a r a b l e q u a n t i t i e s of H2S is negligible, F o r t h e m i x t u r e s of k n o w n gases, t e m p e r a t u r e s ~ 2 7 0 ° K , or larger if H 2 0 is included, are derived.

h ' o m the infrared rotation-vibration spectra. Y o u n g a n d Y o u n g (1972) h a v e shown t h a t the convolution of the B o l t z m a n n r o t a t i o n a l line distributions of two cloud l a y e r s - - o n e high a l t i t u d e a n d scattered, a n d the o t h e r low altitude a n d u n b r o k e n - - w i l l not be d e t e c t a b l y b i m o d a l unless the cloud t e m p e r a t u r e ratio is >~9; instead, it will a p p e a r as a u n i m o d a l B o l t z m a n n distribution, characterized b y an i n t e r m e d i a t e t e m p e r a t u r e . The J o v i a n r o t a t i o n a l t e m p e r a t u r e s of a b o u t 200°K found, e.g., b y Margolis a n d F o x (1969) are i n t e r m e d i a t e b e t w e e n those of a

REFERENCES AUMANN, H. H., GILLESPIE, C. M., AND L o w , F. J . (1969). T h e i n t e r n a l pouters a n d effective t e m p e r a t u r e s of J u p i t e r a n d S a t u r n . A s t r o p h y 8 . J . 157, L69. FARMER, C. B. (1969}. A n e s t i m a t e of line w i d t h a n d pressure f r o m t h e h i g h r e s o l u t i o n s p e c t r u m of J u p i t e r a t l l,000A_, J . A t m o s . Sci. 26, 860. HOGAN, J., ~:~ASOOL, S. I., AND ENCRENAZ, T. (1969). T h e t h e r m a l s t r u c t u r e of t h e J o v i a n a t m o s p h e r e . J . A t m o s . Sci. 26, 898. LEWIS, J . (1969). T h e clouds of J u p i t e r a n d t h e N H a H 2 0 a n d N H 3 H2S s y s t e m s . I c a r u s 10, 365. MARGOLIS, J . S., AND FOX, S . (1969). J . Atraos. ~ci. 26, 862. MCELROY, M. B. (1969). A t m o s p h e r i c c o m p o sition of t h e J o v i a n p l a n e t s . J . A t m o s . Sci. 26, 798. SA(;AN, C. (1966). O n r a d i a t i v e t r a n s f e r in t h e a t m o s p h e r e of J u p i t e r . T r a n s . I n t . Astron. U n i o n X I I B, 215. SAGAN, C., AND POLLACK, J . n . (1969). O n t h e s t r u c t u r e of t h e V e n u s a t m o s p h e r e . I c a r u s 10, 274.

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SAGAN, C., AND KHARE, B. N. (1971). E x perimental Jovian photochemistry: Initial results. Astrophys. J. 168, 563. SAGAN,C., AND MULLEN, G. ( 1971 ). T h e e v o l u t i o n o f E a r t h a n d Mars. Cornell C R S R R e p t . 460.

WESTPHAL, J .

A. (1969). O b s e r v a t i o n s of localized 5-micron r a d i a t i o n f r o m J u p i t e r . Astrophys. J. 157, L63. YOUNG, i . T., AND YOUNG, L. D. G. (1972). To be p u b l i s h e d .