Estimates of methane and ammonia abundance in the Jovian atmosphere with allowance for scattering in the clouds

lCXlws30, 13N 15:t (1977)

Estimates of Methane and Ammonia Abundance in the Jovian Atmosphere with Allowance for Scattering in the Clouds ~,;. (]. TEIFEL

Astrophysical institute of the Kazakh SSR, Academy of Sciences, Alma-Ata, USSR Received October 27, 1975; revised )larch 29, 1976 Results of photoelectric measurements of the intensily in CH4 5430, 6190, and 7250 absorption bands, CH4 absorption lines in the 3u3 band, and the NH3 6457.1 ), line are examined from the point of view of a model which takes into account the role of umltiple scatterlag inside a homogeneous seini-infinite cloud layer in the formation of absorption components in the Jovian spectrum. Introduced are a number of simple ratios between depths of lines and bands and the parametem which characterize lhe properties of the cloud layer and the atmosphere above the cloucLsfor oc(turrence of the Heayey-Gree~stein scattering phase function at various degrees of '~symmetry in g. The CH4 content inside the cloud layer is determined as an equivalent thickness on the mean free path between scattering events. The latter was fotmd to be equal to A L ~ l0 ::~ 2 m-amagat at g = 0.75 or AL ~ 20 ± 3 m-amagat at g = 0.5 along all the above-mentioned CH4 absorption bands. For NHa it is AL ~ 31 ± 4 cm-amagat at g = 0.75 and AL ~ 62 4- 8 cm-amag~t at g = 0.5. The weakening of the CH4 absorption })ands toward tim edges of the Jovian disc requires volume scattering coefficient in the cloud layer of a~ ~ 10 ~ cm% The mean specific abundance of NH3 obtained within the cloud layer does not contradict the c.dculated abundance ,)f saturated gaseotts ammonia. INTRODUCTION T h e q u e s t i o n of t h e q u a n t i t a t i v e c o n t e n t of m e t h a n e a n d a m m o n i a in J u p i t e r ' s a t m o s p h e r e - g a s e s m a d e u p of t h e m o s t i n t e n s e a n d e a s i e s t t o d e t e c t a b s o r p t i o n b a n d s in t h e s p e c t r u m - - h a s b e e n d i s c u s s e d for a very long time. And investigators return t o it a g a i n a n d a g a i n as n e w o b s e r v t t t i o n a l d a t a b e c o m e a v a i l a b l e , b o t h f r o m tile p l a n e t itself a n d f r o m l a b o r a t o r y e x p e r i m e n t s . U n f o r t u n a t e l y , i n t e r p r e t a t i o n of s p e c t r a l o b s e r v a t i o n s of J u p i t e r , w i t h r a r e exceptions, proceeds from the assumption t h a t all o b s e r v a b l e a b s o r p t i o n is f o r m e d in a p u r e l y g a s e o u s a t m o s p h e r e w h i c h lies a b o v e a diffusely r e f l e c t i n g d e n s e c l o u d l a y e r . Y e t , d u r i n g t h e p a s t 10-15 y e a r s a l a r g e q u a n t i t y of d a t a h a s b e e n p u b l i s h e d

w h i c h seems n o t t o fit w i t h i n t h e f r a m e w o r k of t h i s r e f l e c t i n g c l o u d l a y e r m o d e l ( a b b r e v i a t e d as R L M ) . T h e s e d a t a i n d i c a t e t h t t t t h e f o r m a t i o n of low a n d m o d e r a t e p l a n e t a r y a b s o r p t i o n lines a n d b a n d s t a k e s place primarily inside the planetary cloud c o v e r in t h e p r o c e s s of m u l t i p l e s c a t t e r i n g of r a d i a t i o n i n c i d e n t u p o n a e r o s o l p a r t i c l e s . T h i s w o r k a t t e m p t s to e x a m i n e r e c e n t r e s u l t s of p h o t o e l e c t r i c m e a s u r e m e n t s of CH4 a n d N H ~ a b s o r p t i o n b a n d s f r o m t h e p o i n t of view of a m o d e l w h i c h t a k e s i n t o a c c o u n t tile role of m u l t i p l e s c a t t e r i n g inside t h e J o v i a n c l o u d c o v e r in t h e f o r m a t i o n of t h e s e b a n d s , on t h e basis of q u a n t i t a t i v e c a l c u l a t i o n s of t h e r e f l e c t i v e c h a r a c t e r i s t i c s of a s e m i - i n f i n i t e h o m o g eneous scattering-absorption medium. 138

Copyright ~ 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.

JUPITER METHANE AND AMMONIA ABUNDANCE It should be noted at the outset that, as yet, none of the models in use is capable of providing a sufficiently high degree of accuracy and reliability for the derived assessments of the content of absorptive gases in the atmospheres of the giant planets. There are several reasons for this. First of all, the observational data, especially those regarding the absorption lines, are not yet exact : Spectrophotometry is unavoidably burdened by fundamental errors inherent in the photographic method; photoelectric measurements are more reliable, but an increase in spectral resolution is, more often than not, accompanied by losses in spatial (angular) resolution and a greater influence by the Doppler effect, attributable to rotation of the planet. Optical parameters of the planetary atmospheres, which must be known for interpretation of spectral observations, are not yet very accurately defined ; moreover, they are subject to fluctuation much of the time. The increased complexity of models employed in the analysis of planetary spectroscopy results is accompanied by an increase in the number of undefined, and therefore randomly variable, parameters. The two-layer model, under examination in this article, has only one, although much more fundamental, parameter--specifically, the degree of assymmetry in the scattering phase function--and it is given with a high degree of arbitrariness. A second parame t e r - t h e reflective capability of aerosols in a continuous spectrum--plays a smaller role, but can be taken directly from the observations. In contrast to previously published works, in which an analogous model was employed, a simple method is offered here for computing base and unknown quantities which permits easy interpretation of spectral observation results and exposure of the effects of one factor or another on the character of intensity changes in the absorption lines and bands in different zones of the disc. This method, so far, applies

139

only to the occurrence of the HenyeyGreenstein scattering function, with arbitrary values for the asymmetry parameter, but it could also be used to simplify computation in other more complex phase functions if numerical tables of the reflectivity coefficients were compiled for them. TWO-LAYER MODEL WITH HOMOGENEOUS SEMI-INFINITE CLOUD LAYER It is known that the diffusely reflecting semi-infinite homogeneous layer of a gasaerosol medium can be characterized by the scattering phase function x (cosy), where ~ is the angle of scattering, and by the probability of quantum survival (or albedo of single scattering) ~

= ../(.~ + ~o)

(1)

in a continuous spectrum and ~, = . a / ( . ~

+ Ks + K.) = (~o-, + ~ ) - 1

(2)

in the region of molecular absorption bands or lines. Here .~ is the scattering coefficient of the aerosol, K~ and K~are the coefficients of true absorption in aerosols and gas, respectively, and ~. = ~ . I . ~ ;

(3)

thus the depth of the absorption line or band, formed inside the cloud layer, can be found by the respective values of diffuse reflectivity coefficients p~ and p, by the formula R' = 1 - p~(~, g, .0, , ) / p c ( ~ o , g, ,0, ~),

(4)

where ~0 and ~ are the cosines of the angles of incidence and reflection, and g = (cos y) is the parameter of asymmetry in the scattering function. If r~ is the optical thickness of the outer atmosphere (above the cloud layer) in the absorption band region, then, taking for simplicity of further notations tt = t~0, we have R(tL)

1 (p./p¢) exp(--2r~/'~) = 1 -- (1 -- R') exp(--2r,/tL).

=

- -

(5)

140

V. O. TEIFEL

Numerical results of calculations of the refleetivity coetfieients p(c0, g, #) are, currently published for isotropic scattering (g = 0), for the simplest nonspherical scattering funetions, for the submitted binomial and trinomial expansion by I, egendre polynomials, and for the H e n y e y - G r e e n s t e i n sc:tttering function X(COS@ = (1 -- g~)/'(1 + g"- -- 2g('os3');.

((;) Sufficiently detailed tables of p were recently published by Dlugatch and Yanovitskij (1974). With the aid of these tables one can calculate for a given ~0,. and q the dependence between depth R' and the parameter 3~ on the basis of which profiles m a y be plotted for the absorption bands or lines which are formed in the scattering medium, i.e., inside the cloud layer. For ease and speed of calculation of If', the a u t h o r (Teifel, 1975a) offers simple approximating formulas for the dependence R'(5~), one of which is (if #0 = # = 1) Je t = [1 q- (/31:;~,)0"~'6'~6"c1~ 1,

(7)

where 31 is the value of 3~ at Rt' = 0.5 and c, is a q u a n t i t y near unity. Concrete vMues of ~ and ct depend on g and w,,. Examples of the dependencies RI' (3,) are shown in Fig. 1. In general, when the absorption is

also pttrtially formed in the purely gaseous layer above the clouds, the depth of the absorption band is equM to R~ = 1 -

[1 +

(ls/~)

o.~/,,,]

X exp(--2b* 3~), b* = ~,,0H0.

0.4 0.2

-40

(9)

The ratio (9) ensues from the condition of homogeneity of the cloud medium (3~ does not v'~ry in depth within the cloud layer). Since

r~ = ~,I)H(),

(10)

where H0 is the altitude scale for the outer atmosphere and K~0 is the volume absorption coefficient at ils t).tse, then from (3) it, follows that r~ =

3~.oHo

=

b*3~.

1 -- R ' 6 , , #,,) = (t -

R , ' ) (#,,,,) ~. ~,,;

i 0.0 0.0 0.50 0.75 ogo

55

0.75 0.85 075 0.75 C75

-50

,

,, \

"\,

",, " ' ~ \ ",

-. , .

2.5

(11)

]t was shown earlier (Teifel, 197ga) that, in the ease of formation of the absorption line or band in a homogeneous semiinfinite medium, variation in residual intensity with change in angles of incidence and reflection on the p l a n e t a r y disc can be represented (when # /> 0.3) by the simple formula

0.6 I 2 3 4 5

(S)

where

'20

Tib

;.0 l.og )~.,,

""

. ~, \

.0.5

"

0

Fro. 1. Dependence between residual ilL(ensiLy i n ~, lille or band . [ al),sorption 1 -- It'1' and log 3. at several values of the assymmetlT parameter in the scaLtering phase function g and the coefficient of diffuse reflection p~ for a semMnfinite cloud layer in a continuous spectrum.

(r_')

JUPITER METHANE AND AMMONIA ABUNDANCE when g = #0, 1 - R'(#) = (1 - R t ' ) # 2(k.-~°).

(13)

H e r e R~' is the d e p t h of the b a n d at the center of the disc (# = 1), and k, and k~ are the coefficients of darkening t o w a r d the edge of the disc inside the b a n d and in a continuous spectrum, included in the M i n n a e r t formula for distribution of brightness over the disc B = Bo#ok# k-1.

(14)

F o r m u l a (14), as shown b y Binder and M c C a r t h y (1973) and Teifel (1975b, 1975c), presents both the observed and the theoretically calculated variation of brightness on the discs of J u p i t e r and S a t u r n v e r y well. Expression (12) is also derived from (14). I t is not difficult to see t h a t in the absence of absorption in the a t m o s p h e r e a b o v e the clouds, the d e p t h of the absorption bands and lines m u s t decrease t o w a r d the edges of the p l a n e t a r y disc, since 2 ( k ~ - k~) is always negative. T h e same should be observed with low b* values, when absorption in the a t m o s p h e r e a b o v e the clouds is low in comparison with absorption within the cloud layer. Quantities 2 ( k , - k~) can be c o m p u t e d a p p r o x i m a t e l y b y a formula analogous to (7) but with other/32 and c2 p a r a m e t e r s : 2(k.

--

k¢)

=

--

141

F o r a given g and pc one can calculate at w h a t values of b* the d e p t h R2 of the absorption b a n d or line near the edge of the disc (when ~ = 0.5) will be greater t h a n or less t h a n the d e p t h in the center of the disc Rt. T h e critical value of bet* at which R1 = R2 is found with the condition (1 -

R ~ ) / ( 1 - R1) = 0.52(k'-k°) exp(--2bcr*fl~) = 1,

(18)

whence exp(2bcr*~) = 0.52(k'-k°)

(19)

b~,:*fl, = -- 0.3466[2(k, - kc)~.

(20)

or Substituting (15) into (20), we arrive at b~r* = 0.3466/[-(~2/fl~) °.s68~/~2 + l~fl~.

(21)

As can be seen in Fig. 2, bor* takes on m u c h greater values at low Rt depths, i.e., for weak absorption bands and for wings of strong bands and lines. However, even though bet* increases with an increase in the degree of a s y m m e t r y in the phase

']•'* 10 R2 > R 1

8 5

[-(fl21fl.) °.86s6/c. + 1-]-L

(15) I n the final analysis a ratio can be derived between RI' and 2(k~ - ko), which is convenient for calculating the variation of absorption over the p l a n e t a r y disc, and includes the p a r a m e t e r s fl~, /~, Cl, and c2, which depend on the degree of a s y m m e t r y of g in the phase function and on the diffused reflection coefficient in a continuous s p e c t r u m pC (or on we) : 2 ( k , -- k~) = -- E(1/R~' -

1) ~ m + 1-]-~, (16)

where n =

cl/c2,

m

=

(f12/l~l) °.s6s6/~.

(17)

4 2 0 0

.2

.4

.5

.5

1,0 R1

FIG. 2. Dependence of the critical value bet* (for which Ra = R~) on the optical depth of an absorption line or band in the two-layer model at pc = 0.75 and at three values of the asymmetry parameter in the scattering phase function g. ]f b* > bcr*, then R2 > Rl; and, coaversely, when b* < be,:*, R2 < R1.

142

V. G. TEIFEL

function, still it does not exceed 10. This indicates t h a t if the intensity of the absorption lines or bands does not show an increase toward the edges of the p l a n e t a r y disc, then it can be assumed a priori t h a t b* < 10. Spectral obserw~tions of Jupiter provide evidence that, with the exception of some latitudinal variations related to the lowering of the effective b o u n d a r y of the clou(t cover with latitude (Teifel, 1975d), generally within limits of "~ single 1)elt of latitude, the intensity of ('.H4 and N H s absorption bands diminishes toward the edges of the planetary disc. Within the framework of the two-layer model, under s t u d y here, when H0 ~ 2 X 106 cm this indicates t h a t b* cannot be more tha.n 5 to 7 and the scattering coefficient a. must be of order 10 -6 cm-L In contrast to the R L M , the two-layer model can, in principle, provide the content w, of a gas in the atmosphere above the clouds and the q u a n t i t y of a gas (equivalent thickness) A L, falling on the mean free path of photons between scattering events in the cloud layer. For the absorption line the Lorentz profile of dependence of absorption coefficient on frequency is = N,lTraL(1 + a2),

(22)

where S is the integral coefficient of absorption in the line (the line strength), aL is the Lorentz half width, and a = (. -- "0)/aL. The visible equivalent width of the line in the reflecting cloud layer model (RLM) is related to the q u a n t i t y of absorptive gas in the visual ray by simple ratios (see, for example, Moroz, 1967) W =Snw

(23)

if the line is very weak (unsaturated) and })y W = 2 (Snwa L) ' (24) if the line is strong (saturated). These ex-

pressions define tile asymptotes of the curve of growth, which can be conveniently plotted in units o f l o g ( W / a L ) a n d l o g ( S ~ w / ~ a L ) . T h e q u a n t i t y S~w/TraL characterizes absorption in the center of a line formed by a layer of gas with an equivalent thickness w [ m - a m a g a t ] observable from the outside at an angle or angles by which is determined the visible atmospheric mass (localized or averaged over the disc) n ~ 2. In the model which accounts for scattering in the cloud layer (CSM), the equivalent widths of the lines are computed by the formula 1

| V / a t = 2/ d

R,(a)da,

(25)

0

where Rt(a) = 1 - [1 + [~.o '~t (1 -{-a2)] °-s'~:*~} ~ Xexp[--2b*fl~o/(1 + a2)], (26) and as the argument, :~ q u a n t i t y is used which corresponds to the center of the line (, = vl,) 3~o = SAL/TraL.

(27)

The content of gas wl in the "~tmosphere above the ch)uds in this case is w~ = b * A L

(~.~0/z.),

(2S)

where a,~ is the average scattering coefficient at the effective level of absorption layer formation inside the cloud layer. Since our understanding of t~ homogeneous semiinfinite layer is based on the invariability of the quantities 3~ and g with depth, the following condition must l)e m e t :

~.(z)

~ ~(z).

(29)

Consequently, in the homogeneous model one is unavoidably drawn to the ~ssumption that, within the limits of the cloud layer, the law of the scattering coefficient variation with altitude in an aerosol medium is the same as the law of wiriation of the volume absorption coefficient of a gas component. This is the weakest area in the homogeneous cloud hwer models. Com-

JUPITER METHANE AND AMMONIA ABUNDANCE parison of results from observations with theoretical calculations can only expose possible discrepancies, attributable to the inhomogeniety of the cloud cover's actual structure, but it does not allow determination of the true character of dependence of ~a on Z. CH4 ABSORPTION BANDS The greatest number of investigations of methane absorption in the Jovian atmosphere deal with the 6190A band and lines in the 3,3 band near 1.1 ~m. However, in contrast to the 6190 A band Ea substantial amount of work has been published on its intensity variations from the center to the edges of the disc (for example, Hess 1953; Avramchuk, 1970; Teifel, 1959, 1969; Aksenov et al., 1972; Avery et al., 1974)1 , only the work of Bergstralh (1973a) has been devoted to the intensity variations of the 3,~ band on the Jovian disc. In general, studies of methane absorption bands in the visible and near-infrared regions of the spectrum lead to the following conclusions. (a) The intensity of the weak and moderate bands decreases from the center to the edges of the disc within limits of one zonal belt; (b) absorption in the strong bands increases with latitude, with the exception of the Jovian polar regions, where it decreases drastically; (c) the methane content in the Jovian atmosphere assessed in the reflective layer model (RLM) varies from the weak to the strong bands of absorption, decreasing as the band intensity increases; and (d) darkening toward the edges of the disc is ahnost identical both inside the absorption bands and in the adjacent regions of a continuous spectrum. These peculiarities cannot be explained within the framework of the R L M without introducing some rather artificial assumptions about the cloud surface structure. At the same time, these peculiarities can be explained naturally by taking into account the multiple scattering

143

effect in the cloud layer of the two-layer model (CSM). To calculate the curve of growth of methane absorption bands in the visible region of the spectrum, one must know the .~bsorption coefficient S~ and also assume that the rotational structure of the bands does not cause sharp fluctuations in the monochromatic values of S~ within limits of small-wavelength intervals; i.e., that within limits of the band the absorption can be viewed as quasicontinuous. In the opposite case the problem becomes extremely indefinite, since even when using one model or another for the structure of an absorption band we must arbitrarily assign an average distance between the lines, on which depends to an important degree the residual intensity (transmission) distinguishable at various points of the band under low spectral resolution. In this regard, results of laboratory experiments by Lutz et al. (1976) are very important. According to these experiments, the CH4 4410, 4860, 5430, and 5760 A absorption bands alter their profiles and equivalent widths with variation in quantity of absorptive gas in practically exact correlation with calculations by the Bouguer exponential law, which would not take place with a discrete structure of these bands. The same applies to the CH~ 6190/~ band, the profile of which is determined either by closely spaced and unresolvable lines (except for a relatively small number of visible lines not affecting the band profile), or by continuous or diffused absorption (Aksenov et al., 1976). Measuring the depth of an absorption band at the center of the disc (R1) and near the edge (at ~ = 0.5), one can find the quantity D

=

(1

--

R,~)/(1 -- RI) 2.

(30)

This quantity D, where R2 is the band depth at u = 0.5, as can easily be shown, does not depend on the optical thickness of the outer (above the clouds) atmosphere r~ and

144

V.G. TI,;IFEL

should be equal to the ratio ( I - R,/)/ (1 - R , ' ) " - , where R', as before, indicates the band depth, determined by its formation only within the cloud layer. The dependence D (R,'), which can easily be calculated theoretically, does not change greatly with changes in the a s y m m e t r y of the sc,attering phase function. B y graphically equating D(R,') with the q u a n t i t y D calculated b y observable depths Rt and R_., we can find RI' and, accordingly, r~: ~

=

-~

In r ( 1

-

~,),,'(1

-

n?)~.

(;~l)

Since the assessment of the q u a n t i t y R.~ is linked with certain difficulties in measurements near the edges of the p h m e t a r y disc, in photoelectric observations it is advisable to make measurements of the al)sorption band profile at the center of the dis(: (for a fixed R~) and for the entire e(luatorial belt of Jupiter, in tile latter instance intersetting the whole planetary (tisc ahmg its e(luatorial diameter with the input aperture of the spectrometer. Thus the integral depth of the absorption band IL, is f(mnd for tile entire equatorial belt. Now, knowing the q u a n t i t y of R, from observations, one can calculate with this R, value the (lependence between R~ and the variable optical thickness of the atmosphere above the clouds r~ t)y the formula 1 -

Ro =

(1 -

R0

exp('_'~)

×f,)~k,-~exp(-2~X#)d,'/fl,'-'~°-~dr (a2) and then with the Ro wdue found form the observations estimate r . Although R~ is less sensitive to changes in r~ than is R~, determination of r, by the method described can be even more certain, inasmuch as the Re value is almost free of susceptibility to the effects of unfavorat)le ot)serrational conditions. According to our photoele.ctric measurements in 196S :rod 1(.)74 tile central depths R1 :m(l No are as follows : in the CH4 6190 A

band, Rt = 0.209 4- 0.005 and R, = 0.196 4-0.004; in tile C H 4 7250 A band, R, =0.568 ± 0.008 and Ro=0.553 4- 0.00S. The dependence Ro(r,), as shown by calculations, practically does not change with changes in the parameter of a s y m m e t r y g in tile limits 0.5 to 0.75. These limits m a y be regarded as highly probable on tile basis of d'~ta on the distribution of brightness over the Jovian (list; in the hmg-wavelength sector of the visible region of the spectrum, both from terrestrial observations (Binder and MeC'u'thy, 1973; Teifel, 1975b), and from measurements by Pioneer 10 (Tomasko et al., 1974). The coefficient of diffuse reflection of the Jovian cloud cover in red light is taken to be p,, = 0.75 on data from absolute spectrophotometric measurements (Bugaenko, 1(,)72; Teifel, 1971). B y the 1?~ and 17~ values presented above, we :~rrive at r,(6190) ~- 0-0.009 and r~(7250) ~ 0.03-0.07. ('alculating R1 and 1 -- l?t' = (1 -- R~) exp(2r~),

~ = ~l(l/l{t'

-- 1) I.r:)~et,

(:t:3) (33')

one can determine the approximate value of b*, which falls within the limits of 1 to :3. The limiting values of B, for the eentr.d p'~rts of the CH4 6190 ~md 7250 i absorption bands result "ts folh)ws : at g = 0.75, ~(6190) ~ 0.0055-0.0065 "rod ¢L(7250) :~'~-0.025-0.030; at g = 0.50, fl,(6190) 0.010-0.012 "rod ~ ( 7 2 5 0 ) ~ 0.050-0.060. The a m o u n t of absorptive g'~s along "t mean free p a t h within the cloud layer is equal to A L = ~,/S~. (34) Since exact wdues of tile absorption coefficient per unit of equiwflent p~th S, for the Ct[~ 6190 and 7250 .~ bands are not yet known, assessments of AL can only be preliminary, '~ssuming th'~t the visible intensity of these bands correl.~tes with the same equivalent p a t h of absorption nw, de.terinine(1 in the R L M . Another c'~se is presented by the weaker CIt4 5430 ~t band,

JUPITER METHANE AND AMMONIA ABUNDANCE for which there are now valuable results from l a b o r a t o r y measurements of S, (Lutz et al., 1976). Then with the value of vw and the visible depth of the band R1 one can determine the approximate absorption coefficient of S, in the center of CH4 6190 and 7250 A bands and the values of AL b y (34). Therefore we now return to the CH4 5430/~ band. The equivalent width of this band in the Jovian atmosphere is equal to W = 11.4 cm -~ (Lutz et al., 1976) or W = 11.9 ± 1.7 cm -1 (Bugaenko et al., 1972). The latter q u a n t i t y refers to the center of the disc. F r o m our photoelectric measurements (Teifel and Kharitonova, 1975, u n p u b lished), W = 10.2±0.5 cm -~ and R = 0.052. When calculating the curve of growth in the region of small equivalent widths in the cloud scatter model one can disregard the extremely low absorption in the atmosphere above the clouds. Using the S,, presented in the article by Lutz et al. (1976), we computed the curves of growth of the band at g = 0.75 and g = 0.50. I n both instances po = 0.70 was assumed. The curves of growth are depicted in Fig. 3, which also shows t h a t the curve of growth calculated for the purely absorptive gas layer coin-

145

cides with t h a t derived in the lat)oratory experiments of Lutz et al. For the cloud scattering model (CSM), observable equivalent width values for the 5430/~ band lead to the following assessments of the content AL on the mean free p a t h : AL = 10--13 m - a m a g a t at g = 0.75 and Ar~ = 16-22 m - a m a g a t at g = 0.50. I n the R L M on the curve of growth where nw in Fig. 3 correlates with the entire equivalent p a t h of absorption, we arrive at nw = 445 4- 60 m-amagat. The R L M produces the same result, 430 m - a m a g a t (Lutz et al., 1976). If the assumption is now made, as given above, t h a t absorption in the central parts of the CH4 6190 and 7250 /~ bands correlates with the entire equivalent path, then the absorption coefficients of S, in the center of the band can be approximately derived by the ratio S, = - I n (1

--

R1)/~w,

(35)

whence S~(6190) ~ 5.3 X 10 4 m x '~magat -1 and S,(7250) ~- 1.9 X 10-3 m -1 a m a g a t -x. For the CH4 6190 A band, we find AL ~'~ 10-12 m - a m a g a t when g = 0.75 and AL ~ 19-23 m - a m a g a t when g = 0.50. For the CH4 7250 A band with the same g

]IV',CfZ?-I Ioo

C5NI

I

i 10 -~

~

, I ,,,,I

, 10 .2

,

[ ,,,,I

, 1O-;

,

~ l,,,,l

,

,

,

f,'~,

I

10 ALOr T~Ld"

FIG. 3. Curves of growth of the CH4 5430 ~ absorption band for scattering (CSM) and reflective cloud layer (RLM) models: (1) according to laboratory measurements by Lutz et al. (1976), (2) calculation for a purely absorptive gas layer, (3) calculation for CSM at g = 0.75 and pi -~ 0.70, and (4) same as (3) but at g = 0.50 and po = 0.70.

146

v . G . TI,;IFEL

values we derived Aj: ~ 13-16 m - a m a g a t a n d AL ~ 26-32 m - a m a g a t , respectively. Assessments for the 7250 A band shouhl be t r e a t e d with some caution, inasnmch as its intensity in the Jovian spectrum m a y correlate with a lesser equivalent p a t h Wv t h a n t h a t of bands with lesser intensity. According to Bugaenko (1973), wh<) employed unpublished d a t a <)f Cruikshank, the t~bsorption coetticient in the center of the 7250 A t)and is equal to S~ ~ 2.95 X 10 -a In ~ a m a g a t - L A L ~ S . 5 - 1 0 ma m ' t g a t at g = 0.75 and AL ~ 17-20 ma m a g a t at g = 0.50; i.e., for all three absorption bands, AL values are prattle'ally identical: 10 ± 2 and 20 =t= 3 m - a m a g a t at g = 0.75 and 0.50, respectively. T h a t resultant A L values (lepend upon the assume(t g (luantity is quite natural, inasmuch "~s in each obserwd>le ch,u'acteristic (photometric and spectral) the values of fl~ depend on g. Since the C n 4 absorption coefficient ~ in the region of the :d)sorption b a n d formation does not have to depend on the scattering features and density of the aerosol component, obviously then,

o-,,(g,).,'o-,,(.q,~) = ~(,q~).%(,q,)

(3t9

b*

R,

.,50 - -

~0

/

15

.25 .

J2 R, -

.20

0.20

.19 4

.10

,

0

1

I

.02

.04

I

I

.05

I

1

.O8

t

.1@

0

%

lrm. 4. Varialion in Re a n d b* d e p e n d i n g on r. (optical Ofickness of tt~e a t m o s p h e r e a b o v e the clouds) a t a ' c o n s l a n t v a l u e for l h e a b s o r p t i o n b a n d d e p l h a t ' t h e c e n l e r of t h e disc of 1¢i = 0.20.

and the specific content of CH4 per unit of m e a n free path v,~ = A L<~

(37)

m u s t be the same, independent of the ass u m e d g quantity. But for the assessment of w~, it is essential to know with sufficient c e r t a i n t y a,, which cannot be determined with a degree of accuracy higher t h a n a t',~ctor of 2. Here limitations are imposed not only by imprecisions in the theory, but also by the inaccuracy of the usual m e t h o d of spectrophotometrical m e a s u r e m e n t s of at)sorption bands. For instance, one of the m o s t serious errors in estimating depths and equivalent widths of "d)sorption 1)ands or lines relates to determining the level of the continuous spectrum. In nleasurements of weak and m o d e r a t e absorption layers even a small error of this kind can significantly alter the result, especially in studies of the p l a n e t a r y disc near the limbs. Figure 4 depicts graphs of dependence of 1~ and b* on r, where the b a n d depth at the center of the disc R~ = 0.2. In the region of sm'dl r~, we have A r ~ A R / 2 and A b * > 102AR,,, i.e., ~m error in the determination of R2 of 0.010 leads to an error in r~ of a b o u t 0.005 and to an error in b* of more t h a n 1 at values of b* < 5. The actual precision of R1 and R2 depth assessments can be better than 0.005 only with a large n u m b e r of measurements. Single measurem e n t s of band depth and equiwdent width even with photoelectric observations are characterized b y '~ relative error factor of 5-S<~j (of. Avery el (d., 1974); therefore, the requisite n u m b e r of m e a s u r e m e n t s of the t)and profile at a given point on the disc cannot t)e less t h a n 10, even with the best observational con(litions, and one should strive toward m a k i n g the systematic error arising from 1)lotting the level of the continu(ms spectrum at least the same (it, is ahnost impossible to eliminate it) for ol)serv'~tions of various regions of the phmet'try disc.

JUPITER METHANE AND AMMONIA ABUNDANCE CI[4 ABSORPTION LINES IN TIIE 3a BAND

147

shows (Fig. 5) t h a t tile difference betweeu the profiles and equivMent widths at the center and at the edge of the disc is so insignificant t h a t it cannot be detected given p r e s e n t - d a y m e a s u r e m e n t accuracy, whereas in the R L M the difference between profiles is quite distinct. Figure 6 depicts the curves of growth, cMculated for the R L M and CSM. For the C S M three curves are given, plotted in units of log ( W / a L ) and log fl~0, where ~0 relates to the center of the line and is linked with the equivalent p a t h on the m e a n free p a t h A L b y the ratio (27). I n the calculations, pc = 0.65 was assumed as the m o s t probable value of the reflectivity coefficient near 1.1/~m, according to Pilcher et al. (1973), taking into consideration d.tta from absolute s p e c t r o p h o t o m e t r y in the visible region of the s p e c t r u m (Bugaenko, 1972 ; Teifel, 1971). E q u i v a l e n t widths of R-branch lines of the 3va b a n d for J u p i t e r are t a k e n from Fourier s p e c t r o m e t r y d a t a (MMllard et al., 1973). We used only assessments of line

We now examine, from the point of view of the two-layer model, absorption lines in the 3~3 b a n d (1.1 tLm). Essentially, the intensity of these lines does not v a r y with passage from the center to the edge of the disc (Bergstralh, 1973a), which does not agree with the R L M , in which equivalent widths even of s a t u r a t e d lines were supposed to increase toward the edges of the disc at least in proportion to v~'. I n the CSM, the constancy of the line intensity indicates t h a t b* for t h e m cannot exceed 7 to 8, nor can it be less t h a n 1, since in the latter case we would have observed a decrease in line intensity toward the edges of the J o v i a n disc. Since the central residual intensity of these lines m u s t be less t h a n 0.1, it can be ~{ssumed, on the basis of Fig. 2, t h a t their equivalent widths will be almost identical at the center of the disc (~ = 1) and near the edge (# = 0.5) if b* = 4-5 at g = 0.75 or b* = 2-3 at g = 0.50. Actually, calculation of profiles of n e a r - s a t u r a t e d lines with Rt = 0.95 when b* = 5 at g = 0.75 R Q

//

.2

CSIVt

/'

.4

q=0.75 b*,'~5 /

.6

'

~ = 1.0

,

ill,= 1.Q

~=0.5

/t

.8

/ ~,C~

/ i

0

i

'2

i

i

4

I

!

6

i

i

~

i

i

10

L

i

i

i

.-

'~_ 14 0

i

i

2

i

i

4

i

~

5

i

{

5

i

I

IO

]

i

12

I

i

14

FIG. 5. Comparison of profiles of a Lorentz absorption line at the center of the disc (# = 1) and near the edge of the disc (~ = 0.5) in formation of a line in a two-layered atmosphere (CSM) with b* = 5 and in a purely gaseous atmosphere (RLM). Central line depth at ~ = 1 is in both cases assumed equal to R~ = 0.95.

1t8

\'. ( ;.- '.l'l,:I l,'le;l~ L o g { W / a L) 2.0

1.5

j jl ..-J

CSM J 1.O A. A-

Q5

A

RLM

K

O 2

3

-05 A

-10 -30

/-

'

i

-

2'0

i

I0

__

i

u

~

0

x_

i

I0 l.og (SAL./rr,:x,. or

_

_

20 ~SbS/n%_)

FIG. 6. Curves of growth for absorption lines, formed in the two-layered atmosphere (CSM) at p,, = 0.65 for: (l) g = 0.75, b* = 2, (2) g = 0.75, b* = 5; (3) g = 0.50, b* = ] ; and (4) in a purely gaseous medium. i n t e n s i t y R(1) a n d R ( 2 ) , t'~king i n t o acc o u n t t h a t t h e line R ( 2 ) is n o t a singlet. t { a l f - w i d t h s of t h e s e lines as m e a s u r e ( t b y M a i l l a r d et al. a r e e q u a l to 0.06 an(1 0.13 em 1 respectively. The following remarks n m s t be m a d e a b o u t t h e visible h a l f - w i d t h s of t h e a b s o r p t i o n lines f o r m e d in t h e s c a t t e r i n g m e d i u m . A s is e a s y to see in t h e line profile cah, u l a t i o n s , t h e v i s i b l e h a l f w i d t h a, d e f i n a b l e as half t h e w i d t h of t h e line a t its h a l f - i n t e n s i t y level, i n c r e a s e s m a r k e d l y as t h e line a p p r o a c h e s s a t u r a t i o n , in c o m p a r i s o n w i t h t h e a s s i g n e d ~L value. For a purely al)sorptive medium,

a n d for a s c a t t e r i n g m e d i u m ,

(1,"R0-

11] ~'~'')~6~'~ -

1}~.

(39)

V a r i a t i o n of a x A a n d aNs w i t h g r o w t h of t h e c e n t r a l d e p t h of t h e line R0 is i l l u s t r a t e d in Tat)le I. W i t h 'fl)sorption, b o t h in t h e c l o u d l a y e r a n d in t h e a t m o s p h e r e a b o v e t h e clou(ls, t h e v i s i b l e h a l f - w i d t h of t h e line, n a t u r a l l y , will h a v e a lesser a n t h a n in t h e c'~se of t h e s c a t t e r i n g m e d i u m ,done, b u t still will exceed half w i d t h a~. F o l l o w i n g T a b l e I, t h e visible h a l f - w i d t h of t h e lines in t h e 3ua t)and n m s t be d e c r e a s e d b y "~t a ~ x = a a / a t , = f l o g ( l -- R o ) / least 4 to 5 t i m e s in o r d e r to d e r i v e t h e log (I -- R o / 2 ) -- 1~", (3S) l r u e L o r e n t z i a n h a l f - w i d t h at,; t h e r e f o r e ~L m u s t be at)out 0 . 0 2 - 0 . 0 4 c m -4. T h e h a l f TABLE I wi(lth of lines in t h e 3va b a n d p r o d u c e d b y Visible Half-Widths of Lines (in ~L Units) collisions of CIt~ a n d tI2 is e(lual to aL = 0 . 1 0 c m ~ a t m -~ "d T = 1 6 0 ° K a n d 0.11 c m -~ ]~O ¢tNA aNS ]l~O (INA aNN . . . . . a r m -1 a t 7 ' = 13001( ( V a r a n a s i et al., g= ,j=o 0y= 1973), "rod for collisions of C t t 4 a n d t t e , .75 0.75 aL = 0.06 an(t 0.07 c m -1 -~tm -~, respec.2. '32 0.1 1.03 1.22 1.08 0.8 1.47 2.81 3.3',, t i v e l y . I f it is a s s u m e d t h a t in t h e J o v i a n a t 0.2 1.06 1.30 1.15 0.9 1.69 4.20 0.3 1.09 1.40 1.23 0.95 1.91 6.3t 4.7,t m o s p h e r e I t ~ / H e = 5, t h e n a L ( T = 130°K) 7.60 0.4 1.14 1.52 1.33 0.98 2.19 ll.0 lO.9 rw~0.10 c m ~ a t m - L T h e n t h e effective 0.5 1.19 1.68 1.46 0.99 2.40 16.7 0.6 1.25 1.90 1.63 0.999 3.00 67.9 35.s p r e s s u r e in t h e r e g i o n of line f o r m a t i o n is ns 0.7 1.34 2.23 1.89 0.9999 3.51 277 p~ < 0.5 a t m . F v e n if T = 1 9 0 ° K is asg = 0

JUPITEI¢ METHANE AND AMMONIA ABUN1)ANCE

much as in th(' data published later t)y Bergstralh and Margolis (1971) the Sz values differ little from the former. Since Sj depends on temperature, the approximate reduction of S~ to the temperature of the Jovian atmosphere was derived by the formula

sumed as the greatest possible temperature at the effective level of line formation then at aL (T = 190°K) = 0.08 cm -1 atm -1 the effective pressure is not more than 0.5 atm. At the same time calculation in the model of vertical structure of the Jovian atmosphere in the " g r ~ y " approximation at H~/He = 5 and To = 134°K (Fig. 7) shows t h a t the T = 190°K level corresponds to a significantly higher p r e s s u r e - - m o r e t h a n 1.5 atm. I t would still be premature to assign too much meaning to these assessments of po, since the line half-widths are not very firmly defined because of inaccuracies in plotting the continuous spectrum and in calculating the instrument profile, and for a host of other reasons. Therefore, we will assess w and A ~. by curves of growth, using two values for ~L: 0.10 cm -z, presented b y Maillard et al. (1973) as the most probable, and 0.025 cm 1, as accounting for the broadening effect in the visible line profile. Also taken as supplementary d a t a are photoelectric measurements of the line profile R(1) published by Bergstralh (1973b), who found t h a t the half-width of this line in the Jovian spectrum is aL = 0.072 cm 1. The absorption coefficient S~ for each of the lines was determined by M~rgolis and Fox (1969). We also used these d a t a inas100 Z, Krn

S~ (V)/S~ (To) = EZ (To)/Z (T) 3 Xeup[-BhcJ(JH-1) (T - ~ - T0-1)/]c~,

Z(T) ~ 0.115 T~

~00

T,°K

~ m -a t rn.

N

~

\

~

T

UV- BOUNDARY OF \ \ \-_il-T-~E-~~~D-S-~L-L~y~-- ~

I0

- 30

BO

- 40

100 \

-50

, .01

,

I ,,,~l

l .1

(41)

according to Margolis and Fox (1969). Two values were assumed for the temperature, 130°K and 160°K, in view of the fact t h a t the u n c e r t a i n t y of aL has a strong effect on the estimate of the rotational temperature, which was assessed by Maillard et al. (1973) as equal to Trot = 150 :k 15°K at ~ L = 0.10 cm -1. Table I I gives values which were found b y the curve of growth for the case when g = 0.75, po = 0.65, and b* = 2, and also vw, found by the curve of growth calculated for the R L M . The A L values in other cases m a y be derived by multiplying the t a b u lated values by 0.8 (if ff = 0.75 and b* = 5) or by 2 (if g = 0.50 and b* = 1). I n the

\\

20 10

(40)

where B = 5.240 cm -1 is the rotational constant of CH4 molecules and

150

40

119

i

i

I

,

~i,,l

,

1

'~

I .... 10

p, otto

FIG. 7. Variation of temperature and pressure with altitude in the Jovian atmosphere, according to the model calculated in the "gray" approximation with H2/He = 5 and To = 134°K.

150

V. (]. TI,]IFEL TABLE II

A L and ~w 1)erived from Absorption in l,ines of the CH~ 3va Band in Jupiter's Spectrum 7' (OK)

~L (era -l)

R ( t ) ~'

R(2),,

1/(1) ~'

. . . . . . . . . . . . . . . . . AL

~W

AL

rtW

AL

~TW

130 130

0.100 0.075

2.0 61 2.9 91 . . . . . . . . . .

....... 3 . 3 101

130 160 160 160

0.025 0.100 0.075 0.025

5.1 173 10.0 336 2.7 82 3.7 117 .... 6.g 232 12.9 431

7.7 25{) ...... 4 . 4 135

10.2 347

this band the photoelectric measureinents ot profiles of the separate lines in the aovia~ spectrum h a v e been m a d e with high spectra] resolution (Encrenaz et al., 1974). We examine here only the d a t a relating to one ot the m o s t intense and nonblending lines of this band, the 6457.1 A line. A curve of growth for this line in tile CSM is calculated b y the integration of the depths R~', which were c o m p u t e d b y the fornnl[a

R,'(a) = El + ( 1 ~ R e ' -

b Bergstralh (1973a). ( ' S M the equivalent thickness of (!H4 on the m e a n free p a t h along the line R(1) is 2 to 10 m-arm. I n the R L M the q u a n t i t y nw derived from the m e a s u r e m e n t s of the line R(1) lies within the limits from ~ 6 0 to 350 m - a t m . Line R(2) gives greater wducs, p r o b a b l y due to the fact t h a t it represents an unresolved doublet which is not accounted for in the curve of growth e,dculation. I n a s m u c h "~s the true value of ~ , for the lines in the 3,a band of the Jovian spect r u m is not yet known, one should hardly a t t e m p t to extract more probahle values of A ~, or ~w from T a b l e II, although it can t)c note(1 that, in accounting for {he effec~t of scattering on the intensity and visible half-width of the lines, the respective A~. values agree fairly well with those found td)ove along the Ct[4 5430, 6190, and 7250 fi, bands. AMMONIA Since the pressure of N t l a w~por falls sharply with a lowering of temper:tture, it can be assumed t h a t the content of a m monia in the outer a t m o s p h e r e (above the clouds) of J u p i t e r is extremely insignificant, and t h a t weak absorption lines and bands are essentially formed inside the cloud layer only. T h e most-studied N H a absorption band, at this time, is 6450 A, and within

11)

x (1 + a'-')°.~/~-,~ -',

M a i l l a r d et al. ( 1 9 7 3 ) .

(42)

where R J is the depth in the center of the absorption line, which corresponds to ¢~,0, determined by formula (aa). Since the N H a lines are weak, the calculation of the curves of growth in the C S M can also be m a d e with the 'rid of the Sobolev formula (1972) for equivalent widths of weak lines, which in a slightly modified form is written as

W , ' ~ , = 2('~(:i, #)j'(q)Ec0~(i-~0~)/w,0]~, (43) where C~ (g, #) is a p a r a m e t e r , depending on the t y p e of scattering phase function and ,ingles of incidence and reflection, wdues of which were t a b u l a t e d b y Anikonov (1974) for the t l e n y e y - ( ] r e e n s t e i n scattering function ; q = @ , , - w~,,) "(1 -- co,:)

(44)

and j'(q) is the function t a b u l a t e d in Sobolev's p a p e r (1962). When g = 0.75, p~. = 0.75 (c% = 0.9963) and u = 1, the p a r a m e t e r ('~ = 6.68. The curves of growth, calculated by integration of (42) and b y (43), differ little (Fig. 8), which relates to the a p p r o x i m a t e character of both expressions; however, the difference in t h e m cannot have .~ crucial effect on the tinal results. According to l a b o r a t o r y experiments the q u a n t i t y Sa for the N H a 6457.1 A line lies within limits of from 3.25 X 10 -a cm - t m -~ a m a g a t (Mason, 1970) to 4.96 X 10 -a cm -t m -q a m a g a t ~ (Giver el al., 1975). We used the

JUPITER METHANE AND AMMONIA ABUNDANCE d a t a of Giver et al., derived from photoelectric measurements, and estimates of the intensity of this line in the Jovian spectrum, published b y Encrenaz et al. (1974) : W = 0.128 cm -~, Ol = 0.216 cm-L I t can be assumed t h a t the t e m p e r a t u r e in the zone of line of formation on Jupiter is near 160°K; then the l a b o r a t o r y q u a n t i t y Sz, following Encrenaz et al. (1974), must be increased approximately twofold. The 6457.1 A line in the Jovian spectrum has a central depth of R0 >/ 0.2. According to Table I, ass > 1.2; i.e., the visible halfwidth of the line is approximately 20% greater t h a t the Lorentzian half-width aL. At narrow half-widths of the line a tangible role can be played b y the Doppler spread olD

=

( 2 k T / m ) i~o,/C.

(45)

At T -- 160°K, aD = 0.021 cm-1; then in the final calculation aL ~ 0.159 cm-L The effective pressure p~ = po(T/To)'~olL/Cq~o

(46)

is 1.3 arm when aL0 = 0.089 cm -1 arm -~ ( R a n k et al., 1966), P0 = 1 arm and To -- 300°K. B y the curve of growth, calculated for g = 0.75 and p¢ = 0.75, W / o l L = 0.8 and Sz (160°K) = 10 -~ cm -1 m -1 amagat, -1 we arrive at AL ~ 0.31 ± 0.04 m-amagat. At g = 0.50 this q u a n t i t y should be doubled. Thus the equivalent thickness of NHa on the mean free path inside the aerosol layer amounts to about 30 c m - a m a g a t if g = 0.75 and about 60 m - a m a g a t when g = 0.50. Comparison with data on AL along CH4 absorption bands yields a N H 3 / C H 4 molecular content ratio, inside the J o v i a n cloud layer, of NH~/CH4 ~ 3 X 10 -2.

(47)

Inside the cloud layer the partial pressure of NH3 probably (although this still remains only an assumption) should be near the pressure of the a m m o n i a vapors E ( T ) . Therefore the ratio (47) can be viewed as the lower limit; in the zone below the clouds

151

Io 9 (",,V"I (X L) 0.5

-

0.5

o I ® 2

I

-1.0 -

5.5

-

5.0

I -

2.5

I -

2.0

-

1.5

"LOQ ~'~o

FIG. 8. Curves of growth for weak absorption lines in CSM: (1) calculation of equivalent widths by the integration of (42) at g = 0.75 and pC = 0.75 ; (2) calculation of equivalent widths by the Sobolev formula (43) at g = 0.75 and p~ = 0.75; and (3) the same at g = 0.50 and pc = 0.75. the relative content of ammonia should be higher. Let us now make the following illustrative calculation. If we assume A L ~ 30 cma m a g a t and 10-6 cm -1 ~< ~a ~< 10-5 cm -~, we can obtain a specific abundance of a m m o n i a WA ---- ALa~ from 3 X 10 -5 to 3 X 10-4 c m - a m a g a t per 1 cm of the free p a t h length. Then the molecular concentration of NH~ is 8 X 10 ~4 ~< NA ~ 8 X 10 ~Scm -a

(48)

and the density of gaseous ammonia is, accordingly, 2 X 10 -s ~ pA ~ 2 X 10 - ~ g c m -3.

(49)

One m a y suggest t h a t the partial pressure and density of a m m o n i a inside the cloud layer are approximately equal to the pressure and density of the ammoniasaturated vapor ; i.e., p (NH3) = EA (T) and p (NH3) = pE (T), where, according to Lasker (1963), EA(T) = 1.325 X 10 la X e x p ( - 3 7 5 3 . 5 6 / T ) d y n cm -2

(50)

and pE(T) = E A ( T ) M ( N H 3 ) / R T .

(51)

152

V.G. TEIFEL

M ( N l t a ) = 17 is the molecular weight (,f :~mmonia and R is the gas constant. We can see now t h a t pA given by (49) corresponds to p,,: at 136°K <~ T 4 150°K. These temperatures are connected with the levels in the Jovian atmosphere where 0.6 arm 4 p ~< 0.8 arm (Fig. 7). These levels are certainly higher than the level with the effective pressure p o ~ - 1 . 3 atm derived from the half-width measurements of the NHa lines. Thus, the NHa abundance obtained from the line intensity measurements does not agree with the full pressure determined by its Lorentzian half-width. It should be noted, however, t h a t errors in the aL do not significantly affect estimates of abundance for unsaturated lines, whereas po depends to a critical degree on the accuracy of the ~ . measurements. The relative abundance of Nlla obtained inside the cloud layer, about 5 )< 10 r,, is apparently not far from the truth, inasmuch as radioastronomical observations found a relative abundance in the zone below the clouds of about 1.4 ( + 5 , - 1 ) X 10 -4 (Kuzmin and Smirnova, lq73). The concentration of gaseous NIla in the clouds should decrease as a result of condensation and sublimation. We did not consider here the question of tt2 abundance from the analysis of the H2 quadrupole absorption lines because it is necessary to take into account the effect of collisional narrowing of these lines, which depends strongly on the effective pressure on the line formation levels. Nevertheless it is obvious from analogy with the data on the CH4 absorption bands t h a t the tt~ absorption in the atmosphere over the clouds should be about 5 to 7 times less than the observed value because most of the absorption is formed within the cloud layer as a result of multiple scattering. T h e n we have above the clouds an If.., abundance of about 10 to 15 km-amagat instead of the :--75 km-amagat derived from the R L M interpretation. The equiwdent thickness of H2 over the

aerosol layer is about 10 km-amagat, as obt'dned from observations of Jupiter in the vacuum ultraviolet (Steeher, 1965; ()wen and Sagan, 1972) and near ultraviolet (Teifel, 1975b), and there is no contradiction between the quadrupole line measurements and ultraviolet p h o t o m e t r y data if the two-layer CSM is used. CONCLUSIONS The model, which accounts for the effect of scattering in the cloud layer on the formation of molecular absorption lines and [)ands, even in its simplest form, provides a better agreement between the observable variation in absorption over the planetary disc and theoretical calculations than does the reflecting cloud layer model. Here we have shown that in interpreting the observational data in the case of a homogeneous semi-infinite layer, we can use very simple formulas which facilitate easy assessment of the effect of variation in base parameters (reflecting capability and density of aerosols, degree of a s y m m e t r y in the scattering phase function, etc.) and of errors in the observed values on the derived results. As for every model, the two-layer model under discussion naturally permits the derivation of quantitative estimates only within the framework of those assumptions and simplifications built into it. Some uncertainty in the derived results is due, to a significant degree, to these simplifications, but also to insuifieient exactness of the spectral and photometric observations. Therefore, it seems to us (at least at the current stage of study of the giant pl.mets) t h a t primary attention should now be given, not so much to increasing the complexity of the theoretical apparatus used to interpret the not overly reliable observational dut~l, "ts to improving the precision and increasing the n u m b e r of measurements, and also to the search for and analysis of the contradictions which arise during the processing of these measurements through the use of the simplest theoretical models, which inust be

JUPITER METHANE AND AMMONIA ABUNDANCE

153

BUGAENKO,L. A., GALKIN,L. S., AND MOROZHENKO, A. V. (1972). The study of molecular absorption in the atmospheres of major planets. Astron. Vestnik 6, 223-227. ACKNOWLEDGMENTS DLUGATCH, J. M., AND YANOVITSKIJ,E. G. (1974). The optical properties of Venus and the Jovian The author takes this opportunity to thank Din. planets. II. Method and results of calculations T. Owen, B. L. Lutz, and R. D. Cess for kindly of the intensity of radiation diffusely reflected sending a reprint of their paper on laboratory study from semi-infinite homogeneous atmospheres. of the methane absorption spectrum, and also Drs. Icarus 22, 66-81. D. P. Cruikshank, K. Fox, D. Gauthier and E. G. Yanovitskij; constant contact with them greatly ENCRANAZ, T., OWEN, T., AND WOODMAN, J. H. (1974). The abundance of ammonia oll Jupiter, aided the completion of this study. The author is Saturn and Titan. Astron. Astrophys. 37, 49-55. also thankful to the referees for their useful GIVER, L. P., MILLER, J. H., AND BOESE, R. W| comments. (1975). A laboratory atlas of the 5v~ NH3 absorption band at 6475 )~ with application to Jupiter REFERENCES and Saturn. Icarus 25, 34-48. AKSENOV, A. N., GRIGORIEVA,Z. N., TEIFEL, V. G., HEss, S. L. (1953). Variation in atmospheric abAND KHAaITONOVA, G. A. (1972). Study of the sorption over the disks of Jupiter and Saturn. peculiarities of molecular absorption in the Jovian Astrophys. J. 118, 151-160. spectrum. In Physics of the Moon and Planets, pp. KUZMI~, A. D., AND SMIRNOVA, T. V. (1973). The 433-438. Nauka, Moscow. evaluation of ammonia content in the atmosphere AKSENOV, A. N., IBRAGIMOV,N. B., AND TEIFEL, below the clouds of Jupiter on the basis of radioV. G. (1976). On the CH4 absorption band at astronomical data. Astron. Vestnik 7, 139-142. 6190 ~. in the Jovian spectrum. In press. LASKER, B. M. (1963). Wet adiabatic model atmoANIKONOV, A. S. (1974). The interpretation of weak spheres for Jupiter. Astrophys. J. 138, 709-719. absorption bands iu Jupiter's spectrum. Astron. LUTZ, ]~. L., OWEN, T., AND CESS, R. D. (1976). Vestnik 8, 223-228. Laboratory band strengths of methane and their AW~RY,R. W., MICHALSKY,J. J., AND STOKES, R. A. application to the atmospheres of Jupiter, (1974). Variation of Jupiter's CH4 and NHa bands Saturn, Uranus, Neptune, and Titan. Astrophys. with position on the planetary disk. Icarus 21, J. 203, 541-551. 47-54. MAILLARD, J. P., COi~BES, M., ENCRENAZ,T., AND AVRAMCHUK, V. V. (1970). On the results of specLECACHEUX, J. (1973). New infrared spectra of trophotometry of the methane (6190 _~) and amthe Jovian planets from 12 000 to 4000 cm-I by monia (6441 and 6478 ~) absorption bands on Fourier transform spectroscopy. I. Study of Jupiter's disk. Astron. Zh. 47, 577-585. Jupiter in the 3v~ CH, band. Astron. Astrophys. BERGSTRALH, J. W. (1973a). Methane absorption in 25, 219-232. the Jovian atmosphere. II. Absorption line formaMARGOLIS, J. S., AND FOX, K. (1969). Studies of tion. Icarus 19, 390-418. methane absorption in the Jovian atmosphere. BERGSTnALn,J. T. (1973b). Methane absorption in II. Abundance from the 3~3 band. Aslrophys. J. the Jovian atmosphere. I. The Lorentz half158, 1183-1188. width in the 3v3 band at 1.1 #m. Icarus 19, 499MASON, H. P. (1970). The abundance of ammonia in 506. the atmosphere of Jupiter. Astrophys. Space Sci. BERGSTRALFI, J. T., AND MARGOLIS, J. S. (1971). 7, 424-436. Recomputation of the absorption strengths of the methane 3gs J-manifolds at 9050 cm-1. J. Quant. Monoz, V. I. (1967). Physics of the Planets. Nauka, Moscow. Spectrosc. Radiat. Transfer 11, 1285-1287. PILCHER, C. B., PRINN, R. G., AND McCoRD, T. B. BINDER, A. B., AND McCARTHY, D. W. (1973). IR (1973). Spectroscopy of Jupiter: 3200 to 11 200 .~. spectrophotometry of Jupiter and Saturn. Astron. J. Atmos. Sci. 30, 302-307. J. 78, 939-950. BUGAENKO, L. A. (1972). The monochromatic RANK, D. H., FINK, U., AND WIGGINS,T. A. (1966). Measurements on spectra of gases of planetary brightness coefficients of major planets. Astron. interest. II. H20, CO2, NH3, and CH4. Astrophys. Vestnik 6, 19-21. J. 143, 980-988. BUGAENKO, L. A. (1973). The study of molecular absorption in the atmospheres of major planets. SOI~OLEV, V. V. (1972). On the theory of planetary Dissertation. Kiev. spectra. Astron. Zh. 49, 397-405. c h a r a c t e r i z e d b y a m i n i m u m q u a n t i t y of variable parameters.

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