An estimate of the temperature and abundance of CH4 and other molecules in the atmosphere of Uranus

IcA~us 24, 348-357 (1975)

An Estimate of the Temperature and Abundance of CH4 and Other Molecules in the Atmosphere of Uranus M I C H A E L J. S. B E L T O N AND S. H. H A Y E S Kitt Peak National Observatory,* Tucson, Arizona 85726 Received August 29, 1974 We present a preliminary analysis of CH 4 absorptions near 6800 A in new high resolution spectra of Uranus. A curve of growth analysis of the data yields a rotational temperature near 100 K and a CH4/H2 ratio that is 1 to 3 times that expected for a solar type composition. The long pathlengths of CH4, apparently demanded by absorptions near 4700 A, are qualitatively shown to be the result of line formation in a deep, predominantly Rayleigh scattering atmosphere in which continuum absorption is a strong function of wavelength. The analysis of the CH 4 also yields a minimum value for the effective pressure of line formation (~ 2 atm). This value is shown to be twice that expected on Uranus if the atmosphere were predominantly H2. It is speculated that large amounts of some otherwise optically inert gas is present in the Uranus atmosphere. N2 is suggested as a possible candidate since there are cosmogonic reasons why Uranus should contain large amounts of N relative to C, He, and H, and also because the pressureinduced pure rotation spectrum of N2 could possibly account for the low brightness temperatures that have recently been observed at 33 and 350 ~m. If N2 is present the planet probably possesses a surface at the 10-100 atmosphere level. of the above experience t h a t the current values of their CH 4 abundances, o b t a i n e d R e c e n t high resolution studies of ab- b y similar means (Owen, 1967), m a y also sorption in the 3v3Ci.i 4 b a n d in the be too high, especially since present values s p e c t r u m of J u p i t e r (Belton, 1969; for HI2 a n d CI-I4 a b u n d a n c e s lead to a Margolis, 1969; Bergstralh, 1 9 7 3 b ) a n d CH4/H 2 ratio which is a factor of ~ 2 0 - 3 0 S a t u r n (Bergstralh, 1973a; Trafton, 1973, greater t h a n the solar composition value. d e B e r g h et al., 1973) have yielded line of H o w e v e r there are cosmogonic a r g u m e n t s sight a b u n d a n c e s which are considerably (Cameron, 1973; Lewis, 1973) w h y CHH4 below the earlier estimates o f K u i p e r (1952) m i g h t be enriched relative to H 2 on U r a n u s which were based on a comparison o f and particularly Neptune. Also, in an l a b o r a t o r y a n d p l a n e t a r y b a n d complex i m p o r t a n t contribution on v e r y weak CH 4 strengths at low spectral resolution. The absorptions on Uranus, Owen et al. (1974) reduction in line of sight a b u n d a n c e in the have argued t h a t line of sight a b u n d a n c e case of J u p i t e r is a b o u t a factor of 4, while estimates for CH 4 m a y still be grossly in in S a t u r n the reduction m a y be as large as error a n d m a y need to be f u r t h e r increased a factor o f 8 (Bergstralh, 1973a). B o t h b y a considerable factor. planets n o w yield CH4/H 2 ratios which are I n order to m a k e a q u a n t i t a t i v e estimate similar to the solar value of ~7 × 10 -4 for the CHH4/H2 ratio on U r a n u s we h a v e (Trafton, 1973). I n the case o f U r a n u s a n d acquired several high resolution ( A A ~ N e p t u n e it m i g h t be expected on the basis 0.3 A) spectra in the vicinity of a series o f * Kitt Peak National Observatory is operated CH 4 absorption lines near 6800 A (see Fig. by the Association of Universities for Research 1) which Owen (1966) has t e n t a t i v e l y in Astronomy, Inc., under contract with the identified as R - b r a n c h transitions in the 5v 3 band. Owen's, a n d a more recent National Science Foundation. Copyright © 1975 by Academic Press, Inc. 348 I. INTRODUCTION

All rights of reproduction in any form reserved. Printed in Great Britain

CH 4 IN

URANUS

analysis of these features by Teyfel and Kharitonova (1970), have not been entirely satisfactory because the observations (taken at moderate resolution; AA 1.5 A) have yielded very low values for the rotational temperature. Both authors find T ~ 60-70K, a value considerably below t h a t anticipated (cf. Owen (1966)) or the value t h a t has been deduced from observations of the H 2 quadrupole lines (~100 °) (Belton, McElroy and Price, 1971 ; Lutz, 1973; Encrenaz and Owen, 1973). This result appears to place Owen's identification of the band in question ; however a preliminary analysis, outlined below, shows t h a t this problem is simply the result of blends in the planetary spectrum which work to enhance the low J lines at low resolution. We have also made rough estimates of the line of sight abundance of CH 4 on Uranus with a curve of growth analysis which suggest a moderate enhancement of the CH4/H 2 ratio over the solar value, although the uncertainties are sufficiently large so t h a t the solar value is a distinct possibility. The analysis also indicates t h a t the effective pressure for line formation is considerably higher t han what would be expected for a pure hydrogen atmosphere. The quantitative results raise the possibility t h a t large amounts of some other gas which cannot be directly observed could be present in the Uranus atmosphere. Finally we have found what appears to be a reasonable explanation for the ver y large line of sight CH 4 abundances (Owen, 1974) implied b y absorption in the visible region. I n view of the nature of these conclusions plus the current interest in the Uranus atmosphere as planning for a possible Mariner J u p i t e r - U r a n u s probe mission progresses we present these results now, in a preliminary and somewhat speculative form, rather th an waiting the considerable period necessary before a detailed analysis of our spectra can be accomplished. II. METHOD OF ANALYSIS We accept, as a working hypothesis, Owen's (1966) identification of the main features in the CH 4 spectrum near 6800 A (Fig. 1). Furthermore we assume t h a t the

349

ATMOSPHERE

i

i

i

i

7 77 °

URANUS / SUN 5 v CHa R-BRANCH

0

6/9068001

68110 WAVELENGTH(~)

68120

6830

FIC. l. Spectrum of Uranus near 6800/~. The spectrum is the ratio of Uranus to the Sun. Doppler displacements were accounted for and Franuhofer lines and instrumental response are effectively removed. Owen's (1966) line identifications for the 5v3 band are indicated. The assumed continuum for the 5v3 lines is indicated by the broken line. peaks in the spectrum between the low excitation R-branch lines define a continuum level for these lines. As Teyfel and Kharitonova (1970) have pointed out, this procedure m ay be incorrect, but we doubt t h a t it can be grossly wrong. Our view, admittedly intuitive, is t h a t there are m a n y overlapping bands in this spectral region with myriads of weak lines t h a t form a pseudocontinuum background absorption for the stronger and more clearly identifiable lines. With these assumptions we find the equivalent widths listed in Table I. They refer to light integrated over the full disk of the planet. The validity of the results detailed below depends entirely on the acceptance of Owens line and band identifications. It is therefore appropriate to note t h a t the structure seen in the individual line manifolds in our highest resolution spectra seems to emulate the structure observed in the low J lines of the related 3v 3 band (Margolis and Fox, 1968). Further, t he value obtained below for rotational temperature is also entirely reasonable which suggests t h a t our t r e a t m e n t of excitation is correct. While the quality of these two

350

BELTON AND HAYES

TABLE I EQUIVALENT WIDTHS (W) OF LINES ON URA1WU'S

Line

W (cm -1)

W (A)

W (A)a'b

R(0) R(1) R(2) R(3) /~(4) R(5)

0.32 0.26 0.43 0.95 0.76 0.30

0.15 0.12 0.20 0.44 0.35 0.14

0.30 0.27 0.27 0.35 0.22 0.14

a From Teyfel and Kharitonova (1970). b Owen (1966) does not estimate equivalent widths but notes that W(R 1) W(RO) > W(R4). observations is certainly not high we have found nothing in our spectra which conflicts with Owen's identifications; we therefore have considerable confidence in them. The curve of g r o w t h technique which we use closely follows t h a t e m p l o y e d earlier b y Belton (1969) in making a preliminary analysis of the 3v 3CH 4 b a n d on J u p i t e r . We p e r f o r m b o t h a reflecting layer model analysis (RLM) and a scattering atmosphere analysis. The t h e o r y of the l a t t e r is outlined b y Belton (1968) in an application to Venus. Following Belton (1969) we consider each c o m p o n e n t in each r o t a t i o n a l line (i.e., " J manifold") as a separate feature. As a first a p p r o x i m a t i o n we divide the observed equivalent widths among the c o m p o n e n t s according to the theoretical relative intensities (Childs and J a h n , 1939) a n d t h e n a p p l y the curve of g r o w t h to each c o m p o n e n t separately in order to estimate the degree of saturation. This procedure was found to work quite well for J u p i t e r and is in fact precise if the lines are weak. A . B a n d Parameters We require values for aL and ~D, the L o r e n t z and Doppler linewidth p a r a m e t e r s (cf. G o o d y (1964)), and So, the i n t e g r a t e d b a n d absorption. F o r CH 4 lines near 6800 A on U r a n u s with T ~ 1 0 0 K , ao~1.7× 10-2cm -l. I n f o r m a t i o n on aL u n d e r lab-

o r a t o r y conditions and, in certain cases, a t low t e m p e r a t u r e s , is available for lines in the 2v 3 b a n d (Rank, Fink, a n d Wiggins, 1966) and the v3 b a n d (Varanasi, Sarangi, and Pugh, 1973). On the basis o f this work we assume aL.u (T = 3 0 0 K ; 1 a m a g a t ) = 0.075cm -~ for all lines in the 5v 3 b a n d i n d e p e n d e n t of their J value or nuclear spin specie. We e x t r a p o l a t e this value to other pressures and t e m p e r a t u r e s using aL = aL.oP(T/300) -I/2,

(1)

where p is pressure in atmospheres (cf. Varanasi et al. (1973) for direct e x p e r i mental verification of Eq. (1) for C H 4 - H 2 collisions in tile vs fundamental). According to McKellar (1974) the line of sight a b u n d a n c e of H 2 on U r a n u s is between 430 and 680 k m amagats. McKellar's analysis supersedes earlier ones (Lutz, 1973; E n c r e n a z a n d Owen, 1973; F i n k and Belton, 1969) in t h a t it takes into account the desaturating effect of pressure shifts in the quadrupole lines. I f H 2 is the prime line broadening atmospheric constituent this implies 0.54 ~
CH 4 I~" URANUS ATMOSPHERE

I

351

=

I

I

RLM: BOLTZMAN PLOT +

0 _1

-3

0

I

I0

1

I

20 d(d+l)

30

FIo. 2a. Reflecting layer analysis. B o l t z m a n n p l o t of d a t a . T h e s t r a i g h t line is a l e a s t - s q u a r e s fit. F o r definitions of t h e o r d i n a t e see B e l t o n (1969). J is t h e r o t a t i o n a l q u a n t u m n u m b e r . T h e slope of t h e line c o r r e s p o n d s t o 1 0 9 K .

o f this d a t a yielded S O~ 1.6 × 10-Scm -1 (cm amagat) -1. (ii) B y utilizing observations of the R(0) line in the 5v 3 b a n d on S a t u r n m a d e b y us and b y E n c r e n a z a n d Owen (1973). These observations are calibrated b y applying T r a f t o n ' s (1973) and deBergh's et al. (1973) result on the line of sight a b u n d a n c e o f CH4 on S a t u r n as deduced from observations of the 3v 3 band. A R L M curve of g r o w t h analysis gives S 0 ~ 7 × 10-Scm - l (era amagat) -1. Considering the crudeness o f these estimates the a g r e e m e n t to within a f a c t o r of 5 is gratifying. Our preference is however for the l a t t e r m e t h o d and our a d o p t e d value for the b a n d i n t e n s i t y is 7 × 10-5cm - l (cm amagat) -l.

pressure: There is clearly a linear relation between the " o b s e r v e d " equivalent widths and their theoretical intensities and in order to move the d a t a on to the linear p a r t o f the theoretical curve o f growth it was found necessary to raise the effective pressure to 2.4arm. Thus pelf/> 2.4arm!

B. Reflecting Layer Model

(.9 O .J

Figure 2 illustrates the results o f applying the curve of g r o w t h to the d a t a in Table I. I n the curve of growth itself there are more points t h a n J - m a n i f o l d s as a result o f our technique o f t r e a t i n g the individual c o m p o n e n t s as separate lines. I n p a r t (a) the " B o l t z m a n n " plot shows a reasonably good fit to a straight line and yields a t e m p e r a t u r e of 109K. The intercept at J (J + 1) = 0 yields a line of sight a b u n d a n c e ~?Ncrl, = 1.1km amagats. To achieve the fit to the curve o f growth shown in p a r t (b) of Fig. 2 it was f o u n d necessary to a d j u s t the assumed effective

!

I

CURVE OF GROWTH

RLM" 0 --

"1

T = 109 ° K •

7

'E ¢3

/ + /

-I --

"
-2

,,//" -

CIL . GD

I

I

0

I

2

LOG LINE STRENGTH FIG. 25. Reflecting layer analysis. C u r v e of g r o w t h . T h e o r d i n a t e is o b s e r v e d e q u i v a l e n t w i d t h a n d t h e a b s c i s s a is g j G j ( 2 J T 1 ) 2 e x p [--J(J+ 1)heB/kT] w i t h T--- 109K. See B e l t o n (1969) for definitions. T h e solid line is t h e t h e o r e t i c a l c u r v e of g r o w t h w i t h cci/aD -- 5 a n d P c f f = 2 . 4 a r m . T h e d a s h e d line is t h e b e s t fit for Pelf = ] a r m .

352

BELTON AND HAYES '

I -i ~..,~_

I

I

I

SCATTERING MODEL

! ~

-

80LTZMAN PLOT

N

~

-2

°~-3

0

i

I 20 J(d+l)

I0

I 50

Fzo. 3a. Scattering model analysis : B o l t z m a n n p l o t of d a t a . T h e s t r a i g h t line is a l e a s t - s q u a r e fit. See Belfort (1069) for definition of axes. T h e slope of t h e line c o r r e s p o n d s t o 9 2 K .

C. Scattering Model Figure 3 illustrates t h e results. T h e slope o f t h e B o l t z m a n n plot in p a r t (a) yields a t e m p e r a t u r e of 9 2 K a n d t h e intersection o f t h e abscissa a n d t h e least squares regression line a t J ( J + 1 ) = 0 yields a specific a m o u n t , McH ,, of C H 4 o f 0 . S k m a m a g a t s (eft B e l t o n (1968)). Again a n effective pressure o f a t least 2 a r m was required to achieve a reasonable fit to the c u r v e of growth. T h e a s s u m e d p a r a m e t e r s in this model are: (i) isotropic scattering, (ii) homo-

geneous, semiinfmite a t m o s p h e r e w i t h ~ c = 0 . 8 8 ; p-----/~o = 1/%/3. T h e v a l u e ass u m e d for /z a n d /~0 h a s b e e n f o u n d a d e q u a t e to r e p r e s e n t spectral lines in t h e light of t h e full disk, a n d t h e v a l u e for ~c is b a s e d on consideration of t h e p h o t o m e r r y of Y o u n k i n (1970) a n d W a m s t e k e r (1973).

III. INTERPRETATION OF THE RESULTS T h e results of t h e t w o analyses are collected in T a b l e I I . T h e s c a t t e r i n g t r e a t -

I

0-

I

SCATTERING MODEL / CURVE OF GROWTH /J T=92OK ,~/7

Y-

-

/ /

/

f

-

=

I 0 LOG L I N E

I I

2

STRENGTH

FIG. 3b. Scattering model analysis. Curve of growth. The ordinate is observed equivalent width and the abscissa is g~G~(2J ÷ 1)2exp [-J(J ÷ 1)hcB/kT] with T = 92K. The solid line is the theoretical curve of growth for isotropic scattering in a homogeneous, semiinfinite axnosphere with ¢5c = 0.88. Other parameters are aL/ao = 5 and Pcrf = 2arm. The dashed line is the best fit for pelf = 1 arm.

CH 4 I N URANUS ATMOSPHERE

TABLE II RESULTS OF CURVE OF GROWTH AI~ALYSIS a (a) R e f l e c t i n g l a y e r m o d e l Tro t = 109 K ;

~NcH 4 -- 1.1 k m a m a g a t s Pef~ I> 2.4 a r m

(b) S c a t t e r i n g m o d e l Trot -- 9 2 K ;

McH , ----0 . 5 k m a m a g a t s b p~fe/> 2 . 0 a r m

a A b u n d a n c e s b a s e d o n S o = 7 × 10 -5 c m -1 ( c m a m a g a t ) -1 f o r t h e 5v3 b a n d . P e r s c a t t e r i n g m e a n free p a t h .

ment gives a slightly better account of the data (cf. Figs. 2 and 3) which is as it should be considering the demonstrated importance of molecular scattering (Belton, Wallace, and Price, 1973) in the Uranus atmosphere. We do not give any specific estimates of probable or systematic errors in this paper. We note however t h a t t h e y will generally be large.

353

of any foundation by the present results for rotational temperature. B. ~he CH4/H 2 M i x i n g Ratio (i) R L M The concordance of the values of rotational temperature obtained from CH 4 and H 2 lines bolsters a basic assumption t o our analysis t h a t methane and molecular hydrogen are well mixed (i.e., constant mixing ratio) and are in t herm odynam i c equilibrium in the part of the atmosphere probed spectroscopically. Thus the CH4/H z ratio m, is well defined in the Uranus atmosphere. Accepting McKellar's (1974) assessment of the H 2 line of sight abundance t h a t was noted in Section II we find m ~ 2-3 × 10 -3 according to the RLM. This is 3-4 times the solar value. Of course there is considerable uncertainty in our estimated value for So, as mentioned in the previous section. I f the smaller value o f S 0 is preferred then the value for ~Ncn , rises to 4.3km amagats and m ~ 6-10 × 10 -3. We conclude t h a t the RLM indicates a probable enrichment of CH 4 over H 2 relative to solar composition. This enrichment could be as large as ~10 but is more likely to be of the order of 3.

A . Rotational Temperature The rotational temperature is found to C. The CH4/H 2 M i x i n g Ratio (ii) Scattering be essentially 100K. This is in agreement Model with the value deduced from earlier The scattering analysis yields a specific observations of H 2 quadrupole lines in the amount for the CH 4 content and allows us (4-0) and (3-0) vibrational overtones. I t to place a relatively firm lower limit to t he is also in agreement with the value pre- CH4/H 2 ratio: By definition (Belton, 1968), dicted b y simple atmospheric models MCH, = n(CH4) l~, (2) (Belton, McElroy, and Price, 1971). A comparison of the spectrum in Fig. 1 and where l~ is the scattering mean free p a t h the spectra published by Teyfel and and n(CH4) is the number density of CH 4. Kharitonova (1970) immediately shows With l~ 1 = n ( H 2 ) a a + a', where a a is the why both they, and Owen (1966), were led . Rayleigh cross section per H 2 molecule and to such low temperatures for this band. At a' is the volume scattering cross section low spectral resolution the apparent widths due to other atmospheric material. We see of the R(0) and R(1) lines are increased by t h a t blending with other satellite lines in the m = M c H . a a ( 1 + a'/n(H2)aa). (3) planetary spectrum. Thus the states of lowest excitation were presumed to be far Thus M c N . a R is a lower limit to t h e more heavily populated than was actually CH4/H 2 mixing ratio. With M c n , = 0.5kin required. We note also t h a t the conclusion amagats and aR _~ 4 × 10-2Sem2 at 6800/~ of Prinn and Lewis (1973) in which t h e y we find m >/6 × 10 -4, i.e., the lower limit suggest t h a t the lines of this band are is essentially the solar value. We note t h a t formed in a CH 4 haze above the 78- 58K this result is independent of the measured level in the Uranus atmosphere, is robbed amount of H 2 and only assumes t h a t H 2 is

354

BELTON AND HAYES

the prime scattering material. Belton and Spinrad (1973) in an analysis of (3-0) pressure induce vibrational overtone at 8000 A have shown t hat a pure H 2 atmosphere is not adequate to explain the Uranus spectrum and t h a t an effective volume scattering coefficient of 5.5 × 10-gem -~ per amagat of H 2 is required in the semiinfinite scattering model. With the assumption t h a t this value also applies at 6800 A (i.e., the "aerosols" contributing to a' are colorless) we find m ~ 8-~ 10 -4 . With the uncertainty in S Oit appears t h a t with the scattering model m ~ 0 . 8 - 3 × 10 -3 , i.e., essentially solar but with the possibility of CH 4 enrichment over H 2 by as much as a factor ~3 times the solar value.

C. ~ he Effective Pressure In order to fit the data to the curves of growth satisfactorily it was necessary to assume an effective pressure for line formation which is at least 2 atm. As indicated in Section II(a) it is unlikely t hat the effective pressure can be much higher t ha n 1 arm for a pure H 2 atmosphere. The implication of the result could be either (i) t h a t our assumption about line widths is grossly incorrect, or (ii), some other material is present in the Uranus atmosphere in amounts comparable to molecular hydrogen. This additional material would necessarily lack strong transitions in the accessible regions of the visible to prevent its obvious detection: Candidate materials would therefore include He, N2, 02, and noble gases. Varanasi et al. (1973) find t h a t in the u3 fundamental of CH 4 the pressure half width for CH4-He collisions is 0.6 of t h a t for CH4-H 2 collisions. I f we assume t h a t the "missing" constituent is He then literal acceptance of the curve of growth results requires t h a t its partial pressure is ~2 times t h a t due to H 2, and possibly more! Since N 2 and the heavier noble gases (not Ne) have similar polarizability to H 2 their broadening effect on CH 4 lines is probably similar. For these gases the number ratio of the missing substance to H 2 would be about unity or greater if the curve of growth results are taken literally. Enrichment of He relative to H 2 presents considerable cosmogonic diffi-

culties (Cameron, 1973; Lewis, 1973), although the possibility is not excluded by the high bulk density of the planet (Zapolsky and Salpeter, 1969). On the other hand the addition of large quantities of N 2 to the atmospheric mix on Uranus is not without its attractive features: Its pressure induced translational and pure rotational spectrum which peak near 100 cm -~ (Bosomworth and Gush, 1965) could produce much needed opacity in the 30400/~m region and help to account for the very low brightness temperatures recently observed by Rieke and Low (1974) at 33 and 350/zm. Also modern cosmogonic theory (Lewis, 1973; Cameron, 1973) suggests t h a t Uranus and Neptune m ay be strongly enriched in nitrogen and oxygen bearing compounds. On the other hand great difficulties m ay be encountered in explaining the stability of N 2 against its transformation into N H 3 in a hydrogen rich atmosphere. I f N 2 is produced photochemically from N H 3 in the upper troposphere, its density relative to H 2 and its loss at great depth will be controlled primarily by mixing into the interior. According to Strobel (1974) and H u n t e n (1974) one could in principle photochemieally produce some ~1027-25 molecules cm -2 of N 2 on Uranus over the age of the solar system through the photolysis of N H 3. Thus a surface at 10-100 bars, to prevent excessive downward mixing, might explain ;t.s possible presence in the atmosphere.

IV. W A V E L E N G T H DEPENDENCE OF APPARENT CH 4 A B U N D A N C E 0 w e n et al. (1974) and O w e n (1974) have noted that C H 4 bands observed on Uranus (and Neptune) at shorter wavelengths (~4700A) require far longer absorption patMengths for a match than the ~ 1 0 k m amagats t han is currently available in the laboratory. Apparently the bands near 4700A imply considerably larger pathlengths t han do the CH 4 absorptions near 7500A (Owen, 1967). We now illustrate qualitatively t h a t this is a natural result when spectral lines are formed in a deep, scattering and absorbing atmosphere in which Rayleigh scattering predominates.

CH 4 IN URANUS ATMOSPHERE

abundances at different wavelengths. In Fig. 4 we illustrate the results of applying Eq. (5) to the case of Uranus; for ~c(A) we use the continuum defined by Prinn and Lewis (1973). Note t h a t W(2) has a clear maximum near 5000 ttx and it follows t h a t the apparent line of sight abundances derived from RLM will be maximum there ; compared to 7500A we would expect the apparent abundances to be some 5 times greater! For saturated lines and lines of intermediate strength the effect illustrated in Fig. 4 will be considerably reduced.

We consider the case of weak lines only, since the behavior for lines of intermediate strength and those which are saturated is far more complicated and not suited for qualitative arguments. According to Belton (1968) the equivalent of a weak line of strength S(J, T) is given by

W = % 5,~ MS(J, T),

(3)

where no =

1/(1

-

c)1/2;

=

t0

=

Now for a minor constituent in a clear molecular atmosphere whose mixing ratio m, is fixed, the specific amount if given by

IV. CONCLUSIONS In summary we find no fault with Owen's identification of the CH 4 lines near 6800 ttx in the spectrum of Uranus as the 5v 3 band. A treatment of newly observed equivalent widths in high resolution spectra in terms of a scattering model for line formation gives consistent results, and leads to a simple resolution, albeit qualitative, of newly reported, and troublesomely high, estimates ofCH 4 line of sight amounts in the 4700 A region. The analysis yields at rotational temperature of ~100K and a CH4/H 2 mixing ratio t h a t is probably solar, but could be enhanced over solar by perhaps a factor of 3. The analysis also yields

M = ma~ t ~ M 0 • (~/)lo)4. Thus, for a test line of constant strength, the equivalent width will be a strong function of wavelength:

W(a) Wo

~(a) ( ;~ ]4(1 - ,~(ao)] "2 ~-]-%~o)\~! \'i---~--i-~) '

(5)

where W0 is the equivalent width at A0. Note that the single scattering albedo is a function of A also. Since the strength of the test line is assumed invariant it is clear t h a t a simple reflecting layer model analysis may lead to radically different line of sight +1[:

I

I

E[.

355

I

I

I

I

WAVELENGTH VARIATION OF APPARENT EQUIVALENT WIDTH FOR CONSTANT LINE STRENGTH

L

:

-I

.5

.4

I

.5

.6

.7

.8

.9

1.0

WAVELENGTH (MICRONS)

FIG. 4. V a r i a t i o n of a p p a r e n t e q u i v a l e n t w i d t h , W(,~)/Wo,for a t e s t line o f fixed s t r e n g t h as a funct i o n o f w a v e l e n g t h i n t h e U r a n u s a t m o s p h e r e . T h e a t m o s p h e r e is m o d e l e d w i t h a h o m o g e n e o u s , s e m i i n f m i t e m o d e l a n d R a y l e i g h s c a t t e r i n g is a s s u m e d t o p r e d o m i n a t e o v e r o t h e r t y p e s o f s c a t t e r i n g . T h e line is also a s s u m e d weak. N o t e t h a t t h e o r d i n a t e is l o g a r i t h m i c a n d t h a t lines will a p p e a r a n o m a l o u s l y s t r o n g n e a r 5000/~.

356

BELTON AND HAYES

a m i n i m u m v a l u e for t h e effective p r e s s u r e o f l i n e f o r m a t i o n . T h e v a l u e is s o m e t w o t i m e s t h a t a n t i c i p a t e d for a p u r e m o l e c u l a r hydrogen atmosphere. We speculate that, if u n c e r t a i n t i e s in the p r e s s u r e - b r o a d e n e d h a l f - w i d t h c a n b e i g n o r e d , s o m e o t h e r gas must exist in comparable quantities to H 2 i n t h e U r a n u s a t m o s p h e r e . H e , N2, 0 2 a n d noble gases are obvious candidates. N 2 represents a very attractive possibility since its far infrared pressure-induced spectrum may provide the necessary a t m o s p h e r i c o p a c i t y n e e d e d t o a c c o u n t for t h e low b r i g h t n e s s t e m p e r a t u r e s o b s e r v e d a t 33 a n d 350/%m. T h e s t a b i l i t y o f N 2 i n a hydrogen rich atmosphere with presumably deep vertical mixing may however present insurmountable objections to this h y p o t h e s i s u n l e s s a s u r f a c e is p r e s e n t o n t h e p l a n e t b e t w e e n t h e 10-100 a t m o s p h e r e level. ACKNOWLEDGMENTS

We gratefully acknowledge m a n y stimulating conversations with L. Wallace, D. Hunten, and D. Strobel. I~EFERENCES

BELTON, M. J. S. (1968). Theory of the curve of growth and phase effects in a cloudy atmosphere; Application to Venus. J. Atmos. Sci. 25,596. BELTON, M. J. S. (1969). An estimate of the abundance and the rotational temperature of CH14 on Jupiter. Astrophys. J. 157, 469. BELTON, M. J. S., MCELROY, M. B., AND PRICE, M. (1971). The Atmosphere of Uranus. Astrophys. J. 164, 191. BELTON, M. J. S., AND SPIlVI%AD,H. (1973). I-I2 pressure induced lines in the spectra of the major planets. Astrophys. J. 185, 363. BELTON, M. J. S., WALLACE,L., AND PRICE, M. J. (1973). Observation of the raman effect in the spectrum of Uranus. Astrophys. J. 184, L143. DE BERGH, C., VION, M., COMBES, M., AND LECACHEUX, J. (1973). New infrared spectra of the Jovian planets from 12000 to 4000 cm-1 by Fourier transform spectroscopy : II. Study of Saturn in the 3v3CHH4 band. Astron. Astrophys. 28, 457-466. BERGSTRALH, J. T. (1973a). Methane absorption in the atmosphere of Saturn: Rotational temperature and abundance from the 3v3 band. Icarus 18, 605.

BERGSTRALH, J. T. (1973b). Methane absorption in the Jovian atmosphere : I. The Lorentz half width in the 3 v3 band at 1.1 ~m. Icarus 19,499, BOSOI~WORTH, D. R., AND GUSH, H. P. (1965). Collision induced absorption of compressed gases in the far infrared. Part II. Can. J. Phys. 43, 751. CAMERON, A. G. W. {1973). Elemental and isotopic abundances of the volatile elements in the outer planets. Space Sci. Rev. 14, 392. CHILDS, W. 1"1.J., AND JAHN, H. A. (1939). A new Coriolis perturbation in the methane spectrum: I I i . Intensities and optical spectrum. Proc. Roy. Soc. London, Set. A. 169, 451. ENCRENAZ, T., AND OWEN, W. (1973). New observations of the hydrogen quadrupole lines on Saturn and Uranus. Astron. Astrophys. 28, 119. FINK, V., AND BELTON, M. J. S. (1969). Collision narrowed curves of growth for H2 applied to new photoelectric observations of Jupiter. J. Atmos. Sci. 26, 952. GOODY, R. M. (1964). Atmospheric Radiation, Part 1, Oxford University Press, New York. HUNTEN, D. M. (1974). Private communication. IRWNE, W. M. (1974). Meeting Review, I.A.U. Symposium 65. Icarus 21, 202. KUIPER, ~. P. (1952). The Atmospheres of the Earth and Planets, University of Chicago Press, Chicago, Ill. LEWIS, J. S. (1973). Chemistry of the outer solar system. Space Sci. Reviews 14, 401. LUTZ, B. L. (1973). Molecular Hydrogen on Uranus. Observation of the 3-0 Quadrupole Band. Astrophys. J. 182, 989. MARGOLIS, J., AND FOX, K. (1968). Infrared absorption spectrum of CH14 at 9050 cm -1. J. Chem. Phys. 49, 2451. MARGOLIS, J. S. (1969). Studies of methane absorption in the Jovian atmosphere. II. Abundance from the 3ca band. Astrophys. J. 158, 1183. MCKELLAR, A. R. W. (1974). The significance of pressure shifts for the interpretation of H2 quadrupole lines in Planetary Spectra. Icarus 22, 212-219. OWEN, T. (1966). An identification of the 6800ii Methane Band in the spectrum of Uranus and a determination of atmospheric temperature. Astrophys. J. 146, 611. OWEN, T. (1967). Comparisons of Laboratory and Planetary Spectra. IV. The identification of the 7500.~ bands in the spectra of Uranus and Neptune. Icarus 6, 108. OWEN, T. (1974). Private communication. Owen's comments are also reported in Irvine (1974). OWEN, T., LUTZ, B. L., PORCO, C. C., AND

CH 4 IIW D-RANUS A T M O S P H E R E

WOODSMAN,J. H. (1974). On the identification of the 6420A absorption feature in the spect r u m of Uranus. Astrophys. J. 189, 379. PRI~N. R. G., AND LEWIS, J. S. (1973). Uranus atmosphere : Structure and composition. Astrophys. J. 179, 333. ~ A NK, D. H., FIN~, U., A N D WIGGINS, T. A. (1966). l~easurements on spectra of gases of planetary interest. Astrophys. J. 143, 980. RIEKE, G. H., A~rD Low, F. J. (1974). Infrared measurements of Uranus and Neptune. Astrophys. J. 193, L147-148. STROBEL, D. F. (1974). Private communication. TEYFEL, V. G., AND KHARITONOVA,G. A. (1970). The molecular rotational temperature on Uranus and an upper limit to the pressure in its outer atmosphere. Soviet Astron.-AJ. 13, 865.

357

TRAFTON, L. (1967). Model atmospheres of the major planets. Astrophys. J. 147, 765. TR~_VTO~r, L. (1973). Saturn: A study of the 3va methane band, Astrophys. J. 182, 615. VARANASI,P., SARANGI,S., ~-~D PUGH, L. (1973). Measurements on the infrared lines of planetary gases at low temperatures. I. ~a-ftmdamental of methane. Astrophys. J. 179, 977. WA~STEKER, W. (1973). The wavelength dependence of the albedos of Uranus and Neptune from 0.3 to 1.1 micron. Astrophys. J. 184, 1007. YOlr~KI~¢, R. L. (1970). Thesis: Speetrophotomerry of the Moon, Mars, and Uranus. University of California, Los Angeles. ZAPOLSK~x", H. A., AND SALPETER, E. E. (1969). The mass-radius relation for cold spheres of low mass. Astrophys. J. 158, 809.