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On the DC ratio in the atmosphere of Uranus
ICARUS 49, 27-34 (1982)
On the D/C Ratio in the Atmosphere of Uranus TH. E N C R E N A Z AND M. COMBES Observatoire de Meudon, 92190 Meudon, France Received February 16, 1979; revised N o v e m b e r 6, 1981 A m e t h o d for deriving mixing ratios in the o u t e r planets, mostly i n d e p e n d e n t o f scattering p r o c e s s e s , is applied to U r a n u s . It is s h o w n that scattering p r o c e s s e s play a major role in the line formation in the a t m o s p h e r e s of U r a n u s and N e p t u n e ; c o n s e q u e n t l y , a b u n d a n c e ratios derived from a reflecting-layer model can be questionable. U s i n g our m e t h o d , we derive for U r a n u s D / C < 6 × 10-2, which is significantly smaller than o u r result on Jupiter. The simplest explanation implies a C / H e n r i c h m e n t by at least a factor of 6 relative to the solar value.
I. I N T R O D U C T I O N
While the study of the abundance ratios on Jupiter and Saturn has made significant progress during the past few years, these ratios, either elemental or isotopic, are still very poorly known in the case of Uranus and Neptune. An estimate of H J H e was obtained for Uranus, in agreement with the solar value (H2/H2 + He = 0.9 ___0.1), from the inversion of ir data (Courtin et al., 1978); in the case of Neptune, the present ir data are not sufficient to derive the same information. Concerning the C / H ratio, various studies have concluded that there is an enrichment in carbon for both Uranus and Neptune. However, this enrichment factor is still very uncertain. Lutz et al. (1976) suggested a carbon enrichment factor of 20 from the weak visible bands of methane, using the reflecting-layer model. On the basis of this result, theoretical models of the Uranus atmosphere used a very large C / H value (CH4/H2 > 3 x 10-2) (Danielson et al., 1977). More recently, from the study of the limb brightening of Uranus in the region 6000-8500 A, Price and Franz (1978) suggested an upper limit of 3 for the carbon enrichment factor. In the case of the C / H ratio, the problem is complicated even further by the possible satura-
tion of methane; from the inversion of ir data, Courtin et al. (1978, 1979) noticed that CH4 saturation was likely to occur on Uranus but not on Neptune, where supersaturation is required. From the results of a stellar occultation by Uranus, Sicardy et al. (1982) decided on a CH4-saturated model of Uranus in the upper atmosphere, but found no constraint on C / H below the saturation level. According to Gautier and Courtin (1979) an upper limit of 3 × 10-2 is obtained for the C / H ratio on Uranus from the study of the Uranus microwave spectrum. In the case of D / H , a first upper limit of 4 × l0 -4 was derived by Lutz and Owen (1974) using the RLM assumption, from the absence of the (4-0)P1 line of HD; this limit was revised to 1.4 × 10-4 by Mc Kellar et al. (1976) on the basis of a new laboratory measurement of the strength of the HD line. More recently Trafton (1978) lowered this upper limit to 9.6 × l0 -5, using improved data of the region of the (4-0)P1 HD line and an inhomogeneous scattering atmospheric model. At the same time, the (50)R0 line of HD was identified on Uranus by Macy and Smith (1978), who derived a D / H ratio of 3.3 _+ 1.2 × 10-5, using the (40)Sa quadrupole line of H2, on the basis of an inhomogeneous reflecting-layer model. More recently, De Bergh et al. (1981) de27 0019-1035/82/010027-08502.00/0 Copyright © 1982by Academic Press, Inc. All rights of reproduction in any form reserved.
28
ENCRENAZ AND COMBES
rived a CI-IaD/CI-I4 ratio of 9 × 10-~ which corresponds to the D / H interstellar value if CHaD is not enhanced by fractionation. The inability of the reflecting-layer model to describe a planetary atmosphere has been pointed out by many authors in the case of Jupiter (Wallace and Smith, 1977; Hunt and Bergstralh, 1977). Indeed, it has been shown that the RLM could not account for the center-to-limb variations in the visible range, and, more generally, for the whole set of data recorded in the visible and near-infrared range. In a previous paper (Combes and Encrenaz, 1979), hereafter referred to as Paper I, we pointed out the significant error which can result from the use of the RLM in the determination of abundance ratios. It was shown in Paper I that the apparent abundances of an absorber, derived from the RLM, are actually distributed as a function of the strength of the lines or bands. These apparent abundances, which should all be equal for a given absorber if the RLM was valid, vary by a factor of around 2 in the case of CH4, when the strengths of the two lines or bands vary by a factor of 10. Thus, in the case of Jupiter, the error in the resulting abundance ratio may also be wrong by a factor of 2. As explained by McElroy (1969) and Chamberlain (1970), and discussed in detail in Paper I, the observed departure from RLM may be due to scattering effects in the Jovian atmosphere. Such a departure from the RLM is expected in a scattering atmosphere as shown in Fig. 2. Strong lines, for which the true absorption probability greatly exceeds the scattering probability, lead to identical apparent abundances. In contrast, weak lines, even those far from being saturated, lead to various apparent abundances of the absorber, depending on the effective photon path, i.e., on the true absorption probability. A linear relation between the equivalent width and the abundance is valid only for extra-weak lines, for which the absorption probability is negligible with respect to the scattering probability.
In the case of Uranus and Neptune, we expect that the scattering processes involved in the line formation are even stronger than those for Jupiter. Due to the large amounts of hydrogen derived from the observations of the (4-0) and (3-0) quadrupole lines, using either the RLM or scattering models (Belton e t a / . , 1971; Encrenaz and Owen, 1973), Rayleigh scattering cannot be neglected. Moreover, because of the low temperature of these planets various species as NHa, CH4, C2H2 . . . . are expected to condense in much larger amounts than for Jupiter and Saturn, and may produce significant Mie scattering; Trafton (1976) has shown evidence for haze particles on Uranus. Thus, the use of the RLM for determining abundance ratios on Uranus and Neptune is questionable. The purpose of this paper is to analyze how the method described in Paper I, for the determination of abundance ratios on Jupiter, can be applied to the atmospheres of Uranus and Neptune. In Section II, we first demonstrate the inability of the RLM to account for all the data and we evaluate the possible error in the abundance ratios, due to the RLM approximation. In the third section we define an extrapolation of the method described in Paper I, and we analyze its limitations. In Section IV, we apply this method to the D/C ratio on Uranus and discuss its astrophysical implications. II. DEPARTUREFROM THE RLM Figure 1 shows the variations of the apparent abundance of CH4, obtained with the RLM, as a function of the absorption coefficient at the center of a line or band, in the case of (a) Jupiter and (b) Uranus and Neptune. Figure la is similar to Fig. 3 of Paper I, but includes recent observational results by Lutz et a/. (1981). It has already been mentioned in Paper I that there is no implicit assumption in the construction of this curve, since the apparent abundance A, shown on the ordinate, is only a translation of the measured absorption depth p,
THE D/C RATIO ON URANUS
29
band; moreover, the determination o f the continuum level seems very uncertain. • ,< .+< . < .< .< 1.0 Three comments can be made with respect to Fig. 1. First, as explained in Paper i ° JUPITER I, the curves shown in Figs. la and b should be horizontal lines if the reflecting-layer 0.5 model is valid, since all the observations of a given constituent should lead to a unique determination o f the abundance; thus, the I I 0.0 effect of departure from R L M is shown 20 b without any ambiguity in the case of Uranus and Neptune. In addition, the ~",~", ~ NEPTUNE points are regularly distributed as a func10-tion o f (S/zry) for both Uranus and Neptune, and show less dispersion than in the case o f Jupiter. Second, this effect is much I I stronger than that for Jupiter. If we com-6 -5 -4 -7 Log ( S / Y ~ ) (cm-Am) -1 pare two points which differ b y a factor of 10 in the abcissae, for instance S/~3, = 10-5 FIG. 1. Apparent abundances of CH4 (km-am) as a and S/Try = 10-~, we see that the correfunction of (S/~-y). sponding values o f the ordinate differ by a factor of 2 in the case of Jupiter, and around 5 for Uranus and Neptune. Third, we notice through the relationship p = 1 - e -s'Al'~v, that this effect seems to be slightly stronger where S is the strength o f the line or band on Neptune than on Uranus. and 3' is its half-width. For Jupiter, as well We thus conclude that scattering effects as Uranus and Neptune, Fig. 1 is thus a are much more important on Uranus than direct observational result. on Jupiter, and even more important in the In the case o f Uranus and Neptune, the data have been taken from Lutz e t a / . RLM curve of growth (1976, 1981) for the five CI-I4 bands at 4860, 5 o 5430, 5760, 6190, and 7250 .~. The absolute v ~'~linear mode - ~ isquore root +, ~ ~- m,~e strengths of the bands and the corresponding curves of growth were taken from Lutz +3 HSM (1977) and L u t z et al. (1981). The error ~2 bars were estimated from the dispersion ........ ++ . . . . o f the data, and from the uncertainty of the continuum level. As the CH4 absorption J I I I 001 01 1 10 is very strong in the visible spectra of W Uranus and Neptune, the major source of FIG. 2. Apparent abundance as a function of the uncertainty here comes from the definition absorption coefficient a0 at the center of a Lorentz o f the continuum level. At the present time, line, calculated from McElroy (1969). The abscissa it is not possible to draw this curve in the unit is w = ao/(~r + k), where tr andk are the scattering 3va - CH4 band at 1.1 /xm for Uranus and coefficient and the absorption coefficient in the continNeptune, as it has been done for Jupiter: uum, respectively. The single scattering albedo in the the data do not exist for Neptune, and in continuum is toc = cr/(~r + k) = 0.99. The related curve of growth departs from linearity for w ~ 0.01, while for the case of Uranus the observations of a pure absorbing atmosphere (RLM, oJc = 0) the transiTrafton at 3.5/~ resolution do not allow the tion from linear to square-root regime occurs only for measurement of the individual lines o f the W ~ 1.
t
-.
30
ENCRENAZ AND COMBES
case of Neptune. This result is not surprising, as pointed out b y m a n y authors (Belton et al., 1971; Trafton, 1976, 1978). Consequently, we cannot use the reflecting-layer model for a determination o f a b u n d a n c e ratios on Uranus and Neptune. The inaccuracy in the results derived f r o m the R L M , which was already pointed out in the case of Jupiter, is e x p e c t e d to be e v e n stronger for Uranus and Neptune: while, in the case of Jupiter, an abundance ratio derived from the R L M m a y be e r r o n e o u s by a factor of 2 if the intensities of the two lines vary by a factor of 10, it may be wrong b y a factor of 5 on Uranus and Neptune. llI. PRINCIPLE OF THE METHOD AND APPLICATIONS In order to solve this problem, some authors have tried to determine abundance ratios f r o m scattering models. H o w e v e r , because o f the large n u m b e r of possible solutions, the derived values have a large range, at least in the case of Jupiter. F o r this reason, we have tried to use another a p p r o a c h , that of defining a method o f comparison which would be valid w h a t e v e r the scattering processes m a y be. To s u m m a r i z e this method, which has been described in detail in P a p e r I, we have defined a set of four conditions to be fulfilled for a reliable c o m p a r i s o n of two lines or bands. These four conditions are the following: (1) the lines must be at a p p r o x i m a t e l y the same frequency, (2) the depths o f the lines measured on the planetary spectrum must be equal, (3) the mixing ratio of the two absorbers must be constant with altitude, and (4) the absorption coefficient of the two lines or bands must have the same dependence on t e m p e r a t u r e and pressure. In the "'ideal c a s e " defined by these four conditions, the a b u n d a n c e ratio derived from such a c o m p a r i s o n is e x p e c t e d to be valid no matter what the scattering processes m a y be, because the four conditions actually imply that these scattering processes are the same for both lines. As pointed out in P a p e r I, these four con-
ditions limit the "ideal c a s e " to a very few cases only. Taking into account the limited set o f available data, e v e n in the case of Jupiter, we have to consider the effects of a departure f r o m each of these conditions in order to extend the possible applications of the method. It has been shown in Paper I that, a m o n g the four conditions, two are very important (conditions 2 and 3): the lines or bands must have the same depth on the planetary spectrum, and the mixing ratio of the two absorbers has to be constant with height. Figure lb illustrates that this statement seems to be true for Uranus and Neptune: the m e a s u r e d apparent abundance is a strong function of the depth of the line; the small dispersion seems to imply that the role o f the wavelength (condition 1) is minor; the CH4 bands considered here seem to be pressure and t e m p e r a t u r e independent (Lutz et al., 1981) so that condition 4 is fulfilled. In the case of Jupiter we considered four abundance ratios: 12c/~ac, C / H , D / C , and C / N . Only 12C/13C and D / C were ideal cases. F o r Uranus and Neptune, the existing data limit our choice to C / H and, in the case of Uranus, D / C . The C / H ratio is not an ideal case because of the peculiar pressure d e p e n d e n c e o f the H2 quadrupole lines and because of the pressure shift of these lines. It was shown in Paper I that in the case o f Jupiter, the variations of the absorption coefficient with t e m p e r a t u r e and pressure were not too different for the CH4 bands and the H2 lines, at least in the atmospheric region 1-2 atm, where the line formation is e x p e c t e d to occur. Moreover, the pressure shift studied in detail by Mc Kellar (1974) has been shown to be significantly smaller than the half-width of the Hz lines, so that the error on the absorption coefficient at the center is only a few percent. In contrast, for Uranus and Neptune, the situation is different. Because of the high pressures e x p e c t e d in the region where the lines are formed, the dependence of the absorption coefficient on pressure and temperature b e c o m e s very different for H2 and
THE D/C RATIO ON URANUS CH4; for the same reason, the pressure shift at the center o f the H2 line becomes comparable to the half-width o f this line so that it is no longer possible to define, strictly speaking, a central frequency. An estimate o f these effects on the absorption coefficient of the H2 line would require the definition of a model, and thus, at the present state of knowledge, some a priori assumptions. For these reasons, we believe that our method for determining abundance ratios cannot be applied to C / H on Uranus and Neptune in view o f the present uncertainty of these atmospheres. We now have to consider the case o f D/C. In Paper I, we said that D / C was an ideal case for Jupiter. H o w e v e r , for Uranus, there are two effects leading to a departure from the ideal case: (1) there is no weak CH4 singlet to be c o m p a r e d to the H D line and (2) the pressure shift o f this H D line may not be negligible. We can expect the first effect to be minor, if we consider the agreement between the CH4 individual lines and the CH4 bands on Jupiter (Fig. la), as pointed out in Paper I. The second effect is fortunately much smaller than in the case of the H2 line, because the H D line is pressure broadened. If we take the pressure shift coefficients of Mc Kellar et al. (1976) and the pressure-broadening coefficient o f Macy and Smith (1978) we find that at each level of the atmosphere, the total pressure shift is approximately half of the half-width. The total uncertainty on the absorption coefficient at the observed line center is then e x p e c t e d to be less than 20%, which is small c o m p a r e d to the range of error we would e x p e c t if we use the RLM. Thus, we believe that it is worthwhile to use our m e t h o d for a determination o f the D / C ratio in the atmosphere of Uranus. A preliminary result o f this study has been given in E n c r e n a z and Combes (1978). IV. THE D/C RATIO ON URANUS Following our method described in detail in Paper I, we try to derive an estimate of
31
D / C on Uranus by using (1) the C H 4 7qA(S/cry) curve for Uranus shown in Fig. lb, and (2) an observation of the H D (5-0) R(0) line made on Uranus by Macy and Smith (1978) at 6064 A. As explained in Paper I, we first try to find on the C H 4 ~A(S/Try) a point corresponding to a fictitious C H 4 line which would have the same depth as the (5-0) R(0) line on the Jovian spectrum. Once this point is found, we can estimate the H D / C H 4 ratio--i.e., the D / C r a t i o - - b y a direct ratio of the apparent abundances of the two lines: A HD/AcH4. The condition of equal depth for the H D line and the fictitious CH4 " l i n e " is equivalent to (see Paper I) NHD
"
O£HD = HCH4 ' ~CH4
or P (SHD/TrYHD) = SCH4/7"gTCH4,
where p is the H D / C H 4 ratio, S is the strength of the line or band, and Y is its halfwidth. SnD depends upon the temperature and THDis related to the pressure. From a recent analysis of the thermal profile o f Uranus (Courtin et al., 1978), together with the same estimates of the hydrogen abundance (Encrenaz and Owen, 1973), we concluded that the region of H D line formation extends below the 2-atm pressure level (T = 100°K). In this atmospheric range SHD 3.10 -7 c m - 1 / c m - a m and T.D > 0.16 cm -1, so that the (S/WY)HD quantity is smaller than 6 × 10-7 (cm-am) -1. It is reasonable to assume also that on Uranus C / H -> 5 × 10-4, which is the solar value, and that D / H -< 10 -4, in agreement with Trafton (1978) and L u t z e t a l . (1981), so t h a t p -< 0.2. F r o m these estimates it can be shown that the fictitious CH4 line, having the same depth as the H D (5-0) line, is such that its (S/'n'y)cm value is smaller than 1.2 × l0 -7 (cm-am). This value is, as shown in Fig. 3, smaller than the abscissa range, where the CHa curve is defined. Thus we can only obtain a lower limit o f the CH4 apparent
32
ENCRENAZ AND COMBES
20
CH4
lo
.Dsocs-o~
1
"'~""
J 08
.
-8 Log ($/1(~ {era-Am) -1
-5
FIG. 3. Apparent abundances of CH4 (km-am) and HD (km-am x 100)as a function of S/~3,. The squares indicate the range of uncertainty for the HD measurement. abundance, corresponding to the fictitious CH4 line, assuming this line is on the linear regime o f extra-weak lines. F r o m Fig. 3 we obtain rtA(CH4) ~> 14 km-am, with rt = 2.5 ( L u t z e t al., 1976), orA(CH4) ~> 5.6 km-am. The apparent abundance (RLM) o f H D may be derived from Macy and Smith (1978), who obtained, from an inhomogeneous reflecting-layer model, A(HD) = 0.033 --_ 0.0011 km-am. From these values, D / C < 6 × 10-3. This conclusion is largely independent o f the structure of the Uranus atmosphere, since the above inequality is valid in the whole range p(S/¢ry) < 1.2 × 10-7 which actually corresponds to the whole atmospheric range where H D can reasonably be formed and covers the whole range o f plausible values of C / H . Our D / C result has some important astrophysical implications. The D / C ratio that we derive on Uranus (D/C < 6 × 10-3) is significantly lower than the value found in Paper I on Jupiter (1.0 × 10-z < D / C < 2.7 × 10-2). Using the recent C / H determination derived from the Voyager IRIS data ( C / H = 9.7 _+ 1.1 × 10-4; Gautier et al., 1981), we derive, for Jupiter, 0.8 × 10- 5 < D / H <
3 x 10-5
in reasonable agreement with the expected D / H value in the primordial solar nebula
(Geiss and Reeves, 1972) and in the local interstellar medium (Laurent, 1978). Other recent studies in the infrared range, at 5/xm (Kunde et al., 1981; Bjoraker et al., 1981; Drossart et al., 1981) and at 10 /xm (Encrenaz et al., 1980; Kunde et al., 1981), have led to a CH3D/H2 ratio of 2 to 3 × 10-7, which implies a Jovian D / H ratio in the range 2 to 3 x 10-5 . In the case of Uranus, as mentioned above, the only available D / H determination, coming from a CHaD observation ( L u t z e t al., 1981), also falls within the range of the D / H interstellar values. In conclusion, the simplest explanation for the D / C depletion on Uranus is that both hydrogen and deuterium are depleted on Uranus by approximately the same factor, which in turn would imply that the C / H ratio is enriched by a factor of 6 or more relative to the solar value. v. CONCLUSION In this paper we showed the major role played by scattering processes in the line formation in the atmospheres of Uranus and Neptune, and we pointed out the uncertainty which can result from the use of the reflecting-layer model in the determination o f abundance ratios on these two planets. Then we analyzed a possible extension of the method that we defined and used for Jupiter in Paper I, and we applied it to the D / C ratio on Uranus. Our r e s u l t - - D / C < 6 × 10-a--is significantly smaller than the value derived for Jupiter (Paper I). The simplest explanation is probably that both hydrogen and deuterium are depleted on Uranus, so that the D / C depletion implies an enrichment in carbon of a factor of 6 or more relative to the solar value. A reliable determination of the D / H ratio could significantly improve the significance of this result. The method described in this paper could be fruitfully applied to determine the D / C ratio by the use o f weak lines of CH4 with the absorption coefficient in the range of that o f the H D line. Such a study has been done by Macy et al. (1978) on the 6819-~
THE D/C RATIO ON URANUS
33
line, but, unfortunately, the rotational assignment of this line is unknown, which leads to significant uncertainty about the result. Laboratory spectra at low temperatures using very long pathlengths are needed to solve this problem. On the other hand, a better knowledge of the thermal profile and the cloud structure of Uranus and Neptune could allow, in the future, a more precise calculation of the absorption coefficient in the H2 quadrupole lines on these planets; then the present method could be used for a reliable determination of C/H on Uranus and Neptune.
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MACY, W., J. GELFAND, AND W. H. SUIT8 (1978). Interpretation of the 6818.9 ,~ methane line in terms of inhomogeneous scattering models for Uranus and Neptune. Icarus 34, 20-27. MACY, W., AND W. H. SMITH (1978). Detection of liD on Saturn and Uranus, and the D/H ratio. Astrophys. J. 222, L73. PalCE, M. J., AND O. G. FRANZ (1978). Uranus: Narrow-waveband disk profiles in the spectral region 6000-8500 ]k. BAAS 10, 576. SICARDY, B., M. COMBES, A. BRAHIC. P. BOUCHER, C. PERRIER, AND R. COURTIN (1982). The 15 August
1980 occultation by the Uranian system: Structure of the rings and temperature of the upper atmosphere. In preparation. TRAFTON, L. M. (1976). The aerosol distribution in Uranus' atmosphere: Interpretation of the hydrogen spectrum. Astrophys. J. 207, 1007-1024. TRAETON, L. M. (1978). On the deuterium to hydrogen ratio in the atmosphere of Uranus. Astrophys. J. 222, 740-743. WALLACE, L., AND G. R. SMITH (1977). The interpretation of Jovian methane absorptions. Astrophys..I. 212, 252-261.
On the D/C Ratio in the Atmosphere of Uranus TH. E N C R E N A Z AND M. COMBES Observatoire de Meudon, 92190 Meudon, France Received February 16, 1979; revised N o v e m b e r 6, 1981 A m e t h o d for deriving mixing ratios in the o u t e r planets, mostly i n d e p e n d e n t o f scattering p r o c e s s e s , is applied to U r a n u s . It is s h o w n that scattering p r o c e s s e s play a major role in the line formation in the a t m o s p h e r e s of U r a n u s and N e p t u n e ; c o n s e q u e n t l y , a b u n d a n c e ratios derived from a reflecting-layer model can be questionable. U s i n g our m e t h o d , we derive for U r a n u s D / C < 6 × 10-2, which is significantly smaller than o u r result on Jupiter. The simplest explanation implies a C / H e n r i c h m e n t by at least a factor of 6 relative to the solar value.
I. I N T R O D U C T I O N
While the study of the abundance ratios on Jupiter and Saturn has made significant progress during the past few years, these ratios, either elemental or isotopic, are still very poorly known in the case of Uranus and Neptune. An estimate of H J H e was obtained for Uranus, in agreement with the solar value (H2/H2 + He = 0.9 ___0.1), from the inversion of ir data (Courtin et al., 1978); in the case of Neptune, the present ir data are not sufficient to derive the same information. Concerning the C / H ratio, various studies have concluded that there is an enrichment in carbon for both Uranus and Neptune. However, this enrichment factor is still very uncertain. Lutz et al. (1976) suggested a carbon enrichment factor of 20 from the weak visible bands of methane, using the reflecting-layer model. On the basis of this result, theoretical models of the Uranus atmosphere used a very large C / H value (CH4/H2 > 3 x 10-2) (Danielson et al., 1977). More recently, from the study of the limb brightening of Uranus in the region 6000-8500 A, Price and Franz (1978) suggested an upper limit of 3 for the carbon enrichment factor. In the case of the C / H ratio, the problem is complicated even further by the possible satura-
tion of methane; from the inversion of ir data, Courtin et al. (1978, 1979) noticed that CH4 saturation was likely to occur on Uranus but not on Neptune, where supersaturation is required. From the results of a stellar occultation by Uranus, Sicardy et al. (1982) decided on a CH4-saturated model of Uranus in the upper atmosphere, but found no constraint on C / H below the saturation level. According to Gautier and Courtin (1979) an upper limit of 3 × 10-2 is obtained for the C / H ratio on Uranus from the study of the Uranus microwave spectrum. In the case of D / H , a first upper limit of 4 × l0 -4 was derived by Lutz and Owen (1974) using the RLM assumption, from the absence of the (4-0)P1 line of HD; this limit was revised to 1.4 × 10-4 by Mc Kellar et al. (1976) on the basis of a new laboratory measurement of the strength of the HD line. More recently Trafton (1978) lowered this upper limit to 9.6 × l0 -5, using improved data of the region of the (4-0)P1 HD line and an inhomogeneous scattering atmospheric model. At the same time, the (50)R0 line of HD was identified on Uranus by Macy and Smith (1978), who derived a D / H ratio of 3.3 _+ 1.2 × 10-5, using the (40)Sa quadrupole line of H2, on the basis of an inhomogeneous reflecting-layer model. More recently, De Bergh et al. (1981) de27 0019-1035/82/010027-08502.00/0 Copyright © 1982by Academic Press, Inc. All rights of reproduction in any form reserved.
28
ENCRENAZ AND COMBES
rived a CI-IaD/CI-I4 ratio of 9 × 10-~ which corresponds to the D / H interstellar value if CHaD is not enhanced by fractionation. The inability of the reflecting-layer model to describe a planetary atmosphere has been pointed out by many authors in the case of Jupiter (Wallace and Smith, 1977; Hunt and Bergstralh, 1977). Indeed, it has been shown that the RLM could not account for the center-to-limb variations in the visible range, and, more generally, for the whole set of data recorded in the visible and near-infrared range. In a previous paper (Combes and Encrenaz, 1979), hereafter referred to as Paper I, we pointed out the significant error which can result from the use of the RLM in the determination of abundance ratios. It was shown in Paper I that the apparent abundances of an absorber, derived from the RLM, are actually distributed as a function of the strength of the lines or bands. These apparent abundances, which should all be equal for a given absorber if the RLM was valid, vary by a factor of around 2 in the case of CH4, when the strengths of the two lines or bands vary by a factor of 10. Thus, in the case of Jupiter, the error in the resulting abundance ratio may also be wrong by a factor of 2. As explained by McElroy (1969) and Chamberlain (1970), and discussed in detail in Paper I, the observed departure from RLM may be due to scattering effects in the Jovian atmosphere. Such a departure from the RLM is expected in a scattering atmosphere as shown in Fig. 2. Strong lines, for which the true absorption probability greatly exceeds the scattering probability, lead to identical apparent abundances. In contrast, weak lines, even those far from being saturated, lead to various apparent abundances of the absorber, depending on the effective photon path, i.e., on the true absorption probability. A linear relation between the equivalent width and the abundance is valid only for extra-weak lines, for which the absorption probability is negligible with respect to the scattering probability.
In the case of Uranus and Neptune, we expect that the scattering processes involved in the line formation are even stronger than those for Jupiter. Due to the large amounts of hydrogen derived from the observations of the (4-0) and (3-0) quadrupole lines, using either the RLM or scattering models (Belton e t a / . , 1971; Encrenaz and Owen, 1973), Rayleigh scattering cannot be neglected. Moreover, because of the low temperature of these planets various species as NHa, CH4, C2H2 . . . . are expected to condense in much larger amounts than for Jupiter and Saturn, and may produce significant Mie scattering; Trafton (1976) has shown evidence for haze particles on Uranus. Thus, the use of the RLM for determining abundance ratios on Uranus and Neptune is questionable. The purpose of this paper is to analyze how the method described in Paper I, for the determination of abundance ratios on Jupiter, can be applied to the atmospheres of Uranus and Neptune. In Section II, we first demonstrate the inability of the RLM to account for all the data and we evaluate the possible error in the abundance ratios, due to the RLM approximation. In the third section we define an extrapolation of the method described in Paper I, and we analyze its limitations. In Section IV, we apply this method to the D/C ratio on Uranus and discuss its astrophysical implications. II. DEPARTUREFROM THE RLM Figure 1 shows the variations of the apparent abundance of CH4, obtained with the RLM, as a function of the absorption coefficient at the center of a line or band, in the case of (a) Jupiter and (b) Uranus and Neptune. Figure la is similar to Fig. 3 of Paper I, but includes recent observational results by Lutz et a/. (1981). It has already been mentioned in Paper I that there is no implicit assumption in the construction of this curve, since the apparent abundance A, shown on the ordinate, is only a translation of the measured absorption depth p,
THE D/C RATIO ON URANUS
29
band; moreover, the determination o f the continuum level seems very uncertain. • ,< .+< . < .< .< 1.0 Three comments can be made with respect to Fig. 1. First, as explained in Paper i ° JUPITER I, the curves shown in Figs. la and b should be horizontal lines if the reflecting-layer 0.5 model is valid, since all the observations of a given constituent should lead to a unique determination o f the abundance; thus, the I I 0.0 effect of departure from R L M is shown 20 b without any ambiguity in the case of Uranus and Neptune. In addition, the ~",~", ~ NEPTUNE points are regularly distributed as a func10-tion o f (S/zry) for both Uranus and Neptune, and show less dispersion than in the case o f Jupiter. Second, this effect is much I I stronger than that for Jupiter. If we com-6 -5 -4 -7 Log ( S / Y ~ ) (cm-Am) -1 pare two points which differ b y a factor of 10 in the abcissae, for instance S/~3, = 10-5 FIG. 1. Apparent abundances of CH4 (km-am) as a and S/Try = 10-~, we see that the correfunction of (S/~-y). sponding values o f the ordinate differ by a factor of 2 in the case of Jupiter, and around 5 for Uranus and Neptune. Third, we notice through the relationship p = 1 - e -s'Al'~v, that this effect seems to be slightly stronger where S is the strength o f the line or band on Neptune than on Uranus. and 3' is its half-width. For Jupiter, as well We thus conclude that scattering effects as Uranus and Neptune, Fig. 1 is thus a are much more important on Uranus than direct observational result. on Jupiter, and even more important in the In the case o f Uranus and Neptune, the data have been taken from Lutz e t a / . RLM curve of growth (1976, 1981) for the five CI-I4 bands at 4860, 5 o 5430, 5760, 6190, and 7250 .~. The absolute v ~'~linear mode - ~ isquore root +, ~ ~- m,~e strengths of the bands and the corresponding curves of growth were taken from Lutz +3 HSM (1977) and L u t z et al. (1981). The error ~2 bars were estimated from the dispersion ........ ++ . . . . o f the data, and from the uncertainty of the continuum level. As the CH4 absorption J I I I 001 01 1 10 is very strong in the visible spectra of W Uranus and Neptune, the major source of FIG. 2. Apparent abundance as a function of the uncertainty here comes from the definition absorption coefficient a0 at the center of a Lorentz o f the continuum level. At the present time, line, calculated from McElroy (1969). The abscissa it is not possible to draw this curve in the unit is w = ao/(~r + k), where tr andk are the scattering 3va - CH4 band at 1.1 /xm for Uranus and coefficient and the absorption coefficient in the continNeptune, as it has been done for Jupiter: uum, respectively. The single scattering albedo in the the data do not exist for Neptune, and in continuum is toc = cr/(~r + k) = 0.99. The related curve of growth departs from linearity for w ~ 0.01, while for the case of Uranus the observations of a pure absorbing atmosphere (RLM, oJc = 0) the transiTrafton at 3.5/~ resolution do not allow the tion from linear to square-root regime occurs only for measurement of the individual lines o f the W ~ 1.
t
-.
30
ENCRENAZ AND COMBES
case of Neptune. This result is not surprising, as pointed out b y m a n y authors (Belton et al., 1971; Trafton, 1976, 1978). Consequently, we cannot use the reflecting-layer model for a determination o f a b u n d a n c e ratios on Uranus and Neptune. The inaccuracy in the results derived f r o m the R L M , which was already pointed out in the case of Jupiter, is e x p e c t e d to be e v e n stronger for Uranus and Neptune: while, in the case of Jupiter, an abundance ratio derived from the R L M m a y be e r r o n e o u s by a factor of 2 if the intensities of the two lines vary by a factor of 10, it may be wrong b y a factor of 5 on Uranus and Neptune. llI. PRINCIPLE OF THE METHOD AND APPLICATIONS In order to solve this problem, some authors have tried to determine abundance ratios f r o m scattering models. H o w e v e r , because o f the large n u m b e r of possible solutions, the derived values have a large range, at least in the case of Jupiter. F o r this reason, we have tried to use another a p p r o a c h , that of defining a method o f comparison which would be valid w h a t e v e r the scattering processes m a y be. To s u m m a r i z e this method, which has been described in detail in P a p e r I, we have defined a set of four conditions to be fulfilled for a reliable c o m p a r i s o n of two lines or bands. These four conditions are the following: (1) the lines must be at a p p r o x i m a t e l y the same frequency, (2) the depths o f the lines measured on the planetary spectrum must be equal, (3) the mixing ratio of the two absorbers must be constant with altitude, and (4) the absorption coefficient of the two lines or bands must have the same dependence on t e m p e r a t u r e and pressure. In the "'ideal c a s e " defined by these four conditions, the a b u n d a n c e ratio derived from such a c o m p a r i s o n is e x p e c t e d to be valid no matter what the scattering processes m a y be, because the four conditions actually imply that these scattering processes are the same for both lines. As pointed out in P a p e r I, these four con-
ditions limit the "ideal c a s e " to a very few cases only. Taking into account the limited set o f available data, e v e n in the case of Jupiter, we have to consider the effects of a departure f r o m each of these conditions in order to extend the possible applications of the method. It has been shown in Paper I that, a m o n g the four conditions, two are very important (conditions 2 and 3): the lines or bands must have the same depth on the planetary spectrum, and the mixing ratio of the two absorbers has to be constant with height. Figure lb illustrates that this statement seems to be true for Uranus and Neptune: the m e a s u r e d apparent abundance is a strong function of the depth of the line; the small dispersion seems to imply that the role o f the wavelength (condition 1) is minor; the CH4 bands considered here seem to be pressure and t e m p e r a t u r e independent (Lutz et al., 1981) so that condition 4 is fulfilled. In the case of Jupiter we considered four abundance ratios: 12c/~ac, C / H , D / C , and C / N . Only 12C/13C and D / C were ideal cases. F o r Uranus and Neptune, the existing data limit our choice to C / H and, in the case of Uranus, D / C . The C / H ratio is not an ideal case because of the peculiar pressure d e p e n d e n c e o f the H2 quadrupole lines and because of the pressure shift of these lines. It was shown in Paper I that in the case o f Jupiter, the variations of the absorption coefficient with t e m p e r a t u r e and pressure were not too different for the CH4 bands and the H2 lines, at least in the atmospheric region 1-2 atm, where the line formation is e x p e c t e d to occur. Moreover, the pressure shift studied in detail by Mc Kellar (1974) has been shown to be significantly smaller than the half-width of the Hz lines, so that the error on the absorption coefficient at the center is only a few percent. In contrast, for Uranus and Neptune, the situation is different. Because of the high pressures e x p e c t e d in the region where the lines are formed, the dependence of the absorption coefficient on pressure and temperature b e c o m e s very different for H2 and
THE D/C RATIO ON URANUS CH4; for the same reason, the pressure shift at the center o f the H2 line becomes comparable to the half-width o f this line so that it is no longer possible to define, strictly speaking, a central frequency. An estimate o f these effects on the absorption coefficient of the H2 line would require the definition of a model, and thus, at the present state of knowledge, some a priori assumptions. For these reasons, we believe that our method for determining abundance ratios cannot be applied to C / H on Uranus and Neptune in view o f the present uncertainty of these atmospheres. We now have to consider the case o f D/C. In Paper I, we said that D / C was an ideal case for Jupiter. H o w e v e r , for Uranus, there are two effects leading to a departure from the ideal case: (1) there is no weak CH4 singlet to be c o m p a r e d to the H D line and (2) the pressure shift o f this H D line may not be negligible. We can expect the first effect to be minor, if we consider the agreement between the CH4 individual lines and the CH4 bands on Jupiter (Fig. la), as pointed out in Paper I. The second effect is fortunately much smaller than in the case of the H2 line, because the H D line is pressure broadened. If we take the pressure shift coefficients of Mc Kellar et al. (1976) and the pressure-broadening coefficient o f Macy and Smith (1978) we find that at each level of the atmosphere, the total pressure shift is approximately half of the half-width. The total uncertainty on the absorption coefficient at the observed line center is then e x p e c t e d to be less than 20%, which is small c o m p a r e d to the range of error we would e x p e c t if we use the RLM. Thus, we believe that it is worthwhile to use our m e t h o d for a determination o f the D / C ratio in the atmosphere of Uranus. A preliminary result o f this study has been given in E n c r e n a z and Combes (1978). IV. THE D/C RATIO ON URANUS Following our method described in detail in Paper I, we try to derive an estimate of
31
D / C on Uranus by using (1) the C H 4 7qA(S/cry) curve for Uranus shown in Fig. lb, and (2) an observation of the H D (5-0) R(0) line made on Uranus by Macy and Smith (1978) at 6064 A. As explained in Paper I, we first try to find on the C H 4 ~A(S/Try) a point corresponding to a fictitious C H 4 line which would have the same depth as the (5-0) R(0) line on the Jovian spectrum. Once this point is found, we can estimate the H D / C H 4 ratio--i.e., the D / C r a t i o - - b y a direct ratio of the apparent abundances of the two lines: A HD/AcH4. The condition of equal depth for the H D line and the fictitious CH4 " l i n e " is equivalent to (see Paper I) NHD
"
O£HD = HCH4 ' ~CH4
or P (SHD/TrYHD) = SCH4/7"gTCH4,
where p is the H D / C H 4 ratio, S is the strength of the line or band, and Y is its halfwidth. SnD depends upon the temperature and THDis related to the pressure. From a recent analysis of the thermal profile o f Uranus (Courtin et al., 1978), together with the same estimates of the hydrogen abundance (Encrenaz and Owen, 1973), we concluded that the region of H D line formation extends below the 2-atm pressure level (T = 100°K). In this atmospheric range SHD 3.10 -7 c m - 1 / c m - a m and T.D > 0.16 cm -1, so that the (S/WY)HD quantity is smaller than 6 × 10-7 (cm-am) -1. It is reasonable to assume also that on Uranus C / H -> 5 × 10-4, which is the solar value, and that D / H -< 10 -4, in agreement with Trafton (1978) and L u t z e t a l . (1981), so t h a t p -< 0.2. F r o m these estimates it can be shown that the fictitious CH4 line, having the same depth as the H D (5-0) line, is such that its (S/'n'y)cm value is smaller than 1.2 × l0 -7 (cm-am). This value is, as shown in Fig. 3, smaller than the abscissa range, where the CHa curve is defined. Thus we can only obtain a lower limit o f the CH4 apparent
32
ENCRENAZ AND COMBES
20
CH4
lo
.Dsocs-o~
1
"'~""
J 08
.
-8 Log ($/1(~ {era-Am) -1
-5
FIG. 3. Apparent abundances of CH4 (km-am) and HD (km-am x 100)as a function of S/~3,. The squares indicate the range of uncertainty for the HD measurement. abundance, corresponding to the fictitious CH4 line, assuming this line is on the linear regime o f extra-weak lines. F r o m Fig. 3 we obtain rtA(CH4) ~> 14 km-am, with rt = 2.5 ( L u t z e t al., 1976), orA(CH4) ~> 5.6 km-am. The apparent abundance (RLM) o f H D may be derived from Macy and Smith (1978), who obtained, from an inhomogeneous reflecting-layer model, A(HD) = 0.033 --_ 0.0011 km-am. From these values, D / C < 6 × 10-3. This conclusion is largely independent o f the structure of the Uranus atmosphere, since the above inequality is valid in the whole range p(S/¢ry) < 1.2 × 10-7 which actually corresponds to the whole atmospheric range where H D can reasonably be formed and covers the whole range o f plausible values of C / H . Our D / C result has some important astrophysical implications. The D / C ratio that we derive on Uranus (D/C < 6 × 10-3) is significantly lower than the value found in Paper I on Jupiter (1.0 × 10-z < D / C < 2.7 × 10-2). Using the recent C / H determination derived from the Voyager IRIS data ( C / H = 9.7 _+ 1.1 × 10-4; Gautier et al., 1981), we derive, for Jupiter, 0.8 × 10- 5 < D / H <
3 x 10-5
in reasonable agreement with the expected D / H value in the primordial solar nebula
(Geiss and Reeves, 1972) and in the local interstellar medium (Laurent, 1978). Other recent studies in the infrared range, at 5/xm (Kunde et al., 1981; Bjoraker et al., 1981; Drossart et al., 1981) and at 10 /xm (Encrenaz et al., 1980; Kunde et al., 1981), have led to a CH3D/H2 ratio of 2 to 3 × 10-7, which implies a Jovian D / H ratio in the range 2 to 3 x 10-5 . In the case of Uranus, as mentioned above, the only available D / H determination, coming from a CHaD observation ( L u t z e t al., 1981), also falls within the range of the D / H interstellar values. In conclusion, the simplest explanation for the D / C depletion on Uranus is that both hydrogen and deuterium are depleted on Uranus by approximately the same factor, which in turn would imply that the C / H ratio is enriched by a factor of 6 or more relative to the solar value. v. CONCLUSION In this paper we showed the major role played by scattering processes in the line formation in the atmospheres of Uranus and Neptune, and we pointed out the uncertainty which can result from the use of the reflecting-layer model in the determination o f abundance ratios on these two planets. Then we analyzed a possible extension of the method that we defined and used for Jupiter in Paper I, and we applied it to the D / C ratio on Uranus. Our r e s u l t - - D / C < 6 × 10-a--is significantly smaller than the value derived for Jupiter (Paper I). The simplest explanation is probably that both hydrogen and deuterium are depleted on Uranus, so that the D / C depletion implies an enrichment in carbon of a factor of 6 or more relative to the solar value. A reliable determination of the D / H ratio could significantly improve the significance of this result. The method described in this paper could be fruitfully applied to determine the D / C ratio by the use o f weak lines of CH4 with the absorption coefficient in the range of that o f the H D line. Such a study has been done by Macy et al. (1978) on the 6819-~
THE D/C RATIO ON URANUS
33
line, but, unfortunately, the rotational assignment of this line is unknown, which leads to significant uncertainty about the result. Laboratory spectra at low temperatures using very long pathlengths are needed to solve this problem. On the other hand, a better knowledge of the thermal profile and the cloud structure of Uranus and Neptune could allow, in the future, a more precise calculation of the absorption coefficient in the H2 quadrupole lines on these planets; then the present method could be used for a reliable determination of C/H on Uranus and Neptune.
spectrum of Jupiter between 8 and 9/~: Estimates of the jovian C / H and D / H ratios. Astron. Astrophys. 84, 148-153. GAUTIER, D., AND R. COURTIN (1979). Atmospheric thermal structure of the giant planets. Icarus 39, 2845. GAUTIER, D., B. BEZARD, A. MARTEN, J. P. BALUTEAU, A. CHEDIN, N. HUSSON, N. SCOTT, V. KUNDE, AND R. HANEL (1981). The C / H ratio in Jupiter from the Voyager experiment. BAAS 13, 738. GEISS, J., AND H. REEVES (1972). Cosmic and solar system abundances of deuterium and helium 3. Astron. Astrophys. 18, 126-132. HUNT, G. E., AND J. T. BERGSTRAHL (1977). Interpretation of spatial and temporal variation of hydrogen quadrupole absorptions in the Jovian atmosphere observed during the 1972 apparition. Icarus 30, 511-
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