Consistency tests of cosmogonic theories from models of Uranus and Neptune

ICARUS 57, 102--111 (1984)

Consistency Tests of Cosmogonic Theories from Models of Uranus and Neptune M. PODOLAK Department of Geophysics and Planetary Sciences, Tel-Aviv University, Ramat Aviv, Israel 69978 AND

R. T. REYNOLDS Theoretical and Planetary Sciences Branch, NASA Ames Research Center, Moffett Field, California 94035 Received May 23, 1983; revised September 2, 1983 The planetary ratios of ice to rock (I/R) abundances expected in Uranus and Neptune are derived on the basis of several cosmogonic theories. For both Uranus and Neptune the value of I/R lies between about 1.0 and 3.6. This value is difficult to reconcile with a scenario in which N and C are accreted primarily in the form of N~ and CO. It is consistent with some versions of both giant protoplanet theories and equilibrium accretion theories.

INTRODUCTION

A C C R E T I O N A L THEORIES

The processes involved in the formation of the Solar System were undoubtedly complex. For this reason, theorists have often had to fall back on simplified models and qualitative arguments in place of detailed computations, and thus tests of cosmogonic theories are always desirable. In this paper we would like to discuss the significance of one such test, that of the mass ratio of ice to rock (1/R) for Uranus and Neptune. By " i c e " we mean such materials as H20, CH4, and NH3, while " r o c k " is taken to include silicates, nickel, and iron. Note that on Uranus and Neptune the ices will probably be fluid (not crystalline) and can be essentially gaseous (mixed with H2 and He). In what follows we shall briefly review several cosmogonic theories, and determine what each of them predicts for I/R. We shall then examine interior models of Uranus and Neptune to estimate the value of I/R actually present in these planets. In this way, we will try to set constraints on possible cosmogonic theories (see, e.g., Podolak, 1982).

Accretional theories assume that the sun was once surrounded by a gaseous nebular disk of about 10 -1 solar masses. The scenarios envisioned for the emplacement of the disk vary (see, e.g., Prentice, 1978; Safronov, 1972; Alfven and Arrhenius, 1975). No matter how the nebula was constructed, the temperature and pressure in the gas determine which materials will be solid (Lewis, 1972; Grossman, 1972). These solids accumulate into protoplanetary embryos. Near the sun, only refractory, rocky materials are solid and these are the building blocks of the terrestrial planets. Further out, the ices of H20, CH4, and NH3 become available, and, with this additional mass, larger embryos can be formed. If the embryo of rock or rock plus ice grows large enough, a dynamical instability could be induced in the surrounding nebular gas. Some of this gas would fall onto the embryo, and a giant planet could be formed (Perri and Cameron, 1974; Mizuno, 1980). The accretional energy should be sufficient to permit differentiation of ices from silicates.

102 0019-1035/84 $3.00 Copyright © 1984by AcademicPress, Inc. All fightsof reproduction in any form reserved.

TESTS OF COSMOGONIC THEORIES Based on this picture, we conclude that Uranus and Neptune should consist of a core of rock surrounded by ices, hydrogen, and helium. The ices may be confined to a layer surrounding the core, may be mixed entirely with the hydrogen and helium in an envelope, or may be partially around the core and partially in the envelope. In this model, the value of I/R, integrated over the planet, should be the same for Uranus and Neptune as for the solar nebula itself. Unfortunately, the value for I/R for the solar nebula is itself somewhat problematical. The values cited in the literature for the elemental abundances vary from author to author, and there is the additional uncertainty as to the precise distribution of elements among the various possible compounds. Thus, the value of I/R for solar material in equilibrium at T - 50°K is considered to be somewhere between 2.6 (Zharkov and Trubitsyn, 1978) and 3.6 (Cameron, 1981) depending on these details. There are, however, two points that bear on this issue which need clarification. The first point was made by Hubbard and MacFarlane (1980a) who noted that for a gas of solar composition, the relative amount of deuterium that will be confined to ices rather than to gaseous hydrogen depends on the temperature (Richet et al., 1977). At low temperatures (T-< 200°K) the ices will contain between 10 and 103 times more deuterium than at higher temperatures. Models of the interiors of Uranus and Neptune indicate a rather high ratio of ices to hydrogen (Reynolds and Summers, 1965; Podolak and Cameron, 1974; Podolak, 1976; Hubbard and MacFarlane, 1980b; Podolak and Reynolds, 1981). If there is mixing inside the planet so that the deuterium is redistributed among the available species, one would expect a deuterium-to-hydrogen ratio significantly enhanced (factor of more than 10) over the solar value of - 2 0 ppm (Black, 1973; Cameron, 1981). In fact, the observations of Uranus indicate a D/H ratio of only 1-3 times the solar value (Macy and Smith, 1978; Trafton and Ramsey, 1980),

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although recent measurements of the pressure broadening coefficients of the H2 quadrupole lines may require that this value be revised upward somewhat (Cochran and Smith, 1982). It is difficult to imagine that throughout its evolutionary history, Uranus never passed through a high-temperature convective stage which allowed the deuterium to redistribute. In addition, the release of radioactive heat from the rock core (assuming chondritic composition) should be enough to drive mild convection even today. Thus, the deuterium should have a chance to reequilibrate within the planet. A more likely explanation is that for reasons of kinetics the ices that were originally accreted were not completely in equilibrium with respect to deuterium. We will return to this point later, but for now let us consider a second argument for nonequilibrium processes that acted on ices in the solar nebula. A study of the microwave spectrum of Uranus reveals brightness temperatures at centimeter wavelengths higher than one would expect if significant amounts of ammonia were present (Gulkis et al., 1978). A similar effect is found for Neptune (Gulkis, 1981, private communication). The implication is that the atmospheres of Uranus and Neptune (and possibly the planets as a whole) are strongly depleted in NH3. Prinn and Lewis (1973) proposed that the atmospheric depletion was due to the reaction of NH3 with H2S to form NH4SH clouds. These clouds would be relatively transparent at the appropriate wavelengths, and thus provide a good fit to the observed spectrum (Gulkis et al., 1978). As can be seen from the stoichiometry of the reaction, equal amounts of nitrogen and sulfur are required for the reaction to go to completion. However, the solar value of the N/S ratio is about 5 (Cameron, 1981), and so the problem becomes one of supplying enough sulfur. Lewis and Prinn (1980) have suggested a mechanism for enhancing the abundance of sulfur relative to nitrogen. At high temperatures the equilibrium composi-

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PODOLAK AND REYNOLDS

tion of solar mix gas has N2 as the most abundant nitrogen species, while the most abundant carbon species is CO, with about 1% of the carbon in the form of CO2. At lower temperatures, where reduction by hydrogen is expected, reactions proceed extremely slowly. Thus, in the vicinity of Uranus and Neptune most of the nitrogen would still be in the form of N2 if it once passed through a high-temperature region. Since N2 is not expected to condense at temperatures above 25°K (Lewis and Prinn, 1980), the solids accreted into the planetary embryos would have a high S/N ratio. In the later stages, the N2 and CO will be converted to NH3 and CH4, respectively, and the NH3 will be removed from the atmosphere by NH4SH formation. An additional feature of this scenario is that since the vapor pressure of CO is very nearly equal to that of N2, it too will not condense. Thus the major path for carbon and nitrogen accretion would be through relatively minor species such as CO2, NH4COONH2, and NH4NCO3 (see Lewis and Prinn, 1980). Since most of the oxygen is tied up in CO, less H20 ice is available than under equilibrium conditions. For such a scenario we expect I / R ~ 0.5. It is of interest to note that in this case the amount of deuterium expected in Uranus will be considerably less than the amount estimated by Hubbard and MacFarlane (1980a). Not only is the expected value o f I / R about six times smaller, so that the total ice content of the planet is reduced, but a fraction of the ice enters as CO2, which contains no deuterium, thus reducing the expected ratio still further. Indeed, with the starting conditions assumed by Hubbard and MacFarlane, the expected ratio for this scenario turns out to be about three times the solar value, in agreement with the observations. GIANT PROTOPLANET THEORIES

A second group of theories have been suggested for the formation of giant gaseous protoplanets. While these differ in de-

tail (see, e.g., Woolfson, 1978a,b; McCrea, 1978; Cameron, 1978a,b), in all cases they result in protoplanets of solar composition ( I / R ~ 3). To form Uranus and Neptune, however, such protoplanets must lose a large fraction of their hydrogen and helium. How will such a loss mechanism affect the value of 1 / R ? The answer to this question depends to a large extent on the range of pressures and temperatures found inside the protoplanets. The most detailed study, to date, of protoplanetary evolution is that by DeCampli and Cameron (1979). They find that protoplanets contract slowly and heat up. When the central temperature reaches about 2000°K, H2 near the center begins to dissociate, and a hydrodynamic collapse ensues. Although the hydrogen loss mechanism for these planets has not been developed in detail, the basic idea is that since the protoplanets are imbedded in the nebula, there will be an interaction between the nebula and the protoplanet. In particular, an interchange of gas between the protoplanet and the nebula should occur. The temperature at the radiative boundary of the protoplanet will be low (DeCampli and Cameron find effective temperatures of 30-100°K for evolved protoplanets), and there may well be a cold trap which would prevent the ice forming materials from returning to the nebula. This could allow for an enhancement of ices with respect to hydrogen and helium. As Cameron (1978a,b) has pointed out, turbulence in the solar nebula is expected to drive a nebular "breeze" which will greatly reduce the mass of the nebula in the later stages of evolution. If the Uranus and Neptune protoplanets evolved more slowly than their Jovian and Saturnian counterparts, they would have found themselves in a nebula with very different physical conditions at the time of hydrodynamic collapse. This could affect the size of the collapsing envelope. We have applied the criteria for chemical equilibrium to the conditions found in the DeCampli-Cameron protoplanets, and we

TESTS OF COSMOGONIC THEORIES find that for temperatures above, about 800°K, Nz is the dominant nitrogen-bearing species, while CO is the major carbon species above about 1600°K. Such temperatures are reached near the center of the protoplanet in the last stage of contraction several tens of thousands of years before the final collapse (DeCampli and Cameron, 1979). Since most of the protoplanet is convecting with speeds of several meters per second, most of the nitrogen and carbon will be processed through the high-temperature region, and converted into N2 and CO. Although the reconversion of N2 to NH3 is kinetically prohibited, the conversion of CO into hydrocarbons can proceed fairly rapidly at these pressures. Based on data from shock-wave experiments (BarNun and Shaviv, 1975), Bar-Nun (1983) has found a formal rate constant for the reaction CO + 3H2 --~ H20 + CH4 of

105

dence for a considerable enhancement of ices, the cold trap temperature must have been low enough to hold H20. If it was low enough to hold N2 as well, then all the other volatiles of consequence would have been trapped, and the value of I/R would be about 3.5. IfCH4 were able to escape, however, then I/R would be lower, about 2.5. It would not be as low as 0.5, however, since all of the oxygen would be retained in the form of H20. If we allow in addition, for the loss of N2 (or NH3), we find I/R ~ 2. A giant protoplanet scenario will therefore give 2 -< I/R <- 3.5. In addition, since the original composition is solar, and the material is processed through temperatures of several hundred degrees, the D/H ratio should be nearly solar, in agreement with observations. MODELS OF URANUS

The value of I/R for Uranus and Neptune can be determined from theoretical modeling and compared with the values expected where k = 1.1 × 10 -51 e x p ( - E a / R T ) cm 9 for the various cosmogonic theories. The mole -3 sec -~, Ea = 23,000 cal., R is the gas models used here are those described in Poconstant, and T the temperature. The tem- dolak and Reynolds (1981). They consist of perature and pressure range of the shock- two shells, a core of rock surrounded by an wave experiments is quite close to the rele- envelope of H2, He, H20, NH3, and CH4. vant temperatures and pressures inside the The HffHe ratio is taken to be solar and the protoplanets, i.e., - 1 bar and 103 °K so that ices (H20, NH3, and CH4) are taken to be in this rate constant is meaningful. Thus, at a solar ratios to each other. The ratio of H2temperature of 777.5°K and a pressure of He to ices in the envelope is allowed to 0.11 atm, we have d[CO]/[CO] = 4.21 × vary, however. Models are constructed to 10 -4 sec -~ and relatively complete conver- fit the observed mass, radius, 1-bar tempersion will take place on the time scale of an ature, and J2 (quadrupole moment of the hour. In all the cases presented by DeCam- gravitational field). While there are uncerpli and Cameron regions can be found tainties regarding some of the details of the where conversion rates will be of this or- theoretical treatment, such as the equations der. Since under these conditions of tem- of state, phase transformations, the details perature and pressure CH4 is the dominant of the adiabatic temperature distributions, carbon species, we expect that a large frac- etc., the uncertainties are relatively small, tion of the carbon in the protoplanet will, in and have only a quantitative, but not qualifact, be in this form. tative effect on the derived density and Once the conversion to the appropriate temperature profiles, and on the value of I/ species has been accomplished, the deter- R. This can be seen from the rather good mining factor in deciding the I/R ratio will agreement between our models and equivabe the temperature of the cold trap. Since lent models of Hubbard and MacFarlane both Uranus and Neptune show clear evi- (1980b). A more serious problem is the und[CO] dt

= k[CO][H2]3

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PODOLAK AND REYNOLDS

certainty in the observationally determined parameters. This is illustrated in Table I. The presence of rings close to Uranus has enabled the value of J2 to be determined to three significant figures. In addition, two independent techniques give good agreement as to the value of the oblateness. The rotation period, which is crucial in computing J2 for a model density distribution (J2 varies as the square of the rotation rate) is not at all well determined. There is, however, a curious grouping in the data. Except for the result of Trauger et al., (1978), the periods obtained from spectroscopy center around two values, 16 and 24 hr. Purely dynamical considerations, based on the relation between oblateness, rotation period, and J2 require the shorter period, while photometry requires the longer one. Another important datum, J4, has also been measured, but the uncertainty in the measurement is large. Nonetheless, although some of the data is uncertain, some conclusions are possible. If we consider the models described TABLE

I

OBSERVATIONAL D A T A FOR U R A N U S Investigator

Technique

Elliot et al. (1981) Nicholson e t al. (1982) Nicholson e t al. (1982)

J2 x 103 3.352 ± 0,005 3.347 ± 0.008 3.350 ± 0.011

Orbits of ring particles Orbits of ring particles Orbits of ring particles

Elliot e t al. (1981) Nicholson e t al. (1982) Nicholson e t al. (1982)

J4 × 105 -2.9 -+ 1.3 -3.6 ± 1.2 -3.1 ± 1.7

Orbits of ring particles Orbits of ring particles Orbits of ring particles

Oblateness 0.022 +- 0.001 0.024 -+ 0.003

Franklin e t al. (1980) Elliot e t al. (1981)

Photography Stellar occultation

Rotation period (hr) 24 +6 -5

Spectroscopy Spectroscopy Spectroscopy Spectroscopy Photometry Spectroscopy

Munch and Hippelein (1980)

24 ± 3 15.57 -+ 0.80 12.9 +- 1.5 23.92 -+ 0.03 16.2 +- 0.3 +4 15 _ 2.6

Franklin e t al. (1980) Belton e t al. (1980) Elliot e t al. (1981)

16.6 _+ 0.5 24.4 -+ 4 15.5 -+ 1

Oblateness and J2 Spectroscopy Oblateness and J2

Trafton (1977) Hayes and Belton (1977) Brown and Goody (1977) Trauger e t al. (1978) Smith and Slavsky (1979) Brown and Goody (1980)

Spectroscopy

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4~ x l O 3 FIG. I. Variation of J2 and J4 for Uranus two-shell models with fixed I/R (dashed curves) and fixed rotation period (solid curves).

above, it turns out that as the value oflIR is increased, that is as more and more ices are put into the envelope, the value of J2 for a given rotation period is increased. Since J2 depends on the square of the rotation speed, and J4 on its fourth power, the ratio J2/J4 for a given model will increase with increasing period. Thus, if the rotation rate is chosen to match J2, models differing in I/ R will also have different values of JE/J4. This is illustrated in Fig. 1 where we have plotted two-shell models for various rotation periods and values of I/R. The error bars in the figure indicate the uncertainty in J4. By comparison, the appropriate error bars for J2 are too small to be seen in the figure. The three solid curves show the trajectories for models in JE-J4 space for rotation periods of 16, 18, and 24 hr, with I/R increasing from left to right along the curve. The dashed curves show trajectories of models with a fixed I/R (0.27, 0.58, 1.08, 4.2) as the rotation period is varied. We see that for the two shell models a rotation period of 16 hr will always give a J4 too high to be in agreement with the observations, and a period of at least 18 hr is needed. We see

TESTS OF COSMOGONIC THEORIES also that an I/R less than about 0.6 will require a rotation period o f less than 18 hr to m a t c h J2, and will therefore have too high a J4. I f we agree that the rotation period is either close to 16 or close to 24 hrs, then the two-shell models point to a period of 24 hr and I/R ~ 3.5. This is in disagreement with the a b u n d a n c e values resulting f r o m calculations including kinetic inhibition of chemical equilibrium in the solar nebula. The abundances of H 2 - H e , ice, and rock in the two-shell Uranus models are shown in Fig. 2. We can also consider three-shell models of Uranus. T h e s e have a core of rock surrounded by an ice shell, which is in turn surrounded b y an envelope of H 2 and H e in solar proportions, with an admixture of H20, NH3, and CH4 as in the two-shell models. The details of the physics used in the three-shell models has been described in Podolak and Reynolds (1981). The models here were c o m p u t e d in the same w a y except that the specific heat in the ice layer was taken to be 2.9°K per h e a v y particle instead of 2.2°K as had been used previously. This larger value is derived from s h o c k - w a v e e x p e r i m e n t s on water (Lyzenga et al., 1982) and should be relevant to I0

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FIG. 2. Variation of abundances of H2-He, ice, and rock for various two-shell models of Uranus.

107

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FIG. 3. Variation of J4 for three-shell Uranus models with a rotation period chosen to give a fit to ./2. The solid curves are for three-shell models with total I/R of 1.0, 2.0, and 3.6. The dashed curve is for two-shell models. The points with error bars show the observations (circles for spectroscopy, triangles for ./2 oblateness, square for photometry). The solid horizontal lines show the limits on J4. the b e h a v i o r of the ice shell on Uranus and Neptune. Figure 3 shows the results for the three-shell models. H e r e we have plotted the period at which the model will match the o b s e r v e d Jz o f Uranus against the value of J4 for that model and period. The solid horizontal lines near J4 = - 1 . 5 x 10 -5 and J4 = - 5 × 10 -5 show the region where J4 for Uranus is o b s e r v e d to lie. The lines with the error bars are the various determinations of the rotation period listed in Table I. The dashed curve shows the trajectory of the two-shell models, while the solid curves show the trajectories of the three-shell models for values o f I / R = 1.0, 2.0, and 3.6. F o r the two-shell models the value of I/R decreases along the trajectory as we m o v e upward and to the left (i.e., as the ice content of the a t m o s p h e r e decreases, a shorter rotation period is required to match J2 and ( - J 4 ) is correspondingly larger). F o r the three-shell models the fraction of ice confined to the intermediate shell increases along the trajectory as we m o v e upward and

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PODOLAK AND REYNOLDS

to the left. First we note that the three-shell models all converge to the two-shell case at the end of their trajectory. This is simply due to the fact that at this point their entire ice content has been moved into the atmosphere and the ice shell has disappeared. Second, we see that for three-shell models with I/R ~ 1.0, we require a period between 17.5 and 19.5 h, a period poorly supported by observational data. Note that since the trajectories of the three-shell models with I/ R < 0.58 have too high a value of (-J4), three-shell models with I/R < 0.58 will all remain above the region of acceptable J4. If we insist that the rotation period be near (+_ 1 hr) 16 h, we see that I/R must be 2.0 or more. On the other hand, a period of 24 h can be fit only with an I/R of close to 3.5. In such a case the ice shell will be very small, and nearly all of the ices will be in the envelope. MODELS OF N E P T U N E

For Neptune, the rotational period seems fairly well determined. Although spectroscopic measurements are difficult to perform, a number of independent photometric measurements agree to give a period of about 18 hr (Belton et al., 1981; Slavsky and Smith, 1981; Brown et al., 1981). In addition, the value of J2 seems to be fairly well determined at J2 = 0.0033 -+ 0.0003 (Harris, private communication). It is necessary to point out that the oblateness, derived from a stellar occultation and given as 0.026 +- 0.005 (Freeman and Lynga, 1970) and 0.021 -- 0.004 (Kovalevsky and Link, 1969) implies a significantly shorter period: between 11.6 and 14.7 hr in the first case, and between 13.2 and 17.0 hr in the second. It must be stressed, however, that these measurements are difficult to interpret and the photometric value is considered to be more reliable (Belton et al., 1980). Although the rotation period for Neptune is better known than for Uranus, we are hampered by the absence of an observational value for J4. Nonetheless, here too, some progress can be made. Figure 4 shows

~5

/

2.5

/

1.5

i.o

0.5

b

6

,j2x io 3

FIG. 4. Variation of J2 with 1/R for two-shell Neptune models. The vertical solid line shows the observed value for J2, the dashed lines show the uncertainty. The solid curve shows the variation for a period of 18 hr, the dashed curves show the variation for 17and 19-hr periods.

the variation of J2 as a function of I/R for two-shell models for Neptune. The solid vertical line indicates the observed value of J2; the vertical dashed lines are the uncertainties in this value. The solid curve shows the J2 variation for an assumed period of 18 hr; the dashed curves are for 17 and 19 hr. As can be seen, in no case will an I/R < 1.0 give a fit to J2, although values as low as 1.1 cannot be excluded. The maximum value allowed by the two-shell models is about 2.8. This value can be raised considerably, however, by adding an ice layer. Figure 5 shows the variation of Jz as a function of the ratio Ia/R, where Ia is the mass of iceforming material in the atmosphere. As can be seen from a comparison with Fig. 3 [and also from Fig. 1 in Podolak and Reynolds (1981)] the atmospheric ice content is not very dependent on the presence or absence of an ice shell for J2 in the range of the observed value. For this reason we have

TESTS OF COSMOGONIC THEORIES I 3.5

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2

3

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not run intermediate cases of the three-shell models, such as, for example, I/R = 2.0. We see that for the Neptune models, a ratio I/R as low as 0.5 is unacceptable, although, as far as the models are concerned, any value between about 1.2 and 3.6 can fit the available data. CONCLUSIONS AND SPECULATIONS

The first conclusion is that the kinetic inhibition mechanism envisioned by Lewis and Prinn (1980) does not seem, in its present form, to provide an explanation for the I/R values of Uranus or Neptune. This ratio can be explained in the context of an accretion theory, provided that most of the carbon is in the form of CH4 and most of the oxygen is in the form of H20, so that sufficient quantities of these elements can be accreted relative to the rocky materials. A theory based on the formation of giant gaseous protoplanets will provide a ratio greater than about two. This is certainly consistent with the value derived from our models, although the Neptune models al-

109

low for a somewhat smaller value as well. A second conclusion is that the two-shell models for Uranus and a rotation period of less than - 1 8 hr are mutually inconsistent. By excluding the possibility of I/R being as low as 0.5, we have now returned to the difficulty of explaining the apparent absence of NH3 in the upper atmosphere of Uranus and Neptune. If the material was in equilibrium, large amounts of nitrogen relative to sulfur would have been accreted as NH3 ice. If this nitrogen is still in the planet, why do we not see it in the upper atmosphere. Stevenson (1982) has suggested that NH3 and H20 might be soluble in hydrogen at higher pressures, and settle into an ionic " o c e a n " (similar to our ice shell) composed of H3O+, NH4 ÷, and OH-. To bring the nitrogen abundance down low enough so that the remaining NH3 will combine with H2S to form NH4SH, the ocean will have to contain about 80% of the planet's nitrogen, a value that cannot by any means be excluded by our models.~ A second objection to the accretion scenario is that of the deuterium-to-hydrogen ratio, which should be considerably higher than the observed value, if low-temperature equilibrium ratios were achieved for the ices. It is difficult to see how such deuterium could be kept hidden in the deeper layers of the planet so as to make it unobservable. Giant protoplanet theories can deal with the low ammonia and deuterium abundance problems by assuming the following scenario. Since nitrogen is likely to be converted in the inner regions of the protoplanet to N2, and N2 will be kinetically inhibited from forming NH3, most of the nitrogen will be in the form of N2. With its low vapor pressure N2 will pass through the cold trap and back into the solar nebula. J An anonymous referee has pointed out that the absence of NH3 may simply be due to the reduced vapor pressure due to NH3-H20 cloud formation. Although one cannot say for sure until detailed models are computed, it is possible that the problem of an underabundance o f NH3 may be only apparent.

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Thus, the loss mechanism for hydrogen and helium will also operate for nitrogen with the result that the N/S ratio will be much less than 5. Indeed most of the Uranus models have about 2.5-3.0 earth masses of hydrogen and helium. This is about onefifth the amount expected on the basis of a comparison with Jupiter. Reducing the nitrogen abundance by a similar amount will give N/S = I, allowing the complete conversion of ammonia into NH4SH. Finally, since the original protoplanet had a solar ratio of deuterium to hydrogen, and temperatures of several hundred degrees were reached fairly rapidly in the interior, the ices would have reequilibrated at these higher temperatures, and a solar D/H ratio would have been retained. To conclude, more work is certainly needed. The details of the interaction of hydrogen and ices at high pressures must be investigated. If, as Stevenson (1982) suggests, the water and hydrogen are immiscible, this would help us to eliminate some candidates for Uranus and Neptune interiors. The rotation rate of Uranus remains a critical parameter in this analysis, as does J4 for both Uranus and Neptune. It is hoped that the determination of these quantities with greater precision in the near future, as well as improvements in the physics of the interior models will give us stronger constraints on theories of the origin of the solar system. ACKNOWLEDGMENTS We thank Professor A. Bar-Nun, Professor A. G. W. Cameron, and Professor Yu. Mekler for helpful discussions. This work was supported by NASA Grant NCA 2-OR-340-002.

REFERENCES ALFVEN, H., AND G. ARRHENIUS (1975). Structure and Evolutionary History o f the Solar System. Reidel, Dordrecht. BAR-NUN, A. (1983). The conversion of CO to hydrocarbons and its implications for Jupiter, the primitive solar nebula and the satellites of the giant planets. Preprint.

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