Comparative thermal evolution of Uranus and Neptune

We extend a Jovian convective-cooling model to Uranus and Neptune. The model assumes that efficient interior convection prevails, so that escape of interior heat is governed by the radiative properties of the atmosphere. A comparison of the thermal evolution of Uranus and Neptune indicates that the larger amount of solar radiation absorbed in Uranus' atmosphere tends to differentially suppress the escape of interior heat. The model is shown to be consistent with recent infrared observations of the thermal balance of Uranus and Neptune, and with the presumed age of these planets.     

Some dynamical aspects of the accretion of Uranus and Neptune: The exchange of orbital angular momentum with planetesimals

The final stage of the accretion of Uranus and Neptune is numerically investigated. The four Jovian planets are considered with Jupiter and Saturn assumed to have reached their present sizes, whereas Uranus and Neptune are taken with initial masses 0.2 of their present ones. Allowance is made for the orbital variation of the Jovian planets due to the exchange of angular momentum with interacting bodies (“planetesimals”). Two possible effects that may have contributed to the accretion of Uranus and Neptune are incorporated in our model: (1) an enlarged cross section for accretion of incoming planetesimals due to the presence of extended gaseous envelopes and/or circumplanetary swarms of bodies; and (2) intermediate protoplanets in mid-range orbits between the Jovian planets. Significant radial displacements are found for Uranus and Neptune during their accretion and scattering of planetesimals. The orbital angular momentum budgets of Neptune, Uranus, and Saturn turn out to be positive; i.e., they on average gain orbital angular momentum in their interactions with planetesimals and hence they are displaced outwardly. Instead, Jupiter as the main ejector of bodies loses orbital angular momentum so it moves sunward. The gravitational stirring of planetesimals caused by the introduction of intermediate protoplanets has the effect that additional solid matter is injected into the accretion zones of Uranus and Neptune. For moderate enlargements of the radius of the accretion cross section (2–4 times), the accretion time scale of Uranus and Neptune are found to be a few 10⁸ years and the initial amount of solid material required to form them of a few times their present masses. Given the crucial role played by the size of the accretion cross section, questions as to when Uranus and Neptune acquired their gaseous envelopes, when the envelopes collapsed onto the solid cores, and how massive they were are essential in defining the efficiency and time scale of accretion of the two outer Jovian planets.     

The chemical atmospheric composition of the giant planets

For a long time it was believed that the atmospheres of the giant planets, dominated by molecular hydrogen and helium, were similar in composition to the primordial nebula from which they formed. However, this image has strongly evolved over the past twenty years, due to new developments of ground-based infrared spectroscopy, coupled with the success of the Voyager space mission.Significant differences were measured in the abundances of helium, deuterium and carbon of the four giant planets. The variations in the C/H and D/H ratios have given support to the "nucleation" formation scenario, in which the four giant planets first accreted a nucleus of about ten terrestrial masses, big enough to bind gravitationally the surrounding gaseous nebula; the helium depletion in Saturn has been interpreted as a differentiation effect in Saturn's interior; the apparent helium excess in Neptune, coupled with the recent unexpected detection of CO and HCN in this planet, might imply the presence of molecular nitrogen. In the case of Jupiter and Saturn, disequilibrium species have been detected (CO, PH₃, GeH₄, AsH₃), which are tracers of vertical dynamical motions.In the future, significant progress in our knowledge of the Jovian composition, including the noble gases, should be obtained with the mass spectrometer of the Galileo probe. The ISO mission is expected to provide new far-infrared spectroscopic data which should lead to the detection of new minor species and a better determination of the D/H ratio.     

Uranus and Neptune interior models

This paper is concerned with the interior structure of Uranus and Neptune. Our approach is three-fold. First, a set of three-layer models for both Uranus and Neptune are constructed using a method similar to that used in the study of the terrestrial planets. The variations of the mass density (s) and flattening e(s) with fractional mean radius s for two representative models of Uranus and Neptune are calculated. The results are tabulated. A comparison of these models shows that these two planets are probably very similar to each other in their basic dynamical features. Such similarity is very seldom seen in our solar system. Secondly, we check the conformance between the theoretical results and observational data for the two planets. And thirdly, the 6th degree Stokes zonal parameters for Uranus and for Neptune are predicted, based on the interior models put forward in this paper.     

Five-micrometer measurements of Uranus and Neptune

We have obtained 5-μm brightness temperatures and brightness temperature upper limits for Uranus and Neptune which are substantially lower than those of Jupiter and Saturn and which correspond to a geometric albedo of approximately 0.01, in agreement with results reported by F. C. Gillet and G. H. Rieke (1977, Astrophys. J.218, L141–L144). Phospine and CH₃D, which are observed at 5 μm on Jupiter and Saturn, are discussed as possible sources of opacity at 5 μm in the atmospheres of Uranus and Neptune.     

Infrared radiometry of Uranus and Neptune at 21 and 32 μm

Radiometric measurement of Uranus and Neptune near 21 and 32 μm have been made with filters with widths of 8 and 5 μm, respectively. The observations at 21 μm, made on 1985 June 19 at the NASA Infrared telescope facility at Mauna Kea, Hawaii, were calibrated against α Boo and corresponded to brightness temperatures of 54.1 ± 0.3 K for Uranus and 58.1 ± 0.3 K for Neptune. The observations at 32 μm were made on three nights: 1983 May 1 and 1984 May 30 and 31, also at the NASA IRTF. Calibrated against the Jovian satellites Callisto (J4) and Ganymede (J3), these measurements corresponded to brightness temperatures of 51.8 ± 1.5 K for Uranus and 55.6 ± 1.2 K for Neptune. The observations are consistent with higher-resolution studies and confirm the general decrease of brightness temperatures going from about 20 to 30 μm.     

Uranus and Neptune: Shape and rotation

Both Uranus and Neptune are thought to have strong zonal winds with velocities of several 100 m s⁻¹. These wind velocities, however, assume solid-body rotation periods based on Voyager 2 measurements of periodic variations in the planets’ radio signals and of fits to the planets’ magnetic fields; 17.24 h and 16.11 h for Uranus and Neptune, respectively. The realization that the radio period of Saturn does not represent the planet’s deep interior rotation and the complexity of the magnetic fields of Uranus and Neptune raise the possibility that the Voyager 2 radio and magnetic periods might not represent the deep interior rotation periods of the ice giants. Moreover, if there is deep differential rotation within Uranus and Neptune no single solid-body rotation period could characterize the bulk rotation of the planets. We use wind and shape data to investigate the rotation of Uranus and Neptune. The shapes (flattening) of the ice giants are not measured, but only inferred from atmospheric wind speeds and radio occultation measurements at a single latitude. The inferred oblateness values of Uranus and Neptune do not correspond to bodies rotating with the Voyager rotation periods. Minimization of wind velocities or dynamic heights of the 1 bar isosurfaces, constrained by the single occultation radii and gravitational coefficients of the planets, leads to solid-body rotation periods of ∼16.58 h for Uranus and ∼17.46 h for Neptune. Uranus might be rotating faster and Neptune slower than Voyager rotation speeds. We derive shapes for the planets based on these rotation rates. Wind velocities with respect to these rotation periods are essentially identical on Uranus and Neptune and wind speeds are slower than previously thought. Alternatively, if we interpret wind measurements in terms of differential rotation on cylinders there are essentially no residual atmospheric winds.     

The formation of Uranus and Neptune in solid-rich feeding zones: Connecting chemistry and dynamics

The core accretion theory of planet formation has at least two fundamental problems explaining the origins of Uranus and Neptune: (1) dynamical times in the trans-saturnian solar nebula are so long that core growth can take >15 Myr and (2) the onset of runaway gas accretion that begins when cores reach ∼10M_⊕ necessitates a sudden gas accretion cutoff just as Uranus and Neptune’s cores reach critical mass. Both problems may be resolved by allowing the ice giants to migrate outward after their formation in solid-rich feeding zones with planetesimal surface densities well above the minimum-mass solar nebula. We present new simulations of the formation of Uranus and Neptune in the solid-rich disk of Dodson-Robinson et al. (Dodson-Robinson, S.E., Willacy, K., Bodenheimer, P., Turner, N.J., Beichman, C.A. [2009]. Icarus 200, 672-693) using the initial semimajor axis distribution of the Nice model (Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A. [2005]. Nature 435, 466-469; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R. [2005]. Nature 435, 462-465; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F. [2005]. Nature 435, 459-461), with one ice giant forming at 12 AU and the other at 15 AU. The innermost ice giant reaches its present mass after 3.8-4.0 Myr and the outermost after 5.3-6 Myr, a considerable time decrease from previous one-dimensional simulations (e.g. Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak, M., Greenzweig, Y. [1996]. Icarus 124, 62-85). The core masses stay subcritical, eliminating the need for a sudden gas accretion cutoff.Our calculated carbon mass fractions of 22% are in excellent agreement with the ice giant interior models of Podolak et al. (Podolak, M., Weizman, A., Marley, M. [1995]. Planet. Space Sci. 43, 1517-1522) and Marley et al. (Marley, M.S., Gómez, P., Podolak, M. [1995]. J. Geophys. Res. 100, 23349-23354). Based on the requirement that the ice giant-forming planetesimals contain >10% mass fractions of methane ice, we can reject any Solar System formation model that initially places Uranus and Neptune inside of Saturn’s orbit. We also demonstrate that a large population of planetesimals must be present in both ice giant feeding zones throughout the lifetime of the gaseous nebula. This research marks a substantial step forward in connecting both the dynamical and chemical aspects of planet formation. Although we cannot say that the solid-rich solar nebula model of Dodson-Robinson et al. (Dodson-Robinson, S.E., Willacy, K., Bodenheimer, P., Turner, N.J., Beichman, C.A. [2009]. Icarus 200, 672-693) gives exactly the appropriate initial conditions for planet formation, rigorous chemical and dynamical tests have at least revealed it to be a viable model of the early Solar System.     

The phase diagram of water and the magnetic fields of Uranus and Neptune

The interior of giant planets can give valuable information on formation and evolution processes of planetary systems. However, the interior and evolution of Uranus and Neptune is still largely unknown. In this paper, we compare water-rich three-layer structure models of these planets with predictions of shell structures derived from magnetic field models. Uranus and Neptune have unusual non-dipolar magnetic fields contrary to that of the Earth. Extensive three-dimensional simulations of Stanley and Bloxham (Stanley, S., Bloxham, J. [2004]. Nature 428, 151-153) have indicated that such a magnetic field is generated in a rather thin shell of at most 0.3 planetary radii located below the H/He rich outer envelope and a conducting core that is fluid but stably stratified. Interior models rely on equation of state data for the planetary materials which have usually considerable uncertainties in the high-pressure domain. We present interior models for Uranus and Neptune that are based on ab initio equation of state data for hydrogen, helium, and water as the representative of all heavier elements or ices. Based on a detailed high-pressure phase diagram of water we can specify the region where superionic water should occur in the inner envelope. This superionic region correlates well with the location of the stably-stratified region as found in the dynamo models. Hence we suggest a significant impact of the phase diagram of water on the generation of the magnetic fields in Uranus and Neptune.     

Generation of equatorial jets by large-scale latent heating on the giant planets

Three-dimensional numerical simulations show that large-scale latent heating resulting from condensation of water vapor can produce multiple zonal jets similar to those on the gas giants (Jupiter and Saturn) and ice giants (Uranus and Neptune). For plausible water abundances (3-5 times solar on Jupiter/Saturn and 30 times solar on Uranus/Neptune), our simulations produce ∼20 zonal jets for Jupiter and Saturn and 3 zonal jets on Uranus and Neptune, similar to the number of jets observed on these planets. Moreover, these Jupiter/Saturn cases produce equatorial superrotation whereas the Uranus/Neptune cases produce equatorial subrotation, consistent with the observed equatorial-jet direction on these planets. Sensitivity tests show that water abundance, planetary rotation rate, and planetary radius are all controlling factors, with water playing the most important role; modest water abundances, large planetary radii, and fast rotation rates favor equatorial superrotation, whereas large water abundances favor equatorial subrotation regardless of the planetary radius and rotation rate. Given the larger radii, faster rotation rates, and probable lower water abundances of Jupiter and Saturn relative to Uranus and Neptune, our simulations therefore provide a possible mechanism for the existence of equatorial superrotation on Jupiter and Saturn and the lack of superrotation on Uranus and Neptune. Nevertheless, Saturn poses a possible difficulty, as our simulations were unable to explain the unusually high speed (∼) of that planet’s superrotating jet. The zonal jets in our simulations exhibit modest violations of the barotropic and Charney-Stern stability criteria. Overall, our simulations, while idealized, support the idea that latent heating plays an important role in generating the jets on the giant planets.     

Enrichment in volatiles in the giant planets of the Solar System

We propose an interpretation of the enrichments in volatiles observed in the four giant planets with respect to the solar abundance. It is based on the assumption that volatiles were trapped in the form of solid clathrate hydrates and incorporated in planetesimals embedded in the feeding zones of each of the four giant planets. The mass of trapped volatiles is then held constant with time. The mass of hydrogen and of not trapped gaseous species continuously decreased with time until the formation of the planet was completed, resulting in an increase in the ratio of the mass of trapped volatiles to the mass of hydrogen (Gautier et al., Astrophys. J. 550 (2001) L227). The efficiency of the clathration depends upon the amount of ice available in the early feeding zone. The quasi-uniform enrichment in Ar, Kr, Xe, C, N, and S observed in Jupiter is reproduced because all volatiles were trapped. The non-uniform enrichment observed in C, N and S in Saturn is due to the fact that CH₄, NH₃, and H₂S were trapped but not CO and N₂. The non-uniform enrichment in C, N and S in Uranus and Neptune results from the trapping of CH₄, CO, NH₃ and H₂S, while N₂ was not trapped. Our scenario permits us to interpret the strongly oversolar sulfur abundance inferred by various modelers to be present in Saturn, Uranus and Neptune for reproducing the microwave spectra of the three planets. Abundances of Ar, Kr and Xe in these three are also predicted. Only Xe is expected to be substantially oversolar. The large enrichment in oxygen in Neptune with respect to the solar abundance, calculated by Lodders and Fegley (Icarus 112 (1994) 368) from the detection of CO in the upper troposphere of the planet, is consistent with the trapping of volatiles by clathration. The upper limit of CO in Uranus does not exclude that this process also occurred in Uranus.     

The rotational periods of Uranus and Neptune

Observations of tilts of spectral lines in the spectrum of Uranus and Neptune yield the following rotational periods: “Uranus,” 24 ± 3 hr; “Neptune,” 22 ± 4 hr. Neptune is confirmed to rotate in a direct sense. The position angle of the pole of Uranus, projected onto the plane of the sky, is found to be 283 ± 4°. The value for Neptune is 32 ± 11°. These results agree with the direction of the pole of Uranus inferred from the common plane of its four brightest satellites and with the direction of the pole of Neptune as inferred from the precession of Triton's orbit. The rotational period of Uranus is found to be consistent with modern values of its optical and dynamical oblateness and the theory of solid-body rotation with hydrostatic equilibrium. This is barely the case for the period derived for Neptune and we suspect that future observations made under better seeing conditions may lead to a shorter rotation period between 15 and 18 hr. Because of a substantial difference between our results and those of earlier spectroscopic and photometric investigations we include an assessment of several previously published photometric studies and a new reduction of the original Lowell and Slipher spectroscopic plates of Uranus [Lowell Obs. Bull. 2, 17–18, 19–20 (1912)]. The early visual photometry of Campbell (Uranus) and Hall (Neptune) is found to be more satisfactorily accounted for by periods of 21.6 and 23.1 hr, respectively, than by the periods originally suggested by the observers. Our reduction of the Lowell and Slipher Uranus plates yields a period near 33 hr uncorrected for seeing. This value is consistent with the results based on the 4-m echelle date.     

Embedded star clusters and the formation of the Oort cloud: II. The effect of the primordial solar nebula

This paper deals with Oort cloud formation while the Sun was in an embedded cluster and surrounded by its primordial nebula. This work is a continuation of Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82], building on the model presented therein, and adding the aerodynamic drag and gravitational potential of the primordial solar nebula. Results are presented of numerical simulations of comets subject to the gravitational influence of the Sun, Jupiter, Saturn, star cluster and primordial solar nebula; some of the simulations included the gravitational influence of Uranus and Neptune as well. The primordial solar nebula was approximated by the minimum-mass Hayashi model [Hayashi, C., Nakozawa, K., Nakagawa, Y., 1985. In: Black, D.C., Matthews, M.S. (Eds.). Protostars and Planets II. Univ. of Arizona Press, Tucson, AZ] whose inner and outer radii have been truncated at various distances from the Sun. A comet size of 1.7 km was used for most of our simulations. In all of our simulations, the density of the primordial solar nebula decayed exponentially with an e-folding time of 2 Myr. It turns out that when the primordial solar nebula extends much beyond Saturn or Neptune, virtually no material will end up in the Oort cloud (OC) during this phase. Instead, the majority of the material will be on circular orbits inside of Jupiter if the inner edge of the disk is well inside Jupiter's orbit. If the disk's inner edge is beyond Jupiter's orbit, most comets end up on orbits in exterior mean-motion resonances with Saturn when Uranus and Neptune are not present. In those cases where the outer edge of the disk is close to Saturn or Neptune, the fraction of material that ends up in the subsequently formed OC is much less than that found in Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82] for the same cluster densities. This implies that for comets of roughly 2 km in size, the presence of the primordial solar nebula hinders OC formation. A byproduct of some of our simulations are endresults with a substantial fraction of the comets in the Uranus-Neptune scattered disk. A subsequent followup of this material is planned for the near future. In order to determine the effect of the size of the comets on OC formation efficiency, a set of runs with the same initial conditions but different cometary radii have been performed as well, from which it is determined that the threshold comet size to begin producing significant Oort clouds is roughly 20 km. This implies that the presence of the primordial solar nebula acts as a size-sorting mechanism, with large bodies unaffected by the gas drag and ending up in the OC while small bodies remain trapped in the planetary region, in the models studied.     

Evidence for Planetary Forcing of the Cosmic Ray Intensity and Solar Activity Throughout the Past 9400 Years

Paleo-cosmic-ray (PCR) records based on cosmogenic ¹⁰Be and ¹⁴C data are used to study the variations in cosmic-ray intensity and solar activity over the past 9400 years. There are four strong correlations with the motion of the Jovian planets; the probability of occurring by chance being <?10^?5. They are i) the PCR periodicities at 87, 350, 510, and 710 years, which closely approximate integer multiples of half the Uranus–Neptune synodic period; ii) eight periodicities in the torques calculated to be exerted by the planets on an asymmetric tachocline that approximate the periods observed in the PCR; iii) the maxima of the long-term PCR variations are coincident with syzygy (alignment) of the four Jovian planets in 5272 and 644 BP; and iv) in the time domain, the PCR intensity decreases during the first 60 years of the ≈?172 year Jose cycle (Jose, Astron. J. 70, 193, 1965) and increases in the remaining ≈?112 years in association with barycentric anomalies in the distance between the Sun and the center of mass of the solar system. Furthermore, sunspot and neutron-monitor data show that three anomalous sunspot cycles (4th, 7th, and 20th) and the long sunspot minimum of 2006 – 2009 CE coincided with the first and second barycentric anomalies of the 58th and 59th Jose cycles. Phase lags between the planetary and heliospheric effects are ≤?five years. The 20 largest Grand Minima during the past 9400 years coincided with the latter half of the Jose cycle in which they occurred. These correlations are not of terrestrial origin, nor are they due to the planets’ contributing directly to the cosmic-ray modulation process in the heliosphere. Low cosmic-ray intensity (higher solar activity) occurred when Uranus and Neptune were in superior conjunction (mutual cancellation), while high intensities occurred when Uranus–Neptune were in inferior conjunction (additive effects). Many of the prominent peaks in the PCR Fourier spectrum can be explained in terms of the Jose cycle, and the occurrence of barycentric anomalies.     

Consistency tests of cosmogonic theories from models of Uranus and Neptune

The planetary ratios of ice to rock $\text{(}\text{I}\text{R}\text{)}$ abundances expected in Uranus and Neptune are derived on the basis of several cosmogonic theories. For both Uranus and Neptune the value of $\text{I}\text{R}$ 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 N₂ and CO. It is consistent with some versions of both giant protoplanet theories and equilibrium accretion theories.     

Source regions and timescales for the delivery of water to the Earth

Abstract— In the primordial solar system, the most plausible sources of the water accreted by the Earth were in the outer asteroid belt, in the giant planet regions, and in the Kuiper Belt. We investigate the implications on the origin of Earth's water of dynamical models of primordial evolution of solar system bodies and check them with respect to chemical constraints. We find that it is plausible that the Earth accreted water all along its formation, from the early phases when the solar nebula was still present to the late stages of gas‐free sweepup of scattered planetesimals. Asteroids and the comets from the Jupiter‐Saturn region were the first water deliverers, when the Earth was less than half its present mass. The bulk of the water presently on Earth was carried by a few planetary embryos, originally formed in the outer asteroid belt and accreted by the Earth at the final stage of its formation. Finally, a late veneer, accounting for at most 10% of the present water mass, occurred due to comets from the Uranus‐Neptune region and from the Kuiper Belt. The net result of accretion from these several reservoirs is that the water on Earth had essentially the D/H ratio typical of the water condensed in the outer asteroid belt. This is in agreement with the observation that the D/H ratio in the oceans is very close to the mean value of the D/H ratio of the water inclusions in carbonaceous chondrites.     

Observations of Ganymede,Callisto, Ceres,Uranus, and Neptune at 3.33 mm wavelength

We have measured the 3.33 mm wavelength disk brightness temperatures of Ganymede (136 ± 21°K), Callisto (95 ± 17°K), Ceres (137 ± 25°K), Uranus (125 ± 9°K), and Neptune (126 ± 9°K). Our observations of Ganymede are consistent with the radiation from a blackbody in solar equilibrium, whereas Callisto's microwave spectrum indicates a surface similar to that of the Moon. The disk temperature for Ceres agrees with that expected from a rapidly rotating blackbody. The millimeter temperatures of Uranus and Neptune greatly exceed solar equilibrium values, implying atmospheres with large temperature gradients.     

On the DC ratio in the atmosphere of Uranus

A method for deriving mixing ratios in the outer planets, mostly independent of scattering processes, is applied to Uranus. It is shown that scattering processes play a major role in the line formation in the atmospheres of Uranus and Neptune; consequently, abundance ratios derived from a reflecting-layer model can be questionable. Using our method, we derive for Uranus $\text{D}\text{C}\text{< 6 × 10}{}^{\mathrm{?3}}$, which is significantly smaller than our result on Jupiter. The simplest explanation implies a C/H enrichment by at least a factor of 6 relative to the solar value.     

New observational constraints on the temperature inversions of Uranus and Neptune

We present 20-μm photometry of Uranus and Neptune which confirms the presence of a temperature inversion in the lower stratospheres in both planets. We find the brightness temperature difference between 17.8 and 19.6 μm to be 0.8 ± 0.5°K for Uranus and 1.8 ± 0.6°K for Neptune. These results indicate that the temperature inversions on both planets are weaker than previously thought. Comparison to model atmospheres by J. Appleby [Ph.D. thesis, SUNY at Stony Brook 1980] indicates that the temperature inversions can be understood as arising from heating by the absorption of sunlight by CH₄ and aerosols. However, the stratospheric CH₄ mixing ratio on Neptune must be higher than that at the temperature minimum.     

Liquid water oceans in ice giants

Aptly named, ice giants such as Uranus and Neptune contain significant amounts of water. While this water cannot be present near the cloud tops, it must be abundant in the deep interior. We investigate the likelihood of a liquid water ocean existing in the hydrogen-rich region between the cloud tops and deep interior. Starting from an assumed temperature at a given upper tropospheric pressure (the photosphere), we follow a moist adiabat downward. The mixing ratio of water to hydrogen in the gas phase is small in the photosphere and increases with depth. The mixing ratio in the condensed phase is near unity in the photosphere and decreases with depth; this gives two possible outcomes. If at some pressure level the mixing ratio of water in the gas phase is equal to that in the deep interior, then that level is the cloud base. The gas below the cloud base has constant mixing ratio. Alternately, if the mixing ratio of water in the condensed phase reaches that in the deep interior, then the surface of a liquid ocean will occur. Below this ocean surface, the mixing ratio of water will be constant. A cloud base occurs when the photospheric temperature is high. For a family of ice giants with different photospheric temperatures, the cooler ice giants will have warmer cloud bases. For an ice giant with a cool enough photospheric temperature, the cloud base will exist at the critical temperature. For still cooler ice giants, ocean surfaces will result. A high mixing ratio of water in the deep interior favors a liquid ocean. We find that Neptune is both too warm (photospheric temperature too high) and too dry (mixing ratio of water in the deep interior too low) for liquid oceans to exist at present. To have a liquid ocean, Neptune's deep interior water to gas ratio would have to be higher than current models allow, and the density at 19 kbar would have to be ≈0.8 g/cm³. Such a high density is inconsistent with gravitational data obtained during the Voyager flyby. In our model, Neptune's water cloud base occurs around 660 K and 11 kbar, and the density there is consistent with Voyager gravitational data. As Neptune cools, the probability of a liquid ocean increases. Extrasolar “hot Neptunes,” which presumably migrate inward toward their parent stars, cannot harbor liquid water oceans unless they have lost almost all of the hydrogen and helium from their deep interiors.