Numerical dynamo models of Uranus' and Neptune's magnetic fields

The non-axisymmetric, non-dipolar magnetic fields of Uranus and Neptune are markedly different from the axially-dipolar dominated fields of the other planets in our Solar System with active dynamos. Stanley and Bloxham [Stanley, S., Bloxham, J., 2004. Nature 428, 151-153] used numerical modeling to demonstrate that Uranus' and Neptune's unusual fields could be the result of a different convective region geometry in these planets. They found that a numerical dynamo operating in a thin shell surrounding a stably-stratified fluid interior produces magnetic field morphologies similar to those of Uranus and Neptune. This geometry for the convective region was initially proposed by Hubbard et al. [Hubbard, W.B., Podolak, M., Stevenson, D.J., 1995. In: Cruickshank, D. (Ed.), Neptune and Triton. Univ. of Arizona Press, Tucson, pp. 109-138] to explain both the magnetic field morphology as well as the low intrinsic heat flows from these planets. Here we examine the influence of varying the stable layer radius in numerical models and compare the results to thin shell models surrounding solid inner cores. We find that a limited range of stable-layer shell thicknesses exist in which Uranus/Neptune-like field morphologies result. This allows us to put constraints on the size of the convective layers in Uranus and Neptune.     

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.     

Laboratory planetary physics using intense heavy ion beams at the Facility for Antiprotons and Ion Research at Darmstadt: the HEDgeHOB collaboration

Development of ultra-high power lasers has lead to the very interesting and important field of Laboratory Astrophysics. Recent progress and expected near future developments in the technology of strongly bunched intense particle beams has opened up the possibility of studying planetary interiors in the laboratory which hopefully will eventually converge in the new field of Laboratory Planetary Physics. GSI Helmholzzentrum für Schwerionenforschung, Darmstadt is a well known laboratory worldwide due to its unique particle accelerator facilities. Construction of the new huge accelerator complex, the Facility for Antiprotons and Ion Research (FAIR), will substantially improve the existing capabilities of the GSI. A dedicated program named, HEDgeHOB, that aims to study different problems in High Energy Density (HED) Physics at the FAIR facility, has been proposed. One of these proposed experiments LAPLAS (LAboratory PLAnetary Science), aim to study materials at extreme conditions as relevant for the interiors of giant planets. In this paper we present simulation results that show that various regions of the high-pressure phase diagram of water can be probed within the LAPLAS experiments. For instance, the plasma and the superionic phase are predicted to occur in the interior of water-rich planets such as Uranus and Neptune as well as in extrasolar planets such as GJ 436b.     

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.     

试论行星磁场强度分布的成因

行星磁场强度的分布具有规律性,中间巨行星的强度值大,两侧类地行星和远日行星的强度值小。在类地行星和远日行星中,也是中间行星磁场强度值大,如地球和海王星。两侧行星磁场强度值小,如金星、火星、天王星和冥王星。水星磁场强度值比金星大是因为水星环较早的从A组星云环中分裂出来所致。行星磁场强度大小分布的规律性与星云环级式分裂、环体物质中聚即铁磁性物质较快中聚的规律性一致。所以,铁磁性物质多少,可能是行星磁场强度大小分布的一个主要原因。     

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.     

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.     

Comparative models of Uranus and Neptune

Models of Uranus and Neptune are computed based on the assumption that these planets consist of three layers: a rock core, an ice shell, and an atmosphere. Uranus models require that the ice shell have a density some 10% lower than the canonical density for an ice mixture. Two Neptune models are found, one with the canonical density in the ice shell, and one with a density 20% lower. The implications of these models are discussed.     

Dynamical evolution of a cometary swarm in the outer planetary region

The dynamical evolution of bodies under the gravitational influence of the accreting proto-Uranus and proto-Neptune is investigated. The main aim of this study is to analyze the interrelations between the accretion of Uranus and Neptune with other processes of cosmological importance as, for example, the formation of a cometary reservoir from bodies placed into near-parabolic orbits by planetary perturbations and the scattering of bodies to the region of the terrestrial planets. Starting with a mass ratio (initial mass/present mass) of 0.1, Uranus and Neptune acquire masses close to their present ones in a time scale of 10⁸ years. Neptune is found to be the most important contributor of comets to the cometary reservoir. The time scale of bodies scattered by Neptune to reach near-parabolic orbits (semimajor axes a > 10⁴ AU)is about 10⁹ years. The contribution of Uranus was partially inhibited because a large part of the residual bodies of its accretion zone fell under the strong gravitational influence of Jupiter and Saturn. A significant fraction of the bodies dispersed by Uranus and Neptune reached the region of the terrestrial planets in a time scale of some 10⁸ years.     

The internal structures and the relative rotation rates of Uranus and Neptune

The difference between the interior structures of Uranus and Neptune is presented, based on models which fit the observed mass, radius, and gravitational moments for the assumed rotation periods of these planets. If Uranus and Neptune are assumed to be as similar in internal structure as they are in mass and radius, the rotation period for Neptune must be shorter than that for Uranus. It is suggested that the true rotation period is given by Neptune's oblateness, while the photometric period corresponds to the motion of Rossby waves in the upper atmosphere.     

The web of three-planet resonances in the outer Solar System: II. A source of orbital instability for Uranus and Neptune

The motion of the giant planets from Jupiter to Neptune is chaotic with Lyapunov time of approximately 10 Myr. A recent theory explains the presence of this chaos with three-planet mean-motion resonances, i.e. resonances among the orbital periods of at least three planets. We find that the distribution of these resonances with respect to the semi-major axes of all the planets is compatible with orbital instability. In particular, they overlap in a region of 10⁻³ AU with respect to the variation of the semi-major axes of Uranus and Neptune. Fictitious planetary systems with initial conditions in this region can undergo systematic variations of semi-major axes. The true Solar System is marginally in this region, and Uranus and Neptune undergo very slow systematic variations of semi-major axes with speed of order 10⁻⁴ AU/Gyr.     

The formation of the outer planets

One of the outstanding problems in planetary cosmogony is to account for the depletion of hydrogen in the outer planets, Neptune and Uranus. It is suggested that these planets were originally similar to the major planets but that the settling towards the centre of grains, enriched by substances such as methane, ammonia and water because of the low temperatures, released enough energy to cause the evaporation of most of the hydrogen.     

Can magnetic fields be generated in the icy mantles of Uranus and Neptune?

It has been shown by us previously that a hydromagnetic dynamo can operate in the core of Uranus but probably not on Neptune. A similar analysis is made for the “icy” liquid mantles of both planets. It is concluded that pressure ionization and the associated increased conductivity of water is probably not enough to satisfy the necessary conditions for a dynamo on Uranus and that it is marginal for Neptune. On the other hand the expected presence of metallic water in a thick layer around the core of Neptune makes the operation of a dynamo on this planet plausible. A similar layer on Uranus might be too thin to play the same role. It appears that if a magnetic field is indeed present on Uranus it is probably generated in the core of the planet, while on Neptune it is more likely operating in the icy mantle.     

Theoretical predictions of deuterium abundances in the Jovian planets

Using current concepts for the origin of the Jovian planets and current constraints on their interior structure, we argue that the presence of large amounts of “ice” (H₂O, CH₄, and NH₃) in Uranus and Neptune indicates temperatures low enough to condense these species at the time Uranus and Neptune formed. Yet such low temperatures imply orders-of-magnetude fractionation effects for deuterium into the “ice” component if isotopic equilibration can occur. Our models thus imply that Uranus and Neptune should have a D/H ratio at least four times primordial, contrary to observation for Uranus. We find that the Jovian and Saturnian D/H should be close to primordial regardless of formation scenario. The Uranus anomaly could indicate that there was a strong initial radial gradient in D/H in the primordial solar nebula, or that Uranus is so inactive that no significant mixing of its interior has occurred over the age of the solar system. Observation of Neptune's atmospheric D/H may help to resolve the problem.     

Atmospheric thermal structures of the giant planets

Thermal models of planetary atmospheres can be calculated from assumptions of the energy budget of the atmosphere and from the knowledge of the effective temperature of the studied planet. On the other hand, the retrieval of the thermal atmospheric profiles from infrared measurements by means of the numerical inversion of the radiative transfer equation presents the advantages of not requiring such assumptions. The extent of the atmospheric range which can then be sounded is examined and the vertical resolution of the inferred profiles is discussed. Comparisons of thermal models and retrieved thermal profiles are made for the four giant planets. The retrieved profiles lead to brightness temperature spectra which fit all the available infrared measurements fairly well for Jupiter and Saturn but only part of them for Uranus and Neptune. The values of the planetary effective temperatures calculated from the retrieved profiles show that Jupiter, Saturn, and Neptune have strong internal heating sources while Uranus probably has a very small or null one.     

Analysis of photometric variations of Uranus and Neptune since 1953

Photoelectric photometry of Uranus and Neptune, obtained between 1953 and 1976, has been analyzed for evidence of planetary variability on various time scales. There is no evidence for either periodic or secular variability at a level of 0.003 mag or greater over intervals of a few months or less, but slow variations of several hundredths of a magnitude have occured for both planets over many years. Variations at the 0.001 mag level may be present on shorter time scales. Solar phase coefficients for both planets are much larger than predicted for clear molecular atmospheres, and the coefficient for Neptune is significantly variable. The lightcurve of Uranus is consistent with a geometrical oblateness of about 0.03, or polar brightening. While the annual mean magnitudes of the planets are highly correlated with one another, no direct correlation with cyclical solar activity is demonstrated.     

The interiors of the giant planets — 1983

The last few years brought progress in our understanding of the interiors of the giant planets especially of the two larger ones which have been visited by Pioneer and Voyager spacecraft. An analysis of the formation of the giant planets also heped to clarify certain important common features. The presently available model of Jupiter is still based on certain somewhat bothersome approximations but it appears to satisfy the main observational constraints. Saturn's interior is much better understood than it was previously although the quantitative aspects of the role of the miscibility gap in the hydrogen-helium system have not yet been entirely resolved. Much attention has been directed at the interiors of Uranus and Neptune and the outstanding question appears to be the location and the amount of ices and methane present in their outer layers. Both the two-and the three-layer models are moderately successful. Serious difficulties arise from the considerable uncertainties concerning the rotational periods of both planets. Also the estimates of the internal heat fluxes and of the magnetic fields of both planets are not sufficiently certain. It is hoped that the forthcoming flyby of these two planets by a Voyager spacecraft will provide important new data for a future study of their interiors.     

Solar activity and planetary luminosity

The Chree superposition analysis of the luminosities of the planets Jupiter, Saturn, Uranus and Neptune indicates a correlation between solar activity and planetary luminosity. The variations of the solar constant in the visible range are considered to be too small to explain the observed changes in brightness. The interaction of solar extreme ultraviolet or solar wind particles with the atmospheres of these planets is probably responsible for the increased albedo during periods of high solar activity.     

Compressible convection in the deep atmospheres of giant planets

Fast rotating giant planets such as Jupiter and Saturn possess alternate prograde and retrograde zonal winds which are stable over long periods of time. We consider a compressible model of convection in a spherical shell with rapid rotation, using the anelastic approximation, to explore the parameter range for which such zonal flows can be produced.We consider models with a large variation in density across the layer. Our models are based only on the molecular H/He region above the metallic hydrogen transition at about 2 Mbar, and we do not include the hydromagnetic effects which may be important if the electrical conductivity is significant. We find that the convective velocities are significantly higher in the low density regions of the shell, but the zonal flow is almost independent of the z-coordinate parallel to the rotation axis. We analyse how this behaviour is consistent with the Proudman-Taylor theorem.We find that deep prograde zonal flow near the equator is a very robust feature of our models. Prograde and retrograde jets alternating in latitude can occur inside the tangent cylinder in compressible as well as Boussinesq models, particularly at lower Prandtl numbers. However, the zonal jets inside the tangent cylinder are suppressed if a no-slip condition is imposed at the inner boundary. This suggests that deep high latitude jets may be suppressed if there is significant magnetic dissipation.Our compressible calculations include the viscous dissipation in the entropy equation, and we find this is comparable to, and in some cases exceeds, the total heat flux emerging from the surface. For numerical reasons, these simulations cannot reach the extremely low Ekman number found in giant planets, and they necessarily also have a much larger heat flux than planets. We therefore discuss how our results might scale down to give solutions with lower dissipation and lower heat flux.     

Giant planet formation

The accumulation of giant planets involves processes typical for terrestrial planet formation as well as gasdynamic processes that were previously known only in stars. The condensible element cores of the gas-giants grow by solid body accretion while envelope formation is governed by stellar-like equilibria and the dynamic departures thereof. Two hypotheses for forming Uranus/Neptune-type planets — at sufficiently large heliocentric distances while allowing accretion of massive gaseous envelopes, i.e. Jupiter-type planets at intermediate distances — have been worked out in detailed numerical calculations: (1) Hydrostatic gas-accretion models with time-dependent solid body accretion-rates show a slow-down of core-accretion at the appropriate masses of Uranus and Neptune. As a consequence, gas-accretion also stagnates and a window is opened for removing the solar nebula during a time of roughly constant envelope mass. (2) Gasdynamic calculations of envelope accretion for constant planetesimal accretion-rates show a dynamic transition to new envelope equilibria at the so called critical mass. For a wide range of solar nebula conditions the new envelopes have respective masses similar to those of Uranus and Neptune and are more tightly bound to the cores. The transitions occur under lower density conditions typical for the outer parts of the solar nebula, whereas for higher densities, i.e. closer to the Sun, gasdynamic envelope accretion sets in and is able to proceed to Jupiter-masses.