The Evolution and Internal Structure of Jupiter and Saturn with Compositional Gradients

The internal structure of gas giant planets may be more complex than the commonly assumed core-envelope structure with an adiabatic temperature profile. Different primordial internal structures as well as various physical processes can lead to non-homogenous compositional distributions. A non-homogenous internal structure has a significant impact on the thermal evolution and final structure of the planets. In this paper, we present alternative structure and evolution models for Jupiter and Saturn allowing for non-adiabatic primordial structures and the mixing of heavy elements by convection as these planets evolve. We present the evolution of the planets accounting for various initial composition gradients, and in the case of Saturn, include the formation of a helium-rich region as a result of helium rain. We investigate the stability of regions with composition gradients against convection, and find that the helium shell in Saturn remains stable and does not mix with the rest of the envelope. In other cases, convection mixes the planetary interior despite the existence of compositional gradients, leading to the enrichment of the envelope with heavy elements. We show that non-adiabatic structures (and cooling histories) for both Jupiter and Saturn are feasible. The interior temperatures in that case are much higher that for standard adiabatic models. We conclude that the internal structure is directly linked to the formation and evolution history of the planet. These alternative internal structures of Jupiter and Saturn should be considered when interpreting the upcoming Juno and Cassini data.Comment: accepted for publication in Ap

New indication for a dichotomy in the interior structure of Uranus and Neptune from the application of modified shape and rotation data

Since the Voyager fly-bys of Uranus and Neptune, improved gravity field data have been derived from long-term observations of the planets' satellite motions, and modified shape and solid-body rotation periods were suggested. A faster rotation period (-40 min) for Uranus and a slower rotation period (+1h20) of Neptune compared to the Voyager data were found to minimize the dynamical heights and wind speeds. We apply the improved gravity data, the modified shape and rotation data, and the physical LM-R equation of state to compute adiabatic three-layer structure models, where rocks are confined to the core, and homogeneous thermal evolution models of Uranus and Neptune. We present the full range of structure models for both the Voyager and the modified shape and rotation data. In contrast to previous studies based solely on the Voyager data or on empirical EOS, we find that Uranus and Neptune may differ to an observationally significant level in their atmospheric heavy element mass fraction Z1 and nondimensional moment of inertia, nI. For Uranus, we find Z1 < 8% and nI=0.2224(1), while for Neptune Z1 < 65% and nI=0.2555(2) when applying the modified shape and rotation data, while for the unmodified data we compute Z1 < 17% and nI=0.230(1) for Uranus and Z1 < 54% and nI=0.2410(8) for Neptune. In each of these cases, solar metallicity models (Z1=0.015) are still possible. The cooling times obtained for each planet are similar to recent calculations with the Voyager rotation periods: Neptune's luminosity can be explained by assuming an adiabatic interior while Uranus cools far too slowly. More accurate determinations of these planets' gravity fields, shapes, rotation periods, atmospheric heavy element abundances, and intrinsic luminosities are essential for improving our understanding of the internal structure and evolution of icy planets.Comment: accepted to Planet. Space Sci., special editio

On the Location of the Snow Line in a Protoplanetary Disk

In a protoplanetary disk, the inner edge of the region where the temperature falls below the condensation temperature of water is referred to as the 'snow line'. Outside the snow line, water ice increases the surface density of solids by a factor of 4. The mass of the fastest growing planetesimal (the 'isolation mass') scales as the surface density to the 3/2 power. It is thought that ice-enhanced surface densities are required to make the cores of the gas giants (Jupiter and Saturn) before the disk gas dissipates. Observations of the Solar System's asteroid belt suggest that the snow line occurred near 2.7 AU. In this paper we revisit the theoretical determination of the snow line. In a minimum-mass disk characterized by conventional opacities and a mass accretion rate of 10^-8 solar masses per year, the snow line lies at 1.6-1.8 AU, just past the orbit of Mars. The minimum-mass disk, with a mass of 0.02 solar, has a life time of 2 million years with the assumed accretion rate. Moving the snow line past 2.7 AU requires that we increase the disk opacity, accretion rate, and/or disk mass by factors ranging up to an order of magnitude above our assumed baseline values.Comment: Accepted for publication in ApJ, 9 pages, 4 figure

Interior structure models of GJ 436b

GJ 436b is the first extrasolar planet discovered that resembles Neptune in mass and radius. The particularly interesting property of Neptune-sized planets is that their mass Mp and radius Rp are close to theoretical M-R relations of water planets. Given Mp, Rp, and equilibrium temperature, however, various internal compositions are possible. A broad set of interior structure models is presented here that illustrates the dependence of internal composition and possible phases of water occurring in presumably water-rich planets, such as GJ 436b on the uncertainty in atmospheric temperature profile and mean density. We show how the set of solutions can be narrowed down if theoretical constraints from formation and model atmospheres are applied or potentially observational constraints for the atmospheric metallicity Z1 and the tidal Love number k2. We model the interior by assuming either three layers (hydrogen-helium envelope, water layer, rock core) or two layers (H/He/H2O envelope, rocky core). For water, we use the equation of state H2O-REOS based on FT-DFT-MD simulations. Some admixture of H/He appears mandatory for explaining the measured radius. For the warmest considered models, the H/He mass fraction can reduce to 10^-3, still extending over ~0.7 REarth. If water occurs, it will be essentially in the plasma phase or in the superionic phase, but not in an ice phase. Metal-free envelope models have 0.02<k2<0.2, and the core mass cannot be determined from a measurement of k2. In contrast, models with 0.3<k2<0.82 require high metallicities Z1<0.89 in the outer envelope. The uncertainty in core mass decreases to 0.4 Mp, if k2>0.3, and further to 0.2 Mp, if k2>0.5, and core mass and Z1 become sensitive functions of k2. To further narrow the set of solutions, a proper treatment of the atmosphere and the evolution is necessary.Comment: 9 pages, accepted to A&

The growth and hydrodynamic collapse of a protoplanet envelope

We have conducted three-dimensional self-gravitating radiation hydrodynamical models of gas accretion onto high mass cores (15-33 Earth masses) over hundreds of orbits. Of these models, one case accretes more than a third of a Jupiter mass of gas, before eventually undergoing a hydrodynamic collapse. This collapse causes the density near the core to increase by more than an order of magnitude, and the outer envelope to evolve into a circumplanetary disc. A small reduction in the mass within the Hill radius (R_H) accompanies this collapse as a shock propagates outwards. This collapse leads to a new hydrostatic equilibrium for the protoplanetary envelope, at which point 97 per cent of the mass contained within the Hill radius is within the inner 0.03 R_H which had previously contained less than 40 per cent. Following this collapse the protoplanet resumes accretion at its prior rate. The net flow of mass towards this dense protoplanet is predominantly from high latitudes, whilst at the outer edge of the circumplanetary disc there is net outflow of gas along the midplane. We also find a turnover of gas deep within the bound envelope that may be caused by the establishment of convection cells.Comment: 16 pages, 16 figures. Accepted for publication in MNRA

A Gas-poor Planetesimal Capture Model for the Formation of Giant Planet Satellite Systems

Assuming that an unknown mechanism (e.g., gas turbulence) removes most of the subnebula gas disk in a timescale shorter than that for satellite formation, we develop a model for the formation of regular (and possibly at least some of the irregular) satellites around giant planets in a gas-poor environment. In this model, which follows along the lines of the work of Safronov et al. (1986), heliocentric planetesimals collide within the planet's Hill sphere and generate a circumplanetary disk of prograde and retrograde satellitesimals extending as far out as $\sim R_H/2$. At first, the net angular momentum of this proto-satellite swarm is small, and collisions among satellitesimals leads to loss of mass from the outer disk, and delivers mass to the inner disk (where regular satellites form) in a timescale $\lesssim 10^5$ years. This mass loss may be offset by continued collisional capture of sufficiently small $< 1$ km interlopers resulting from the disruption of planetesimals in the feeding zone of the giant planet. As the planet's feeding zone is cleared in a timescale $\lesssim 10^5$ years, enough angular momentum may be delivered to the proto-satellite swarm to account for the angular momentum of the regular satellites of Jupiter and Saturn.(abridged)Comment: 45 pages, 11 figures, 3 appendices, uses rgfmacro.tex, accepted for publication to Icaru

Chemistry in a gravitationally unstable protoplanetary disc

Until now, axisymmetric, alpha-disc models have been adopted for calculations of the chemical composition of protoplanetary discs. While this approach is reasonable for many discs, it is not appropriate when self-gravity is important. In this case, spiral waves and shocks cause temperature and density variations that affect the chemistry. We have adopted a dynamical model of a solar-mass star surrounded by a massive (0.39 Msun), self-gravitating disc, similar to those that may be found around Class 0 and early Class I protostars, in a study of disc chemistry. We find that for each of a number of species, e.g. H2O, adsorption and desorption dominate the changes in the gas-phase fractional abundance; because the desorption rates are very sensitive to temperature, maps of the emissions from such species should reveal the locations of shocks of varying strengths. The gas-phase fractional abundances of some other species, e.g. CS, are also affected by gas-phase reactions, particularly in warm shocked regions. We conclude that the dynamics of massive discs have a strong impact on how they appear when imaged in the emission lines of various molecular species.Comment: 10 figures and 3 tables, accepted for publication in MNRA