Interior Models of Uranus and Neptune

'Empirical' models (pressure vs. density) of Uranus and Neptune interiors constrained by the gravitational coefficients J_2, J_4, the planetary radii and masses, and Voyager solid-body rotation periods are presented. The empirical pressure-density profiles are then interpreted in terms of physical equations of state of hydrogen, helium, ice (H_2O), and rock (SiO_2) to test the physical plausibility of the models. The compositions of Uranus and Neptune are found to be similar with somewhat different distributions of the high-Z material. The big difference between the two planets is that Neptune requires a non-solar envelope while Uranus is best matched with a solar composition envelope. Our analysis suggests that the heavier elements in both Uranus' and Neptune's interior might increase gradually towards the planetary centers. Indeed it is possible to fit the gravitational moments without sharp compositional transitions.Comment: 16 pages, accepted for publication in Ap

The opacity of grains in protoplanetary atmospheres

We have computed the size distribution of silicate grains in the outer radiative region of the envelope of a protoplanet evolving according to the scenario of Pollack et al. (1996). Our computation includes grain growth due to Brownian motion and overtake of smaller grains by larger ones. We also include the input of new grains due to the breakup of planetesimals in the atmosphere. We follow the procedure of Podolak (2003), but have speeded it up significantly. This allows us to test the sensitivity of the code to various parameters. We have also made a more careful estimate of the resulting grain opacity. We find that the grain opacity is of the order of $10^{-2}\ \mathrm{cm^2 g^{-1}}$throughout most of the outer radiative zone as Hubickyj et al. (2005) assumed for their low opacity case, but near the outer edge of the envelope, the opacity can increase to$\sim{1} \mathrm{cm^2 g^{-1}}$. We discuss the effect of this on the evolution of the models.Comment: 28 pages, 13 Figs., to be published in Icarus (accepted Sep. 2007

The Location of the Snow Line in Protostellar Disks

The snow line in a gas disk is defined as the distance from the star beyond which the water ice is stable against evaporation. Since oxygen is the most abundant element after hydrogen and helium, the presence of ice grains can have important consequences for disk evolution. However, determining the position of the snow line is not simple. I discuss some of the important processes that affect the position of the snow line.Comment: 8 pages, 5 figures. Invited talk at IAU Symposium 263 - Icy Bodies in the Solar System. Rio de Janeiro, Aug. 200

Why Water Markets Are Not Quick Fixes for Droughts in the Western United States

Water in the western United States can be bought and sold, but the transactions will always be complicated. Transfers of water will always be expensive and time consuming because of the hydrologic and institutional interconnections inherent to water. Our data show that most of the water rights in the West are messy. Therefore, markets cannot be quick fixes, and using markets for future water allocation, even if it is economically efficient, will take time and resources to set up. Untangling serial uses and negotiating multiple ownership claims are hurdles, not barriers, and they can be overcome in time but will require both time and money. Buying existing water rights may be less costly than building infrastructure to transport available water from long distances or desalinating seawater, but the transactions will come at a price. Municipalities may purchase water from farmers and thus bear the transaction costs directly, or the private sector may purchase agricultural water (e.g., Two Rivers Water and Farming, Colorado (Landry 2012)), bear the associated risk and transaction costs, and sell it on to municipalities. In either case, the end users will inevitably pay higher prices for water. Markets can and will be part of western U.S. water allocation, but they do not provide quick solutions. Droughts can focus public attention on the value of water and potentially increase the willingness-to-pay prices that reflect the transaction costs of tangled western water markets

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

Are the aerosols on Uranus and Neptune composed of methane photopolymers?

The measured optical properties of photochemically produced aerosols in an adding-doubling radiative transfer code were used to match various points in the spectra of Uranus and Neptune. How well these points are fit are shown by different assumptions regarding the size and distribution of these aerosols in the Uranus and Neptune atmospheres. The consistency of these derived distributions with those expected from computations of the sedimentation rate of such aerosols is discussed