The radii and orbital periods of 4000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. Yet an important question about the composition of planets ranging from 2 to 4 Earth radii (RÅ) still remains. They may either have a rocky core enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant amount of multi-component, H2O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 MÅ, if half-ice and half-rock by mass, have radii of 2.5 RÅ, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2-4 RÅ range requires a gas envelope of at most a few mass%, regardless of the core composition. To resolve the ambiguity of internal compositions, we use a growth model and conduct Monte Carlo simulations to demonstrate that many intermediate-size planets are "water worlds". Keywords: exoplanets / bimodal distribution / ices / water worlds / planet formation Significance Statement: The discovery of numerous exoplanet systems containing diverse populations of planets orbiting very close to their host stars challenges the planet formation theories based on the Solar system. Here we focus on the planets with radii of 2-4 RÅ, whose compositions are debated. They are thought to be either gas dwarfs consisting of rocky cores embedded in H2-rich gas envelopes or water worlds containing significant amounts of H2Odominated fluid/ice in addition to rock and gas. We argue that these planets are water worlds.

Eighty years ago, it was proposed that solid hydrogen would become metallic at sufficiently high density. Despite numerous investigations, this transition has not yet been experimentally observed. More recently, there has been much interest in the analog of this predicted metallic transition in the dense liquid, due to its relevance to planetary science. Here, we show direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium. Experimental determination of the location of this transition provides a much-needed benchmark for theory and may constrain the region of hydrogen-helium immiscibility and the boundary-layer pressure in standard models of the internal structure of gas-giant planets.

We present QMD simulations of water in the ultra-high-pressure regime up to conditions typical for the deep interior of Jupiter and Saturn. We calculate the equation of state and the Hugoniot curve and study the structural properties via pair correlation functions and self-diffusion coefficients. In the ultradense superionic phase, we find a continuous transition in the protonic structure. With rising density, the mobile protons stay with increasing probability at the octahedral sites while leaving the ice X positions to the same degree unoccupied. Water forms a fluid dense plasma at the conditions of Jupiter's core ͑i.e., 20 000 K, 50 Mbar, 11 g / cm 3 ͒, while it may be superionic in the core of Saturn. We expect a substantial amount of superionic water inside Neptune.

Density functional theory (DFT) methods for calculating the quantum mechanical ground states of condensed matter systems are now a common and significant component of materials research. The growing importance of DFT reflects the development of sufficiently accurate functionals, efficient algorithms and continuing improvements in computing capabilities. As the materials problems to which DFT is applied have become large and complex, so have the sets of calculations necessary for investigating a given problem. Highly versatile, powerful codes exist to serve the practitioner, but designing useful simulations is a complicated task, involving intricate manipulation of many variables, with many pitfalls for the unwary and the inexperienced. We discuss several of the most important issues that go into designing a meaningful DFT calculation. We emphasize the necessity of investigating these issues and reporting the critical details.

We show that the AM05 functional ͓Armiento and Mattsson, Phys. Rev. B 72, 085108 ͑2005͔͒ has the same excellent performance for solids as the hybrid density functionals tested in Paier et al. ͓J. Chem. Phys. 124, 154709 ͑2006͒; 125, 249901 ͑2006͔͒. This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. Hartree-Fock hybrid calculations are typically an order of magnitude slower than local or semilocal density functionals such as AM05, which is of a regular semilocal generalized gradient approximation form. The performance of AM05 is on average found to be superior to selecting the best of local density approximation and PBE for each solid. By comparing data from several different electronic-structure codes, we have determined that the numerical errors in this study are equal to or smaller than the corresponding experimental uncertainties.

No abstract

We have revealed, and resolved, an apparent inability of density functional theory, within the local density and generalized gradient approximations, to describe vacancies in Al accurately and consistently. The shortcoming is due to electron correlation effects near electronic edges and we show how to correct for them. We find that the divacancy in Al is energetically unstable and we show that anharmonic atomic vibrations explain the non-Arrhenius temperature dependence of the vacancy concentration.

No abstract