Three-dimensional calculations of high- and low-mass planets embedded in protoplanetary discs

We analyse the non-linear, three-dimensional response of a gaseous, viscous protoplanetary disc to the presence of a planet of mass ranging from 1 Earth mass (1 M_⊕) to 1 Jupiter mass (1 M_J) by using the zeus hydrodynamics code. We determine the gas flow pattern, and the accretion and migration rates of the planet. The planet is assumed to be in a fixed circular orbit about the central star. It is also assumed to be able to accrete gas without expansion on the scale of its Roche radius. Only planets with masses   M _p≳ 0.1 M_J  produce significant perturbations in the surface density of the disc. The flow within the Roche lobe of the planet is fully three-dimensional. Gas streams generally enter the Roche lobe close to the disc mid-plane, but produce much weaker shocks than the streams in two-dimensional models. The streams supply material to a circumplanetary disc that rotates in the same sense as the orbit of the planet. Much of the mass supply to the circumplanetary disc comes from non-coplanar flow. The accretion rate peaks with a planet mass of approximately 0.1 M_J and is highly efficient, occurring at the local viscous rate. The migration time-scales for planets of mass less than 0.1 M_J, based on torques from disc material outside the Roche lobes of the planets, are in excellent agreement with the linear theory of type I (non-gap) migration for three-dimensional discs. The transition from type I to type II (gap) migration is smooth, with changes in migration times of about a factor of 2. Starting with a core which can undergo runaway growth, a planet can gain up to a few M_J with little migration. Planets with final masses of the order of 10 M_J would undergo large migration, which makes formation and survival difficult.     

Star-Driven Wind and Jet Models

We outline some main results from recent analytical modelling of axisymmetric jets from the coronae of young stars and compare them to disk-wind and X-wind models. We emphazise the roles of the magnetic rotator and the disk in the formation and the evolution of the jet. We conjecture that with time both the efficiency of the magnetic rotator and the role of the disk as a primary source for the wind decline.     

Loss of water from Mars:: Implications for the oxidation of the soil

The evolution of the martian atmosphere with regard to its H₂O inventory is influenced by thermal loss processes of H, H₂, nonthermal atmospheric loss processes of H⁺, H₂⁺, O, O⁺, CO₂, and O₂⁺ into space, as well as by chemical weathering of the surface soil. The evolution of thermal and nonthermal escape processes depend on the history of the intensity of the solar XUV radiation and the solar wind density. Thus, we use actual data from the observation of solar proxies with different ages from the Sun in Time program for reconstructing the Sun's radiation and particle environment from the present to 3.5 Gyr ago. The correlation between mass loss and X-ray surface flux of solar proxies follows a power law relationship, which indicates a solar wind density up to 1000 times higher at the beginning of the Sun's main sequence lifetime. For the study of various atmospheric escape processes we used a gas dynamic test particle model for the estimation of the pick up ion loss rates and considered pick up ion sputtering, as well as dissociative recombination. The loss of H₂O from Mars over the last 3.5 Gyr was estimated to be equivalent to a global martian H₂O ocean with a depth of about 12 m, which is smaller than the values reported by previous studies. If ion momentum transport, a process studied in detail by Mars Express is significant on Mars, the water loss may be enhanced by a factor of about 2. In our investigation we found that the sum of thermal and nonthermal atmospheric loss rates of H and all nonthermal escape processes of O to space are not compatible with a ratio of 2:1, and is currently close to about 20:1. Escape to space cannot therefore be the only sink for oxygen on Mars. Our results suggest that the missing oxygen (needed for the validation of the 2:1 ratio between H and O) can be explained by the incorporation into the martian surface by chemical weathering processes since the onset of intense oxidation about 2 Gyr ago. Based on the evolution of the atmosphere-surface-interaction on Mars, an overall global surface sink of about 2×10⁴² oxygen particles in the regolith can be expected. Because of the intense oxidation of inorganic matter, this process may have led to the formation of considerable amounts of sulfates and ferric oxides on Mars. To model this effect we consider several factors: (1) the amount of incorporated oxygen, (2) the inorganic composition of the martian soil and (3) meteoritic gardening. We show that the oxygen incorporation has also implications for the oxidant extinction depth, which is an important parameter to determine required sampling depths on Mars aimed at finding putative organic material. We found that the oxidant extinction depth is expected to lie in a range between 2 and 5 m for global mean values.     

Bianchi VI0 cosmological model in Saez and Ballester theory

The problem of perfect fluid distribution in spatially homogeneous and anisotropic Bianchi type VI₀ space-time is considered in a scalar tensor theory of gravitation proposed by Saez and Ballester (1985). Exact solutions of the field equations are derived when the metric potentials are functions of cosmic time only. Some physical and geometrical properties of the solutions are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.