Thermal Evolution and Core Formation on Asteroid 4 Vesta in the Magma Ocean Regime

Geochemical observations of the eucrite and diogenite meteorites, together with observations made by NASAs Dawn spacecraft while orbiting asteroid 4 Vesta, indicate that Vesta has differentiated to form a crust, mantle, and core. Eucrite and diogenite petrology is best explained by solidification of the crust from a magma ocean constituting 60-70% of Vestas silicates [3], or a temperature of ~1550 C. The abundances of moderately siderophile elements (Ni, Co, Mo, W, and P) in eucrites require that essentially all of the metallic phase in Vesta segregated to form a core prior to eucrite formation and likely reached a temperature of 1450- 1575 C. These observations provide important constraints on Vestas thermal evolution. The high inferred temperature indicates that convective heat transport must have been important during part of Vestas thermal evolution. In this study, we model Vestas thermal evolution in the magma ocean regime

Wetland mapping from digitized aerial photography

Computer assisted interpretation of small scale aerial imagery was found to be a cost effective and accurate method of mapping complex vegetation patterns if high resolution information is desired. This type of technique is suited for problems such as monitoring changes in species composition due to environmental factors and is a feasible method of monitoring and mapping large areas of wetlands. The technique has the added advantage of being in a computer compatible form which can be transformed into any georeference system of interest

A dynamic model of Venus's gravity field

Unlike Earth, long wavelength gravity anomalies and topography correlate well on Venus. Venus's admittance curve from spherical harmonic degree 2 to 18 is inconsistent with either Airy or Pratt isostasy, but is consistent with dynamic support from mantle convection. A model using whole mantle flow and a high viscosity near surface layer overlying a constant viscosity mantle reproduces this admittance curve. On Earth, the effective viscosity deduced from geoid modeling increases by a factor of 300 from the asthenosphere to the lower mantle. These viscosity estimates may be biased by the neglect of lateral variations in mantle viscosity associated with hot plumes and cold subducted slabs. The different effective viscosity profiles for Earth and Venus may reflect their convective styles, with tectonism and mantle heat transport dominated by hot plumes on Venus and by subducted slabs on Earth. Convection at degree 2 appears much stronger on Earth than on Venus. A degree 2 convective structure may be unstable on Venus, but may have been stabilized on Earth by the insulating effects of the Pangean supercontinental assemblage

Core Formation and Evolution of Asteroid 4 Vesta

The howardites, eucrites, and diogenites (HEDs) are a suite of related meteorite types that formed by igneous and impact processes on the same parent body. Multiple lines of evidence, including infrared spectroscopy of the asteroid belt and the petrology and geochemistry of the HEDs, suggest that the asteroid 4 Vesta is the parent body for the HEDs. Observations by NASA's Dawn spacecraft mission strongly support the conclusion that the HEDs are from Vesta. The abundances of the moderately siderophile elements Ni, Co, Mo, W, and P in eucrites require that most or all of the metallic phase in Vesta segregated to form a core prior to eucrite solidification. These observations place important constraints on the mode and timescale of core formation on Vesta. Possible core formation mechanisms include porous flow, which potentially could occur prior to initiation of silicate melting, and metallic rain in a largely molten silicate magma ocean. Once the core forms, convection within the core could possible sustain a magnetic dynamo for a period of time. We consider each process in turn

Core Formation on Asteroid 4 Vesta: Iron Rain in a Silicate Magma Ocean

Geochemical observations of the eucrite and diogenite meteorites, together with observations made by NASA's Dawn spacecraft, suggest that Vesta resembles H chondrites in bulk chemical composition, possibly with about 25% of a CM-chondrite like composition added in. For this model, the core is 15% by mass (or 8 volume %) of the asteroid. The abundances of moderately siderophile elements (Ni, Co, Mo, W, and P) in eucrites require that essentially all of the metallic phase in Vesta segregated to form a core prior to eucrite solidification. Melting in the Fe-Ni-S system begins at a cotectic temperature of ~940 deg. C. Only about 40% of the total metal phase, or 3-4 volume % of Vesta, melts prior to the onset of silicate melting. Liquid iron in solid silicate initially forms isolated pockets of melt; connected melt channels, which are necessary if the metal is to segregate from the silicate, are only possible when the metal phase exceeds about 5 volume %. Thus, metal segregation to form a core does not occur prior to the onset of silicate melting

Semiclassical approximation to supersymmetric quantum gravity

We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schrodinger equation, and quantum gravitational correction terms to this Schrodinger equation. In particular, the following consequences are found: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many fingered) local time parameter has to be present on $SuperRiem \Sigma$ (the space of all possible tetrad and gravitino fields), (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early universe. The physical meaning of these equations and results, in particular the similarities to and differences from the pure bosonic case, are discussed.Comment: 34 pages, clarifications added, typos correcte

Quantum phantom cosmology

We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative cosmological constant. In all these cases we calculate the classical trajectories in configuration space and give solutions to the Wheeler-DeWitt equation in quantum cosmology. In the cases of the toy model and the model with exponential potential we are able to solve the Wheeler-DeWitt equation exactly. For comparison, we also give the corresponding solutions for an ordinary scalar field. We discuss in particular the behaviour of wave packets in minisuperspace. For the phantom field these packets disperse in the region that corresponds to the Big Rip singularity. This thus constitutes a genuine quantum region at large scales, described by a regular solution of the Wheeler-DeWitt equation. For the ordinary scalar field, the Big-Bang singularity is avoided. Some remarks on the arrow of time in phantom models as well as on the relation of phantom models to loop quantum cosmology are given.Comment: 21 pages, 6 figure

Quantum state of the multiverse

A third quantization formalism is applied to a simplified multiverse scenario. A well defined quantum state of the multiverse is obtained which agrees with standard boundary condition proposals. These states are found to be squeezed, and related to accelerating universes: they share similar properties to those obtained previously by Grishchuk and Siderov. We also comment on related works that have criticized the third quantization approach.Comment: 15 pages, 2 figure

Evolutionary quantum cosmology in a gauge-fixed picture

We study the classical and quantum models of a flat Friedmann-Robertson-Walker (FRW) space-time, coupled to a perfect fluid, in the context of the consensus and a gauge-fixed Lagrangian frameworks. It is shown that, either in the usual or in the gauge-fixed actions, the evolution of the universe based on the classical cosmology represents a late time power law expansion, coming from a big-bang singularity in which the scale factor goes to zero for the standard matter, and tending towards a big-rip singularity in which the scale factor diverges for the phantom fluid. We then employ the familiar canonical quantization procedure in the given cosmological setting to find the cosmological wave functions in the corresponding minisuperspace. Using a gauge-fixed (reduced) Lagrangian, we show that, it may lead to a Schr\"{o}dinger equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the time dependent wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.Comment: 15 pages, 10 figures, typos corrected, Refs. adde

Starobinsky Model in Schroedinger Description

In the Starobinsky inflationary model inflation is driven by quantum corrections to the vacuum Einstein equation. We reduce the Wheeler-DeWitt equation corresponding to the Starobinsky model to a Schroedinger form containing time. The Schroedinger equation is solved with a Gaussian ansatz. Using the prescription for the normalization constant of the wavefunction given in our previous work, we show that the Gaussian ansatz demands Hawking type initial conditions for the wavefunction of the universe. The wormholes induce randomness in initial states suggesting a basis for time-contained description of the Wheeler-DeWitt equation.Comment: 19 Pages, LaTeX, no figure, gross typographical mistake