Theoretical astrophysics and plasma physics at RPC

Abstract:

A conserved stress energy tensorfor weak field gravitational waves propagating in vacuum is derived directly from the linearized general relativistic wave equation alone, for an arbitrary gauge. In any harmonic gauge, the form of the tensor leads directly to the classical expression for the outgoing wave energy. The method described here, however, is a much simpler,shorter, and more physically motivated approach than is the customary procedure, which involves a lengthy and cumbersome second-order (in wave-amplitude) calculation starting with the Einstein tensor. Our method has the added advantage of exhibiting the direct coupling between the outgoing wave energy flux and the work done by the gravitational field on the sources. For nonharmonic gauges, the directly derived wave stress tensor has an apparent index asymmetry. This coordinate artifact may be straightforwardly removed, and the symmetrized (still gauge-invariant) tensor then takes on its widely used form. Angular momentum conservation follows immediately. For any harmonic gauge, however, the stress tensor found is manifestly symmetric from the start, and its derivation depends, in its entirety, on the structure of the linearized wave equation.

Abstract:

In protoplanetary discs, planetary cores must be at least 0.1 M+ at 1 au for migration to be significant; this mass rises to 1 M+ at 5 au. Planet formation models indicate that these cores form on million year timescales. We report here a study of the evolution of 0.1 M+ and 1 M+ cores, migrating from about 2 and 5 au respectively, in million year old photoevaporating discs. In such a disc, a gap opens up at around 2 au after a few million years. The inner region subsequently accrete onto the star on a smaller timescale. We find that, typically, the smallest cores form systems of non{resonant planets beyond 0.5 au with masses up to about 1.5 M+. In low mass discs, the same cores may evolve in situ. More massive cores form systems of a few earth masses planets. They migrate within the inner edge of the disc gap only in the most massive discs. Delivery of material to the inner parts of the disc ceases with opening of the gap. Interestingly, when the heavy cores do not migrate significantly, the type of systems that are produced resembles our solar system. This study suggests that low mm ux transition discs may not form systems of planets on short orbits but may instead harbour earth mass planets in the habitable zone.