Stability of the viscously spreading ring

We study analytically and numerically the stability of the pressure-less, viscously spreading accretion ring. We show that the ring is unstable to small non-axisymmetric perturbations. To perform the perturbation analysis of the ring we use a stretching transformation of the time coordinate. We find that to 1st order, one-armed spiral structures, and to 2nd order additionally two-armed spiral features may appear. Furthermore, we identify a dispersion relation determining the instability of the ring. The theoretical results are confirmed in several simulations, using two different numerical methods. These computations prove independently the existence of a secular spiral instability driven by viscosity, which evolves into persisting leading and trailing spiral waves. Our results settle the question whether the spiral structures found in earlier simulations of the spreading ring are numerical artifacts or genuine instabilities.Comment: 13 pages, 12 figures; A&A accepte

On relativistic discs and rings

Sequences of infinitesimally thin, uniformly rotating, self-gravitating relativistic discs with internal two-dimensional pressure have been constructed. It is shown that in weaker relativistic configurations the sequences undergo a continuous bifurcation from a disc to a ring structure, while in stronger relativistic cases the sequences terminate at the mass-shed limit where gravitational forces are exactly balanced by centrifugal forces.Comment: 9 pages, requires mn.sty and epsf.sty, 12 figures included, accepted by Monthly Notices of the Royal Astronomical Societ

Quantile-Based Spectral Analysis in an Object-Oriented Framework and a Reference Implementation in R: The quantspec Package

Quantile-based approaches to the spectral analysis of time series have recently attracted a lot of attention. Despite a growing literature that contains various estimation proposals, no systematic methods for computing the new estimators are available to date. This paper contains two main contributions. First, an extensible framework for quantile-based spectral analysis of time series is developed and documented using object-oriented models. A comprehensive, open source, reference implementation of this framework, the R package quantspec, was recently contributed to CRAN by the author of this paper. The second contribution of the present paper is to provide a detailed tutorial, with worked examples, to this R package. A reader who is already familiar with quantile-based spectral analysis and whose primary interest is not the design of the quantspec package, but how to use it, can read the tutorial and worked examples (Sections 3 and 4) independently.Comment: 27 pages, 11 figures, R package available via CRAN (http://cran.r-project.org/web/packages/quantspec) or GitHub (https://github.com/tobiaskley/quantspec

Formation of massive planets in binary star systems

As of today over 40 planetary systems have been discovered in binary star systems. In all cases the configuration appears to be circumstellar, where the planets orbit around one of the stars, the secondary acting as a perturber. The formation of planets in binary star systems is more difficult than around single stars due to the gravitational action of the companion on the dynamics of the protoplanetary disk. In this contribution we first briefly present the relevant observational evidence for planets in binary systems. Then the dynamical influence that a secondary companion has on a circumstellar disk will be analyzed through fully hydrodynamical simulations. We demonstrate that the disk becomes eccentric and shows a coherent precession around the primary star. Finally, fully hydrodynamical simulations of evolving protoplanets embedded in disks in binary star systems are presented. We investigate how the orbital evolution of protoplanetary embryos and their mass growth from cores to massive planets might be affected in this very dynamical environment. We consider, in particular, the planet orbiting the primary in the system Gamma Cephei.Comment: To appear in Proceedings: Extrasolar Planets in Multi-body Systems: Theory and Observations Eds. K. Gozdziewski, A. Niedzielski and J. Schneide

Mass Flow and Accretion through gaps in Accretion Discs

We study the structure and dynamics of the gap created by a protoplanet in an accretion disc. The hydrodynamic equations for a flat, two-dimensional, non-selfgravitating protostellar accretion disc with an embedded, Jupiter sized protoplanet on a circular orbit are solved. To simulate possible accretion of mass onto the protoplanet we continually remove mass from the interior of the planet's Roche lobe which is monitored. Firstly, it is shown that consistent results independent on numerical issues (such as boundary or initial conditions, artificial viscosity or resolution) can be obtained. Then, a detailed parameter study delineates the influence of the disc viscosity and pressure on the magnitude of the accretion rate. We find that, even after the formation of a gap in the disc, the planet is still able to accrete more mass from the disc. This accretion occurs from regions of the disc which are radially exterior and interior to the planet's orbital radius. The rate depends on the magnitude of the viscosity and vertical thickness of the disc. For a disc viscosity alpha=10^{-3} and vertical thickness H/r=0.05 we estimate the time scale for the accumulation of one Jupiter mass to be of order hundred thousand years. For a larger(smaller) viscosity and disc thickness this accretion rate is increasing(decreasing). For a very small viscosity (alpha < 5 10^{-4}) the mass accretion rate through the gap onto the planet is markedly reduced, and the corresponding accretion time scale becomes larger than the viscous evolution time of the disc.Comment: 15 pages, Latex, uses MN Latex style v1.4, accepted by MN. Paper, figures and mpeg simulation available at http://www.tpi.uni-jena.de/~wak/research/gap/gap.htm

Modelling the evolution of planets in disks

To explain important properties of extrasolar planetary systems (eg. close-in hot Jupiters, resonant planets) an evolutionary scenario which allows for radial migration of planets in disks is required. During their formation protoplanets undergo a phase in which they are embedded in the disk and interact gravitationally with it. This planet-disk interaction results in torques (through gravitational forces) acting on the planet that will change its angular momentum and result in a radial migration of the planet through the disk. To determine the outcome of this very important process for planet formation, dedicated high resolution numerical modeling is required. This contribution focusses on some important aspects of the numerical approach that we found essential for obtaining successful results. We specifically mention the treatment of Coriolis forces, Cartesian grids, and the FARGO method.Comment: Talk given at JENAM meeting, Vienna 200