International Summer Institute for Modeling in Astrophysics

We carry out two-dimensional hydrodynamical simulations to investigate the effects of the turbulence caused by gravitational instability on the migration of a 10 Jupiter-mass planet. We model three discs with different amounts of turbulence and model two scenarios: the first scenario allows the planet to migrate immediately and we find that the migration rates are similar in all three discs, regardless of the amount of turbulence. The second method involves keeping the planet fixed on a circular orbit such that it opens up a gap, before allowing it to migrate. We find that although the gap properties appear to be similar in all three cases, the migration rate is faster in a disc with a lower amount of turbulence.

The project is an extension of the work on f-plane magnetohydrodynamic (MHD) turbulence and its consequences on momentum transport. A somewhat detailed overview is given, with the physical mechanisms explained. The quasi-geostrophic equations, so well known in the Geophysical Fluid Dynamics (GFD) community, is derived with the Lorentz force present. The two-layer model is proposed as a simplified model for our studies. Progress with magnetically influenced barotropic and baroclinic instabilities are given, and some proposed future work concludes the document.

Following the work on ray orbits in spatially hyperbolic systems by Mass and Lam (1995) and Rieutord and Valdettaro (1997) we seek to examine the behaviour of the shear layer emitted at the critical latitude in 3D in a spherical shell fllled with rotating fluid. We compare the (previously known) 3D and the 2D solutions for a sphere in an infinite domain to find the major difference being a logarithmic singularity on the rotation axis formed by a cone of shear converging to an apex. We then consider the "split disc" arrangement first considered by Walton to examine this singularity in more detail. We also consider the behaviour of the Moore and Saffman shear layers under the influence of a large-scale forcing; our motivation is primarily the dissipation of tidal energiesin astrophysical binary systems.

The effects of a uniform horizontal magnetic field on jets dynamics in 2D Boussinesq turbulence, i.e. Howard-Krishnamurti problem are studied with a numerical simulation. For a fixed fluid and magnetic diffusivity, it is shown that as the imposed field strength becomes larger jets start behaving in a more organized way, i.e. achieve stationary state and are finally quenched. The time evolution of total stress, Reynolds stress, Maxwell stress is examined and all the stresses are shown to vanish when jets are quenched. The quenching of jets is confirmed for different values of magnetic diffusivity, albeit the required field strength increases. It is also shown that the inclusion of overstable modes reinforces jets where Maxwell stress overcomes Reynolds stress. For a larger imposed field jets are shown to quench. A possible mechanism for the transition to the reinforcement of jets by Maxwell stress is discussed based on the transition in the most unstable mode in the underlying turbulence.

This project investigates the role of radiation in Rayleigh-Taylor instabilities by performing linear stability analyses of a plane parallel background equilibrium, with a semi-infinite medium 1 overlying a semi-infinite medium 2, in a gravitational field g and a radiation flux F normal to the discontinuity.

In this project we address the question of whether a flow that is not a dynamo can be made to exhibit dynamo-like properties by feeding it with a small amount of magnetic field. This may be pertinent to the solar dynamo and the processes that sustain it. We present a 3-D fully nonlinear magnetohydrodynamic simulation of the dynamo properties of a time-dependent ABC flow and discuss a method for leaking magnetic field into the computational domain. Our results suggest that sufficient magnetic feeding significantly boosts the magnetic energy of nondynamo flows and can maintain a mangetic field for long times.

Motivated by recent observations of retrograde planets, we investigated the orbital decay of a retrograde planet embedded in a protoplanetary disk. We treated both gravitational and hydrodynamic drag, and found the migration time scale ranges from 10³ to 10⁵ years for planet masses between 10^-3 to 10¹ Jupiter masses. We also found that a highly inclined orbit can increase this time scale by a factor of 10 and that due to inclination damping, the final inclination is unlikely to be greater than 50 degrees.

We investigate local radiative hydrodynamic instabilities in the envelopes of massive stars. Two different stellar models are considered, a simple polytropic model and a more realistic stellar evolution code model. For both cases, we compare the local optical depth and radiative flux with analytically derived instability criteria. Only a thin outer shell of the star, containing a mass of about 10^-6 M_star to 10^-5 M_star, can be subjected to this instability. However, the growth rate of the instability is relatively fast (about 10,000s) indicating a possible run-away effect.

The aim of the work is to perform numerical simulations of the propagation of stellar jets with consistent nozzle conditions obtained from launching simulations. This novel approach provides a global picture of the jet from its launching to its interaction with the ambient medium. The flow parameters observed at a distance of a few AU from the protostellar jet DG Tau were used to constrain the global inflow conditions whereas the actual profiles of different quantities are obtained from steady-state launching simulations. A new simulation was run on time and length scales typical of stellar jets. We also investigated the effects of cooling in these jets. We find evidence of density knots in our adiabatic simulations whereas simulations with cooling have much fewer and weaker knots.

Recent SPH and grid code simulations showed, that ionizing radiation can amplify overdensities in turbulent molecular clouds and produce molecular pillars. The relevance of magnetic fields for the structure and stability of molecular clouds is still under discussion. We investigate whether an ionization front hitting a medium with small distortions of the magnetic field can produce the observed pillar-like structures in star forming regions (e.g. Eagle Nebula). Numerical MHD simulations with the Athena 2.0 grid code with ionizing radiation were performed. It turns out that the ionizing radiation drives a shock wave into the cold magnetized cloud and amplifies overdensities seeded by Alfven waves. Alfven waves can be seeds for molecular pillars. However, the magnetic field in structures created by Alfven waves makes these regions hostile to star formation.