Numerical Astrophysics: 3-D Dynamics and Visualization

Åke Nordlund, Projects and Papers

Short-cuts to:

Magnetohydrodynamic Turbulence and Dynamo Action

Together with Axel Brandenburg (Newcastle) and Bob Stein (MSU), I am trying to understand how astrophysical dynamos work, by analyzing and visualizing numerical simulations of 3D MHD turbulence. We recently published a summary paper, where we discuss among other things whether or not dynamo action is suppressed at high magnetic Reynolds numbers (we believe that is is not).

Supersonic MHD-Turbulence and Star Formation

Together with Paolo Padoan, I work on topics related to interstellar turbulence and star formation. Paolo's PhD thesis. is about highly supersonic turbulence and star formation in molecular clouds.

Some rather sensational results have come out of this project; in particular it turns out that supersonic, nearly isothermal turbulence has statistical properties that are entirely generic, and that these may be used to derive a theoretical Initial Mass Function, describing the distribution over mass of protostars.

In connection with the PhD thesis examination, we made some volume visualization movies that illustrate the highly intermittent nature of supersonic turbulence.

For current status, please check Paolo's lists of papers and conference reports,

For a brief overview of the subject, see the color viewgraphs and figures prepared for talks in Garching and Stockholm in May -97.

MHD simulations of Cooling Flows in Galaxy Clusters

Together with PhD student Örnólfur Einar Rögnvaldsson (TAC) and Vincenzo Antonuccio (presently a visiting scientist at TAC), I am using a two-fluid (hot gas + CDM) MHD code to study the evolution of structure and magnetic fields in the Universe.

The current focus is on cooling flows in clusters, where some intriguing results are emerging.

Accretion Discs

This is a joint project with Axel Brandenburg (NORDITA), Bob Stein (MSU) and Ulf Torkelson. The main results are in a paper in the June 20 1995 issue of ApJ, with additional results in a Letter to the ApJ and various other papers (see my BibTeX file).

The Solar Dynamo

Bertil Dorch's Masters thesis is about the buoyant rise of magnetic flux tubes in the Sun.

His PhD project aims at a qualitative understanding of processes involved in the solar dynamo; in particular the storage of the strong toroidal field and the diffusion and drift of the surface magnetic field.

A paper on magnetic flux tubes is under publication.

Coronal Heating

This was the PhD project of Klaus Galsgaard, who is now with Eric Priest in St. Andrews. Klaus studied the dissipation of magnetic energy in a low beta plasma stressed from two opposing boundaries. This is a mock-up of the solar corona, which is being stressed by the turbulent motions in the solar photosphere. The thesis consists of a summary and five papers. A recent review paper summarizes the issues.

In the first, scaling relations are derived that allow a precise estimate of the heating of the solar corona by solar convective motions (.ps.Z version) -- unpacks to 8 Mb. The work turns out to be consistent with the required coronal heating. This paper has nice figures, some of which are color, but print OK in grey scale.

The second paper is about the kink instability (.ps.Z version) -- unpacks to 15 Mb, and its evolution past the saturation of the kink. The kink loop turns into a region with a messy topology, where the magnetic energy keeps growing steadily, if the boundary rotation is continued after the kink instability has saturated.

The third paper looks at the activity in a region containing magnetic null points (.ps.Z version) -- ungpacks to 22 Mb. A lot of activity takes place when such a region is stressed by boundary motions, and nice arcade filament systems eventually forms along the boundaries. This paper contains color postscript, but is also available in grey scale.

The fourth paper is about self-organised criticality in a simplified model of the coronal field, along the lines of Lu and Hamilton. We are ready to bet a small amount of money on that the coronal field is in a self-organized critical state, similar to a sand pile, where the distribution of solar flares correspond to the avalanches in a sand pile. Since this cannot yet be proven, you have a fair chance with a counter bet, but sooner or later you may loose.

The fifth paper is about the numerical methods.

There is also a thesis summary, with lots of color illustrations, but this expands to an 80 Mb PostScript file, so be careful with your WWW browsers use of temporary space (you can set this from Netscape preferences), and use a symbolic link print method ("lpr -s" or "lp"), to avoid overflowing the print spool directory. Also, unless you have a fast color printer, you may prefer to print this in black and white (even though it is a pity on some of the illustrations).

Some of the viewgraphs from the PhD lecture are available as postscript files in a directory, and as a compressed SGI ShowCase file.

Solar Convection

We (this is work done together with Bob Stein, Michigan State University) are able to match the observed properties of solar granulation (the surface manifestation of turbulent heat convection on the Sun) quantitatively, using numerical simulations with detailed equations of state and radiative energy transfer. With this result in hand, we can demonstrate that the structure of convection below the solar surface is quite different than has hitherto been assumed; convection occurs in the form of plumes of cold surface fluid, descending in a nearly isentropic background. Here is one viewgraph that explain the background and one that shows a comparison of numerical results with observations from La Palma (prepared for the TAC inauguration in October 1994).

More illustrations are included in a talk given at the Liege Colloquium 1995. A reprint is available, with color or grey scale images.

There is also an invited talk from the Bombay meeting in October 1995 (some misprints are corrected relative to the printed version).

Sample data is in this directory. There are also some movies.

A review paper by Henk Spruit explains the new paradigm that has come out of the numerical simulations.

Solar and Stellar Oscillations

Together with Bob Stein, Michigan State University at East Lancing, I am working on understanding the excitation and damping of solar oscillations.

A group in Århus has discover p-mode oscillations in the nearby sub-giant eta-Boo. The discovery was reported in this paper. Jørgen Christensen Dalsgaard and friends have submitted a paper where they discuss models that fit the p-mode spectrum quite well, except for a phase factor which may have to do with the detailed structure near the surface.

In collaboration with Regner Trampedach and Colin Rosenthal in Århus I am making 3D models of eta-Boo, to study the structure of the surface layers. We have a contribution at a meeting in Cape Town, and two posters at a GONG meeting; one poster on "Seismology of the Solar Surface Regions" and another one on "Convective Perturbations To Solar Oscillations: The f Mode".

3-D Non-LTE Spectral Line Formation

Together with Dan Kiselman (Stockholm Observatory and La Palma), I am working on understanding 3-D effects in spectral line formation. We have a paper available as html and ps.gz).


Some of the projects mentioned above are discussed in a popular article, with Jørgen Christensen Dalsgaard, in Naturens Verden (in danish)
For exact references to papers, see my BibTeX file
Last updated 07-06-97 /