Volume 514, May 2010
|Number of page(s)||11|
|Published online||07 May 2010|
Three-dimensional solutions of the magnetohydrostatic equations: rigidly rotating magnetized coronae in cylindrical geometry
School of Mathematics and Statistics, University of St. Andrews, St. Andrews KY16 9SS,
UK e-mail: firstname.lastname@example.org;email@example.com
Accepted: 1 February 2010
Context. Solutions of the magnetohydrostatic (MHS) equations are very important for modelling astrophysical plasmas, such as the coronae of magnetized stars. Realistic models should be three-dimensional, i.e., should not have any spatial symmetries, but finding three-dimensional solutions of the MHS equations is a formidable task.
Aims. We present a general theoretical framework for calculating three-dimensional MHS solutions outside massive rigidly rotating central bodies, together with example solutions. A possible future application is to model the closed field region of the coronae of fast-rotating stars.
Methods. As a first step, we present in this paper the theory and solutions for the case of a massive rigidly rotating magnetized cylinder, but the theory can easily be extended to other geometries, We assume that the solutions are stationary in the co-rotating frame of reference. To simplify the MHS equations, we use a special form for the current density, which leads to a single linear partial differential equation for a pseudo-potential U. The magnetic field can be derived from U by differentiation. The plasma density, pressure, and temperature are also part of the solution.
Results. We derive the fundamental equation for the pseudo-potential both in coordinate independent form and in cylindrical coordinates. We present numerical example solutions for the case of cylindrical coordinates.
Key words: magnetic fields / magnetohydrodynamics (MHD) / stars: magnetic field / stars: coronae / stars: activity
© ESO, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.