Three-dimensional solutions of the magnetohydrostatic equations: Rigidly rotating magnetized coronae in cylindrical geometry

N. Al-Salti, T. Neukirch, R. Ryan

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article numberA38
JournalAstronomy and Astrophysics
Volume514
Issue number3
DOIs
Publication statusPublished - May 7 2010

Fingerprint

magnetohydrostatics
coronas
corona
geometry
cylindrical coordinates
plasma
stars
rotating cylinders
symmetry
partial differential equations
plasma density
astrophysics
magnetic field
current density
modeling
magnetic fields
temperature

Keywords

  • Magnetic fields
  • Magnetohydrodynamics (MHD)
  • Stars: activity
  • Stars: coronae
  • Stars: magnetic field

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Three-dimensional solutions of the magnetohydrostatic equations : Rigidly rotating magnetized coronae in cylindrical geometry. / Al-Salti, N.; Neukirch, T.; Ryan, R.

In: Astronomy and Astrophysics, Vol. 514, No. 3, A38, 07.05.2010.

Research output: Contribution to journalArticle

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AB - 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.

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