The three-dimensional structure of magnetostatic atmospheres. II - Modeling the large-scale corona

Bogdan, T. J.; Low, B. C.

doi:10.1086/164341

Cited by 97 publications

(81 citation statements)

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“…This approach allows linearizing the MS equations and solving them with a separation ansatz (see Low 1991;Bogdan and Low 1986;Neukirch 1995, for one cartesian and two spherical approaches, respectively). Because of the linearity of the underlying equations, a field-parallel electric current can be superposed (for a constant value of α).…”

Section: Mhs Modelsmentioning

confidence: 99%

The magnetic field in the solar atmosphere

Wiegelmann

Thalmann

Solanki

2014

Astron Astrophys Rev

183

125

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This publication provides an overview of magnetic fields in the solar atmosphere with the focus lying on the corona. The solar magnetic field couples the solar interior with the visible surface of the Sun and with its atmosphere. It is also responsible for all solar activity in its numerous manifestations. Thus, dynamic phenomena such as coronal mass ejections and flares are magnetically driven. In addition, the field also plays a crucial role in heating the solar chromosphere and corona as well as in accelerating the solar wind. Our main emphasis is the magnetic field in the upper solar atmosphere so that photospheric and chromospheric magnetic structures are mainly discussed where relevant for higher solar layers. Also, the discussion of the solar atmosphere and activity is limited to those topics of direct relevance to the magnetic field. After giving a brief overview about the solar magnetic field in general and its global structure, we discuss in more detail the magnetic field in active regions, the quiet Sun and coronal holes.

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Section: Mhs Modelsmentioning

confidence: 99%

The magnetic field in the solar atmosphere

Wiegelmann

Thalmann

Solanki

2014

Astron Astrophys Rev

183

125

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“…A systematic method for calculating a special class of 3D MHS equilibria for the case when external forces have to included, has been developed in a series of papers by Low (1985Low ( , 1991Low ( , 1992Low ( , 1993aLow ( ,b, 2005 and Bogdan & Low (1986). The method is applicable to all external forces derived from a potential and assumes a special form for the electric current density to allow analytical progress.…”

Section: Introductionmentioning

confidence: 99%

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

Al-Salti¹,

Neukirch²,

Ryan³

2010

A&A

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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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“…In spite of the general difficulties associated with finding three-dimensional analytical solutions of the MHS equations, some useful solutions are available (Low 1985;Bogdan & Low 1986;Low 1991Low , 1992Low , 1993aNeukirch 1995Neukirch , 1997Neukirch & Rastätter 1999;Petrie & Neukirch 2000). This class of solutions has a volume current density that flows in surfaces perpendicular to the direction of the gravitational force and a possible additional field-aligned current density.…”

Section: Introductionmentioning

confidence: 99%

A first step in reconstructing the solar corona self-consistently with a magnetohydrostatic model during solar activity minimum

Ruan¹,

Wiegelmann²,

Inhester³

et al. 2008

A&A

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Aims. We compute the distribution of the magnetic field and the plasma in the global corona with a self-consistent magnetohydrostatic (MHS) model. Methods. Because direct measurements of the solar coronal magnetic field and plasma are extremely difficult and inaccurate, we use a modeling approach based on observational quantities, e.g. the measured photospheric magnetic field, to reconstruct the structure of the global solar corona. We take an analytic magnetohydrostatic model to extrapolate the magnetic field in the corona from photospheric magnetic field measurement. In the model, the electric current density can be decomposed into two components: one component is aligned with the magnetic field lines, whereas the other component flows in spherical shells. The second component of the current produces finite Lorentz forces that are balanced by the pressure gradient and the gravity force. We derive the 3D distribution of the magnetic field and plasma self-consistently in one model. The boundary conditions are given by a synoptic magnetogram on the inner boundary and by a source surface model at the outer boundary. Results. The density in the model is higher in the equatorial plane than in the polar region. We compare the magnetic field distribution of our model with potential and force-free field models for the same boundary conditions and find that our model differs noticeably from both. We discuss how to apply the model and how to improve it.

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The three-dimensional structure of magnetostatic atmospheres. II - Modeling the large-scale corona

Cited by 97 publications

References 0 publications

The magnetic field in the solar atmosphere

The magnetic field in the solar atmosphere

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

A first step in reconstructing the solar corona self-consistently with a magnetohydrostatic model during solar activity minimum

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