Observations have shown that active region flux tubes often emerge in a twisted state and that the active region formed has magnetic helicity of the same sense as the flux tube that forms it. Separate theoretical models have been developed for coronal magnetic fields with helicity and for flux tubes with twist. Here we present a dynamical model that connects a twisted subphotospheric flux tube to a force-free coronal field. With this model it is possible to explore the emergence of a flux tube into the corona and its effect on both the coronal field and the subphotospheric flux tube. In particular, the model shows that only a fraction of the current carried by the twisted flux tube will pass into the corona. As a consequence of this "mismatch," a torsional Alfven wave is launched downward along the flux tube at the instant of emergence. As the flux tube continues to emerge, the helicity of the coronal field increases owing to rotation of the footpoints. Our model predicts that the level of rotation will depend upon the rapidity of flux emergence. After this transient period the helicity of the active region will reflect the twist in its parent tube.

A Model for the Emergence of a Twisted Magnetic Flux Tube

Brown D. S. and Priest E. R. 2001, The topological behaviour of 3D null points in the Sun's corona, Astronomy and Astrophysics, 367, 339-346

https://pure.aber.ac.uk/portal/files/71712/BrownandPriest2001.pdf

The topological behaviour of 3D null points in the Sun's corona

We present a method to include stereoscopic information about the three-dimensional structure of flux tubes into the reconstruction of the coronal magnetic field. Due to the low plasma beta in the corona we can assume a force-free magnetic field, with the current density parallel to the magnetic field lines. Here we use linear force-free fields for simplicity. The method uses the line-of-sight magnetic field on the photosphere as observational input. The value of α is determined iteratively by comparing the reconstructed magnetic field with the observed structures. The final configuration is the optimal linear force-free solution constrained by both the photospheric magnetogram and the observed plasma structures. As an example we apply our method to SOHO MDI/EIT data of an active region. In the future it is planned to apply the method to analyse data from the SECCHI instrument aboard the STEREO mission.

/pdf/including-stereoscopic-information-in-the-reconstruction-of-28jyirn30x.pdf

Including stereoscopic information in the reconstruction of coronal magnetic fields

We undertake a first attempt towards a consistent reconstruction of the coronal magnetic field and the coronal density structure. We consider a stationary solar corona which has to obey the equations of magnetohydrostatics. We solve these equations with help of a newly developed optimization scheme. As a first step we illustrate how tomographic information can be included into the reconstruction of coronal magnetic fields. In a second step we use coronal magnetic field infor- mation to improve the tomographic inversion process. As input the scheme requires magnetic field measurements on the photosphere from vector-magnetographs and the line-of-sight integrated den- sity distribution from coronagraphs. We test our codes with well-known analytic magnetohydrostatic equilibria and models. The program is planned for use within the STEREO mission. The solar magnetic field is an important quantity which couples the solar interior, the photosphere and the atmosphere. The quasi stationary coronal magnetic field configuration is an interesting and challenging topic on its own right. But even to understand basic processes like coronal mass ejections and flares it is important to understand the quiescent magnetic configuration out of which these dynamic phenomena arise. Unfortunately the coronal magnetic field cannot be measured di- rectly, but it has to be reconstructed from photospheric measurements. A magnetic field reconstruction of the solar corona has to be consistent with the observed spa- tial variation of the coronal plasma (density, pressure, temperature) often elongated along the magnetic field. Here we are mainly interested in long-living structures which are time- independent in first order. We also concentrate on closed magnetic configurations where a stationary plasma flow (solar wind) does not significantly contribute to the force balance. Such configurations are static equilibria and have to obey the magnetohydrostatic equations (MHS). As the magnetic field B and the density distribution N are physically closely related their model reconstruction should also be linked as much as possible. In this paper we attempt to show how this can be achieved. We propose variational principles which if they can be solved should give a consistent model for an isother-

/pdf/magnetic-modelling-and-tomography-first-steps-towards-a-3pcnat9g8k.pdf

Magnetic modelling and tomography: First steps towards a consistent reconstruction of the solar corona

Many authors use magnetic-field models to extrapolate the field in the solar corona from magnetic data in the photosphere. The accuracy of such extrapolations is usually judged qualitatively by eye, where a less judgemental quantitative approach would be more desirable. In this paper, a robust method for obtaining the best fit between a theoretical magnetic field and intensity observations of coronal loops on the solar disk will be presented. The method will be applied to Yohkoh data using a linear force-free field as an illustration. Any other theoretical model for the magnetic field can be used, provided there is enough freedom in the model to optimize the fit.

/pdf/a-quantitative-method-to-optimise-magnetic-field-line-wzp75p03sl.pdf

A Quantitative Method to Optimise Magnetic Field Line Fitting of Observed Coronal Loops

A model of the equilibrium structure of the coronal magnetic field is developed, taking account of the fact that field lines are rooted in the photosphere, where field is concentrated into isolated flux tubes. The field is force-free, described by ∇ ×B =αB, withα constant; this field has special physical significance, being the state of mininum energy after small-scale reconnections, and is also mathematically convenient in that the principle of superposition can be used to construct complex geometries. First a model of a single loop is presented, with a flux source and sink pair at the photosphere; both point flux tubes and finite radius flux tubes are considered. Then more complex topologies with multiple sources and sinks are investigated. It is shown that significant topology changes arise for different values ofα, indicating the possibility that there can be energy changes through magnetic reconnection if the field evolves ideally and then relaxes to a linear state.

R. M. Lothian

Papers

Coronal magnetic field equilibrium with discrete flux sources