32. Twisted flux tube emergence: rigid rise or nonlinear deformation?

Author: David MacTaggart, University of Abertay Dundee.

Introduction

Solar atmospheric activity is driven by the emergence of magnetic flux from within the Sun’s interior. The large concentrations of strong magnetic field that appear on the surface, known as active regions, occur in characteristic time-dependent configurations. Such regions can vary in complexity but are generally bipolar, with two fairly distinct areas of opposite polarity [1].

With the increase in parallel computing capabilities over the past decade, researchers have been able to construct sophisticated computational models of flux emergence [2,3]. Such models normally span the interior (convection zone) to the low corona. In most models, a particular magnetic structure, e.g. a twisted flux tube, is placed in the interior at the start of a simulation, and allowed to rise to the photosphere through imposed deformation or buoyancy. The temperature profile of the interior means that buoyancy alone cannot carry the flux tube all the way to the photosphere, and the rise stops. But the magnetic field can still expand into the corona, via the magnetic buoyancy instability [4].

The success of these models lies in their ability to produce a host of active region phenomena, from sigmoids to CME-like eruptions. For the interested reader, a recent review of a wide class of flux emergence simulations and their use in modelling specific solar phenomena is given in [3].

Different interpretations

Recent photospheric observations of the much-studied NOAA active region 10953 have been interpreted as evidence of the rigid emergence of a twisted magnetic flux tube from the solar interior to the atmosphere [5,6]. Observations are made at the active region’s polarity inversion line (PIL) and underneath an overlying magnetic arcade. The two photospheric signatures used as evidence of the emergence of a rigid twisted flux tube are

The ‘sliding doors’ effect – as the tube rises through the photosphere along the PIL, it initially pushes the opposite polarities of the overlying arcade apart. Once it has passed through, the opposite polarities come together again.
The reversal of the horizontal magnetic field component at the PIL as the (twisted) flux tube passes through the photosphere.

This interpretation of rigid emergence is at odds with the picture of flux emergence given by the simulations of twisted flux tubes, which involves flux tube expansion. This prompted us [7] to investigate the two signatures above in a flux emergence model. The model domain spans a region from the top of the solar interior to the low corona. In the initial equilibrium, a magnetic arcade, anchored in the solar interior, is placed in the atmosphere. Directly below the PIL of the arcade, a twisted flux tube is placed in the interior (see Figure 1). This is made buoyant and rises to the photosphere.

Figure 1: The model initial condition. The magnetogram of Bz at the base of the photosphere shows the opposite polarities of the arcade (blue – negative, red – positive and green – horizontal field). Some of the arcade field lines
are traced in purple from the base of the photosphere. An isosurface of the twisted flux rope in the solar interior is also displayed. (From [7])

At the photosphere, the rising flux tube halts and then expands horizontally, perpendicular to the PIL. This is followed by the magnetic buoyancy instability, which carries part of the flux tube into the atmosphere. The action of these nonlinear deformations is to produce a ‘sliding doors’ effect in line-of-sight magnetograms taken at the base of the photosphere, as shown in Figure 2 (see [7] for a more detailed explanation). The second signature is also found in the model. Here, the tube axis rises above the plane of the magnetograms but remains in the photosphere, i.e. in the model, the axis does not rise to the corona. The tube axis can reach the corona by considering different geometries for the initial magnetic field that are not suitable for this particular application [8].

Figure 2: Time-slice image showing the ‘sliding doors’
effect. These slices are taken across the PIL at the base of the photosphere in the model. The colour scheme corresponds to that of Figure 1. (From [7])

The main result of our model is that the two signatures can be found for a flux tube emerging according to the standard theoretical picture, i.e. the two observational signatures are not sufficient to determine which type of emergence is occurring.

To progress, we consider additional signatures that can be investigated within the model and which should also be detectable observationally. These are

The increase of magnetic flux at the PIL due to the presence of the emerging tube.
Horizontal flows at the PIL. Perpendicular to the PIL there is an expansion and parallel to it there are shear flows.

We searched for these signatures in active region 10953 by revisiting the observations [9]. Finding the first signature would be strong evidence of flux emergence. By calculating the negative flux next to the PIL in a contour deforming in time, we demonstrate that the flux is decreasing rather than increasing (see Figure 3). The contour deforms with time so that any polarities not associated with emergence, e.g. those peeling off the neighbouring sunspot, are not included.

Figure 3: The negative vertical flux, calculated within the deforming contour, as a function of time. (From [9])

The second signature comes from two physical aspects of an emerging flux tube. The radial expansion is a natural consequence of rising through an atmosphere where the plasma pressure decreases rapidly with height. The shear flows are driven by the Lorentz force of the emerging tube [3]. We looked for these flows using local correlation tracking. The results, however, only indicate flows emanating from the neighbouring sunspot. There are no clear signatures of flux emergence.

The model of [7] and the observational study of [9] both point towards emergence not occurring at the PIL in active region 10953. This emphasises the important dialogue that must take place between theory and observation.

Conclusions

We have taken a flux emergence model, where the magnetic field expands into the atmosphere via the magnetic buoyancy instability, and shown that we can reproduce the observational signatures used as evidence for rigid emergence. This means that these signatures are not sufficient to determine which type of emergence is occurring. Although these studies do not categorically disprove rigid emergence, they cast a shadow of doubt over it. To achieve general acceptance, rigid emergence will have to undergo the same scrutiny as the ‘standard model’ of flux emergence. Although this model is highly nonlinear, each stage of the evolution has a sound physical basis with results that are testable by observations.

Acknowledgements

I would like to thank Alan Hood, Santiago Vargas Domíguez, Lucie Green and Lidia van Driel-Gesztelyi for their collaboration in the publications [7] and [9].

References

[1] Schrijver, C.J. & Zwaan, C. 2000, Solar and Stellar Magnetic Activity, CUP
[2] Fan, Y. 2009, Living Rev. Solar Phys., 6
[3] Hood, A.W., Archontis, V. & MacTaggart, D., 2012, Solar Phys., 278, 3
[4] Paris, R.B., 1984, Annales de Physique, 9, 347
[5] Okamoto et al., 2008, ApJ Lett., 673, L215
[6] Okamoto et al., 2009, ApJ, 697, 913
[7] MacTaggart, D. & Hood, A.W. 2010, ApJ Lett., 716, L222
[8] MacTaggart, D. & Hood, A.W. 2009, A&A, 507, 995
[9] Vargas Domíguez, S., MacTaggart, D., Green, L., van Driel-Gesztelyi, L. & Hood, A.W. 2012, Solar Phys., 278, 33