Tilaye Tadesse¹, T. Wiegelmann², P.J. MacNeice¹, B. Inhester², K. Olson³, and A. A. Pevtsov⁴

1. NASA Goddard Space Flight Center, Space Weather Lab., Greenbelt, MD, USA
2. Max-Planck Institute for Solar System Research, Germany
3. Department of Physics, Drexel University, Philadelphia, PA, USA
4. National Solar Observatory, Sunspot, NM, USA

Corona models in Cartesian geometry, e.g. based on the potential field and nonlinear force-free (NLFFF) field approach, are not well suited for larger domains, since the spherical nature of the solar surface cannot be neglected when the field of view is large^[1,2,3]. One of the most significant results of the SDO mission to date has been repeated observations of large, almost global scale events in which large-scale connection between active regions may play a fundamental role^[4]. Therefore, it appears prudent to implement a NLFFF procedure in spherical geometry for use when large-scale boundary data are available, such as from the HMI on board SDO^[5].

Fig 1.Full-disk SDO/HMI magnetogram from 9 November 2011. The rectangles outline the main active regions during this observation and the yellow line indicates the solar equator (θ = 0^◦).

We investigated the coronal magnetic field associated with full solar disk on 9 Nov 2011 by using SDO/HMI photospheric magnetograms as boundary condition for potential and NLFFF models. During this particular observation, there were three active regions in the northern hemisphere and one active region surrounded by magnetic patches in the south (see Fig 1). We have used spherical NLFFF and potential field codes to compute the magnetic field solutions over the full solar disk. For computing the potential field, we used the preprocessed radial component Br of the HMI-data using a spherical harmonic expansion. We implement spherical NLFFF code initialized by the potential field solution (except for the observed bottom boundary) during relaxation towards a force-free state in the computational volume.

Fig 2. Field lines of (a) the potential field model and (b) the NLFFF model at 17:33 UT overlaid on the AIA 171 Å image. Green and red lines represent open and closed magnetic field lines.

We have compared the magnetic field solutions from both models. The qualitative com- parison between the model magnetic field lines and the observed EUV loops indicates that the NLFFF model agrees significantly better with coronal magnetic loops as observed in SDO/AIA images (see Fig 2a,b). The study also investigated the magnetic connectivity between ARs located on either side of the solar equator (see Fig 3). For this particular observation, much of the trans-equatorial loops (TELs) connecting the active regions in the northern and southern hemispheres are potential (current-free). This indicates that the two solar hemispheres are more magnetically connected but hardly share electric currents.

Figure 3.Model magnetic field configurations connecting strong magnetic fields on either side of the solar equator. Selected field lines are calculated from a global (a) potential field and (b) a NLFFF model connecting AR 11339 and AR 11338. Potential and NLFFF model field lines connecting two ARs (11342 and 11341) to strong magnetic patches are shown in (c) and (d), respectively. Red and green line colors indicate closed and open magnetic field lines, respectively. The gray-scale background reflects the measured radial SDO/HMI magnetic field. It can be seen that the non-potential TELs deviate only little from a potential configuration

References

[1] Wiegelmann, T. 2007, Solar Phys. 240, 227.
[2] DeRosa, M.L., Schrijver, C., et al. 2009, Astrophys. J. 696, 1780.
[3] Tadesse, T., Wiegelmann, T., Inhester, B. 2009, Astron. Astrophys. 508, 421.
[4] Pesnell, W.D., Thompson, B.J., Chamberlin, P.C. 2012, Solar Phys. 275, 3.
[5] Schou, J., Scherrer, P.H., Bush, R.I., et al. 2012, Solar Phys. 275, 229.