# THE INFLUENCE OF SPATIAL RESOLUTION ON NONLINEAR FORCE-FREE MODELING

## Abstract

The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/Solar Optical Telescope Spectro-Polarimeter scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, ofmore »

- Authors:

- Lockheed Martin Solar and Astrophysics Laboratory, 3251 Hanover St. B/252, Palo Alto, CA 94304 (United States)
- Sydney Institute for Astronomy, School of Physics, The University of Sydney, Sydney, NSW 2006 (Australia)
- NorthWest Research Associates, 3380 Mitchell Ln., Boulder, CO 80301 (United States)
- CNRS, Centre de Physique Théorique de l’École Polytechnique, F-91128, Palaiseau Cedex (France)
- Institute of Physics/IGAM, University of Graz, Universitätsplatz 5, A-8010 Graz (Austria)
- Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey, RH5 6NT (United Kingdom)
- Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077, Göttingen (Germany)
- Department of Physics, Montana State University, Bozeman, MT 59717 (United States)
- W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305 (United States)
- Department of Mathematics and Information Sciences, Faculty of Engineering and Environment, Northumbria University, Newcastle-Upon-Tyne, NE1 8ST (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22525352

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 811; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; FREE ENERGY; HELICITY; MAGNETIC FIELDS; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; PHOTOSPHERE; SENSITIVITY; SOLAR CORONA; SPATIAL RESOLUTION; SUN; TELESCOPES

### Citation Formats

```
DeRosa, M. L., Schrijver, C. J., Wheatland, M. S., Gilchrist, S. A., Leka, K. D., Barnes, G., Amari, T., Canou, A., Thalmann, J. K., Valori, G., Wiegelmann, T., Malanushenko, A., Sun, X., and Régnier, S.
```*THE INFLUENCE OF SPATIAL RESOLUTION ON NONLINEAR FORCE-FREE MODELING*. United States: N. p., 2015.
Web. doi:10.1088/0004-637X/811/2/107.

```
DeRosa, M. L., Schrijver, C. J., Wheatland, M. S., Gilchrist, S. A., Leka, K. D., Barnes, G., Amari, T., Canou, A., Thalmann, J. K., Valori, G., Wiegelmann, T., Malanushenko, A., Sun, X., & Régnier, S.
```*THE INFLUENCE OF SPATIAL RESOLUTION ON NONLINEAR FORCE-FREE MODELING*. United States. doi:10.1088/0004-637X/811/2/107.

```
DeRosa, M. L., Schrijver, C. J., Wheatland, M. S., Gilchrist, S. A., Leka, K. D., Barnes, G., Amari, T., Canou, A., Thalmann, J. K., Valori, G., Wiegelmann, T., Malanushenko, A., Sun, X., and Régnier, S. Thu .
"THE INFLUENCE OF SPATIAL RESOLUTION ON NONLINEAR FORCE-FREE MODELING". United States. doi:10.1088/0004-637X/811/2/107.
```

```
@article{osti_22525352,
```

title = {THE INFLUENCE OF SPATIAL RESOLUTION ON NONLINEAR FORCE-FREE MODELING},

author = {DeRosa, M. L. and Schrijver, C. J. and Wheatland, M. S. and Gilchrist, S. A. and Leka, K. D. and Barnes, G. and Amari, T. and Canou, A. and Thalmann, J. K. and Valori, G. and Wiegelmann, T. and Malanushenko, A. and Sun, X. and Régnier, S.},

abstractNote = {The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/Solar Optical Telescope Spectro-Polarimeter scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, of the vector magnetogram boundary field in excess of nominal uncertainties in the data. The solutions produced by the various methods are significantly different at each resolution level. We continue to recommend verifying agreement between the modeled field lines and corresponding coronal loop images before any NLFFF model is used in a scientific setting.},

doi = {10.1088/0004-637X/811/2/107},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 2,

volume = 811,

place = {United States},

year = {2015},

month = {10}

}