Magnetic fields play a key role in the existence and variability of a wide variety of phenomena on the Sun. These range from relatively stable, slowly evolving features such as sunspots (Solanki, 2003), coronal loops (Reale, 2010), and solar prominences (Labrosse et al., 2010; Mackay et al., 2010), to highly dynamic phenomena such as solar flares (Benz, 2008) and coronal mass ejections (Forbes et al., 2006; Chen, 2011). Solar magnetic fields may directly or indirectly affect the Earth through the Sun’s open magnetic flux (Balogh et al., 1995), solar wind (Hollweg, 2008), and total solar irradiance variations (Fröhlich and Lean, 1998).
Our present day understanding of solar magnetic fields dates back to 1908 when G.E. Hale made the first magnetic field observations of sunspots (Hale, 1908). However, it was not until the systematic mapping of the Sun’s magnetic field carried out by the Babcocks (Babcock and Babcock, 1952; Babcock and Livingston, 1958; Babcock, 1959) that the true nature of solar magnetic activity became apparent. While significant advances in observations have been made over the last 50 years, only the strength and distribution of the line-of-sight component at the level of the photosphere has been regularly measured over solar cycle time-scales. However, over the last 5 years, vector magnetic field measurements at the photospheric level have been systematically carried out by the satellite missions of Hinode since 2006 (Kosugi et al., 2007) and SDO (Solar Dynamics Observatory) since 2010 (Pesnell et al., 2012). In addition, systematic ground based measurements of vector magnetic fields have been made by SOLIS (Synoptic Optical Long-term Investigations of the Sun) since 2009 (Keller et al., 2003). While Hinode only observes vector magnetic fields over localised areas, the global capabilities of SDO and SOLIS provide us with a unique opportunity to observe the large-scale spatial distribution of vector magnetic fields across the solar surface. Over time scales of years, SDO and SOLIS will significantly enhance our understanding of the emergence and transport of magnetic fields at the level of the photosphere and their subsequent effect on the global corona. While magnetic fields may be observed directly at the photospheric level, due to low densities the same is not true for the corona. As many important phenomena occur in the solar corona, a key component in our understanding of solar magnetic fields – and the build up of energy within them – is the use of theoretical models to construct (or extrapolate) coronal magnetic fields from photospheric data.
While solar magnetic fields have been observed in detail over long periods of time, the same is not true for other stars. In recent years however, the technique of Zeeman Doppler Imaging (Semel, 1989) has lead to a significant advance in our understanding of magnetic fields on other stars. Results show a wide range of magnetic distributions across stars of varying mass and spectral type (Donati et al., 2009). With the accurate measurement of stellar magnetic fields, techniques developed to model solar magnetic fields, both at photospheric and coronal levels, are now widely applied in the stellar context (Cohen et al., 2010; Jardine et al., 2011).
In this review, we primarily focus on our present day understanding of global solar magnetic fields from both observations and theoretical models. The reader should note that we focus on quasi-static or steady-state coronal models and will not consider fully dynamic eruptive models. Within the review we also restrict ourselves to global aspects of the Sun’s magnetic field so will consider neither the Sun’s small-scale field nor limited field-of-view models. The review will focus in particular on advances made in the last 15 years, although we have not aimed at completeness in material or references. Additional topics will be added in future revisions. Where appropriate, we expand this discussion into stellar magnetic fields to summarise new results or to describe the application of models developed for the Sun in the stellar context. The review is split into three distinct parts, where each part is largely self-contained. Thus the reader may focus on each part separately if desired. The review is split in the following way:
Finally, in Section 5 a brief summary is given and some outstanding problems or areas of advancement are outlined.
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