List of Figures

View Image Figure 1:
(a) The Solar Butterfly Diagram (reproduced from Hathaway, 2010). Yellow represents positive flux and blue negative flux where the field saturates at ± 10 G. (b) Example of a typical radial magnetic field distribution for AB Dor taken through Zeeman Doppler Imaging (ZDI, data from Donati et al., 2003) where the image saturates at ± 300 G. White/black denotes positive/negative flux. Due to the tilt angle of AB Dor, measurements can only be made in its northern hemisphere. Image reproduced by permission from Mackay et al. (2004), copyright by RAS.
View Image Figure 2:
Evolution of the radial component of the magnetic field (Br) at the solar surface for a single bipole in the northern hemisphere with (a) – (c) initial tilt angle of γ = 20° and (d) – (f) γ = 0°. The surface distributions are shown for (a) and (d) the initial distribution, (b) and (e) after 15 rotations, and (c) and (f) after 30 rotations. White represents positive flux and black negative flux and the thin solid line is the Polarity Inversion Line. The saturation levels for the field are set to 100 G, 10 G, and 5 G after 0, 15, and 30 rotations, respectively.
View Image Figure 3:
(a) Profile of differential rotation Ω versus latitude (Snodgrass, 1983) that is most commonly used in magnetic flux transport simulations. (b) Profiles of meridional flow u versus latitude used in various studies. The profiles are from Schüssler and Baumann (2006) (solid line), van Ballegooijen et al. (1998) (dashed line), Schrijver (2001) (dotted line), and Wang et al. (2002b) (dash-dot and dash-dot-dot-dot lines). This figure is based on Figure 3 of Schüssler and Baumann (2006).
View Image Figure 4:
Example of the magnetic flux transport simulations of Schrijver (2001) which apply a particle-tracking concept to simulate global magnetic fields down to the scale of ephemeral regions. Image reproduced by permission from Schrijver (2001), copyright by AAS.
View Image Figure 5:
Comparison of (a) solar and (b) stellar magnetic field configurations from Schrijver and Title (2001). For the stellar system all flux transport parameters are held fixed to solar values and only the emergence rate is increased to 30 times solar values. For the case of the Sun the magnetic fields saturate at ± 70 Mx cm–2 and for the star ± 700 Mx cm–2. Image reproduced by permission from Schrijver and Title (2001), copyright by AAS.
View Image Figure 6:
Comparison between (a) a drawing of the real eclipse corona, (b) the standard PFSS model, and (c) the Schatten (1971) current sheet model. The current sheet model better reproduces the shapes of polar plumes and of streamer axes. Image adapted from Figure 1 of Zhao and Hoeksema (1994).
View Image Figure 7:
Twisted magnetic fields. Panels (a) and (b) show the direction of twist for a force-free field line with (a) positive α, and (b) negative α, with respect to the potential field α = 0. Panels (c) and (d) show X-ray sigmoid structures with each sign of twist, observed in active regions with the Hinode X-ray Telescope (SAO, NASA, JAXA, NAOJ). These images were taken on 2007 February 16 and 2007 February 5, respectively.
View Image Figure 8:
Test of the optimisation method for nonlinear force-free fields with an analytical solution (figure adapted from Wiegelmann, 2007). Panel (a) shows the analytical solution (Low and Lou, 1990) and (b) shows the PFSS extrapolation used to initialise the computation. Panel (c) shows the resulting NLFFF when the boundary conditions at both r = R ⊙ and r = Rss are set to match the analytical solution, while panel (d) shows how the agreement is poorer if the analytical boundary conditions are applied only at the photosphere (the more realistic case for solar application).
View Image Figure 9:
A force-free magnetic field produced by the force-free electrodynamics method for Carrington rotation 2009. Field line colours show the twist parameter α, coloured red where α > 0, blue where α < 0, and light green where α ≈ 0. Image reproduced by permission from Contopoulos et al. (2011), copyright by Springer.
View Image Figure 10:
(a) Example of a Potential Field Source Surface extrapolation. (b) Example of a non-potential coronal field produced by the global coronal evolution model of Mackay and van Ballegooijen (2006) and Yeates et al. (2008b). The grey-scale image shows the radial field at the photosphere and the thin lines the coronal field lines. Image reproduced by permission from Yeates et al. (2010b), copyright by AGU.
View Image Figure 11:
Effect of the parameters a and α in the MHS solution for a simple dipolar photospheric magnetic field. Closed magnetic field lines expand when a is changed (left column), while the shear increases as the field-aligned current parameter α is increased (middle column). If both current systems act together (right column) then the field expands and becomes twisted. Image reproduced by permission from Zhao et al. (2000), copyright by AAS.
View Image Figure 12:
Comparison of PFSS extrapolations (right column) with steady state MHD solutions (left column) for two Carrington rotations. Image reproduced by permission from Figure 5 of Riley et al. (2006), copyright by AAS.
View Image Figure 13:
Graph of open flux variation (top) and sunspot number (bottom) for cycles 20 – 23. Image reproduced by permission from Lockwood et al. (2004), copyright by EGU.
View Image Figure 14:
Graph of (a) IMF variation (grey line) and PFSS approximations to the IMF field (collared lines). (b) Non-potential open flux estimate (thick black line) along with IMF variation (grey line) and PFSS approximations to the IMF (coloured lines) over a 6 month period. Image reproduced by permission from Yeates et al. (2010b), copyright by AGU.
View Image Figure 15:
Effect of differential rotation on open field regions for a bipole (black/white) located in a dipolar background field (red/dark blue). The open region (“coronal hole”) in the North (yellow) rotates almost rigidly, while that in the South (light blue) is sheared. Image reproduced by permission from Wang et al. (1996), copyright by AAAS.
View Image Figure 16:
Simulation results from the paper of Linker et al. (2011) where a bipole is advected from an open field region (shaded area on the solar surface) to a closed field region across the boundary of a coronal hole. Red denotes positive photospheric flux and blue negative flux. The green lines denote (a) initially open field lines of the bipole which then successively close down (b) – (d) as the bipole is advected across the coronal hole boundary. Image reproduced by permission, copyright by AAS.
View Image Figure 17:
Example of the comparison of theory and observations performed by Yeates et al. (2008b). (a) Magnetic field distribution in the global simulation after 108 days of evolution, showing highly twisted flux ropes, weakly sheared arcades, and near potential open fields. On the central image white/black represents positive/negative flux. (b) Close up view of a dextral flux rope lying above a PIL within the simulation. (c) BBSO Hα image of the dextral filament observed at this location.
View Image Figure 18:
Comparison of observations and simulated emissions from a global steady-state MHD model. The observations are shown in the first column, while the emissions due to different coronal heating profiles are shown in the other columns. Image reproduced by permission from Figure 8 of Lionello et al. (2009), copyright by AAS.