List of Figures

View Image Figure 1:
Stokes V in blue wing of 630.2 nm line from Hinode. Around a sunspot (a) and in the quiet Sun (b), showing the wide range in size of magnetic structures on the Sun. The dimensions of both figures are 110 Mm and the pixel size is 108 km. Image reproduced by permission from Parnell et al. (2009), copyright by AAS.
View Image Figure 2:
Histogram of feature frequency vs. magnetic flux. Image reproduced by permission from Parnell et al. (2009), copyright by AAS.
View Image Figure 3:
Magnetic butterfly diagram from longitudinally averaged radial magnetic field. This illustrates Hale’s polarity law, Joy’s law, transport of flux toward the poles and migration of active region emergence sites toward the equator. Image reproduced by permission from Hathaway (2010).
View Image Figure 4:
Comparison of G-band intensity at viewing angle μ = 0.63 of observations (left) and at μ = 0.6 simulated (right).
View Image Figure 5:
Emergence of a small magnetic loop in the quiet solar photosphere. Top: continuum intensity at 630 nm. Center: total linear polarization (Stokes Q,U) in the 630.25 line. Bottom: total circular polarization (Stokes V). Signal is clipped at ± 0.1 pm. Red contours are linear polarization > 0.22 pm, while black and white contours are circular polarization > ± 0.1 pm. Distances are in acrsec. Image reproduced by permission from Martínez González and Bellot Rubio (2009), copyright by AAS.
View Image Figure 6:
Dynamo energy transfers in the kinematic phase. The dominant process is turbulent stretching of magnetic field lines against the magnetic tension component of the Lorentz force. Image reproduced by permission from Pietarila Graham et al. (2010), copyright by AAS.
View Image Figure 7:
Dynamo net energy transfer rates as a function of horizontal spatial scale in the kinematic dynamo phase. Left: work against magnetic tension (pink dashed line) and work against magnetic pressure (green dotted line) as a function of the fluid motion spatial frequency. Right: dynamo stretching (blue dot-dash line), dynamo compression (black solid line), and magnetic energy removed by compression (red dotted line) as a function of the magnetic field spatial frequency. Image reproduced by permission from Pietarila Graham et al. (2010), copyright by AAS.
View Image Figure 8:
Photospheric magnetic field lines showing many low-lying, horizontally directed magnetic structure from a simulation from the upper convection zone to the corona. Image reproduced by permission from Abbett (2007), copyright by AAS.
View Image Figure 9:
Image of Log horizontal B in vertical slice through saturated phase of dynamo simulation of Vögler and Schüssler (2007). Mean optical depth unity is at approximately 0.9 Mm. Note many loops of different sizes closing in the photosphere. Image reproduced by permission from Schüssler and Vögler (2008), copyright by ESO.
Watch/download Movie Figure 10: (mpg-Movie; 37039 KB)
Movie: Log B showing multiple loops and several vertical flux concentrations, one of which has become a pore (see Section 4.4). The movie shows that most of the magnetic features are being pushed down by convective downflows, but some of the loops are rising toward the surface and in places loops have opened out through the top boundary leaving vertical “flux tubes” behind. Movie produced by Sandstrom, CSC, NASA Ames Res. Ctr.
Watch/download Movie Figure 11: (mov-Movie; 270352 KB)
Movie: Rise and emergence of initially uniform, untwisted horizontal magnetic field continuously being advected into the computational domain by inflows in the centers of supergranule cells at the bottom. Left: |B | image and velocity vectors. Right: |B| image and magnetic field vectors both in a vertical plane. The boundary field strength was gradually increased from 0.2 kG with an e-folding time of 5 hrs until it reached 5 kG and thereafter held constant.
Watch/download Movie Figure 11: (mov-Movie; 190181 KB)
Movie: Rise and emergence of initially uniform, untwisted horizontal magnetic field continuously being advected into the computational domain by inflows in the centers of supergranule cells at the bottom. Left: |B | image and velocity vectors. Right: |B| image and magnetic field vectors both in a vertical plane. The boundary field strength was gradually increased from 0.2 kG with an e-folding time of 5 hrs until it reached 5 kG and thereafter held constant.
View Image Figure 12:
Several magnetic field lines showing large scale loops with smaller serpentine loops riding piggy-back on them. Shading shows downflows.
View Image Figure 13:
Time sequence of vertical cross-sections perpendicular to an initial coherent twisted flux tube. The grey scale is temperature and the color coding is magnetic field strength |B |. The purple line is the τ500 = 1. Image reproduced by permission from Cheung et al. (2007), copyright by ESO.
Watch/download Movie Figure 14: (mov-Movie; 106111 KB)
Movie: Time sequence of emergent continuum intensity (left), vertical magnetic field at τRoss = 0.1 (right), for an initial twisted flux half torus driven into the computational domain at 7.5 Mm depth. The initial central field strength was 21 kG and total flux 7.6 × 1021 Mx. The domain is 92 × 49 Mm wide. Image reproduced by permission from Cheung et al. (2010), copyright by AAS.
View Image Figure 15:
Sweeping of magnetic field into intergranular lanes. Initially the entire surface is covered with 30 G horizontal field. Surface magnetic field strength is shown at 0.5 min (left), 10 min (center) and 30 min (right). Black contours are zero velocity contours which outline the granules. Fields stronger than 0.5 kG appear as white and black. Field magnitudes less than 30 G are shown in grey. Diverging upflows first sweep the granules clear of strong fields and on a longer time scale sweep the interiors of mesogranules free of strong fields. Image reproduced by permission from Stein and Nordlund (2006), copyright by AAS.
View Image Figure 16:
Schematic scenario of how granular motions pinch off U-tubes to produce O-loops in 2D and plasmoides in 3D. Image reproduced by permission from Cheung et al. (2010), copyright by AAS.
Watch/download Movie Figure 17: (mov-Movie; 165960 KB)
Movie: Emergent continuum intensity (left) and vertical magnetic field at τcont = 0.01 (right) from simulation with initial/boundary condition of convective inflows advecting 1 kG uniform, untwisted, horizontal field into the computational domain at 20 Mm depth. The intensity range is I∕ ⟨I ⟩ = [0.13,2.5] and the magnetic field range is ± 3.5 kG. The pores may form spontaneously in vertical flux tubes from magnetic loops that have reached the surface and opened out through top boundary. Compare this with Figure 14 for the rise of a coherent twisted flux tube. (Movie shows the initial “pepper and salt” emergence, the horizontal advection of the field, its concentration into unipolar regions with cancellation where opposite polarities meet and merging of like polarities to form pores. Resolution was increased from 48 km to 24 km horizontally at time 51.7 hrs.)
View Image Figure 18:
Magnetic field lines in a simulation snapshot viewed from an angle. The red line in the lower left is horizontal field being advected into the domain. In the lower center is a loop like flux concentration rising toward the surface. In the upper right is a vertical flux concentration or “flux tube” through the surface with its field lines connecting chaotically to the outside below the surface. Image reproduced by permission from Stein and Nordlund (2006), copyright by AAS.
View Image Figure 19:
Magnetic flux concentration at the solar surface and magnetic field lines showing the complex field line connections below the surface. The “flux tube” is a local surface phenomena. Image reproduced by permission from Schaffenberger et al. (2005).
View Image Figure 20:
Emergent continuum intensity as a twisted flux tube emerges through the solar surface. Image reproduced by permission from Yelles Chaouche et al. (2005).
View Image Figure 21:
Radiative heating and cooling (1010 erg/g/s) in a vertical slice through a magnetic flux concentration. The top two panels show the net heating (yellow & red)/cooling (green & blue) with superimposed contours of temperature (top) and magnetic field (next to top). The bottom three panels show the net heating/cooling for vertical (cos𝜃ray,vertical = μ = 1 ), slanted (μ = 0.5), and nearly horizontal rays (μ = 0.05). Image reproduced by permission from Bercik (2002).
View Image Figure 22:
Temperature, density, and magnetic field strength along a vertical slice through magnetic and non-magnetic regions, with the average formation height for the G-band intensity for a vertical ray (black line) and at μ = 0.6 (white line). Axes are distances in Mm. The bottom panel shows temperature as function of lg τ500. Image reproduced by permission from Carlsson et al. (2004), copyright by AAS.
View Image Figure 23:
Schematic sketch of a magnetic flux concentration (region between the thin lines) and adjacent granules (thick lines). The dashed lines enclose the region where 80% of the continuum radiation is formed. Bright facular radiation originates from a thin layer at the hot granule wall behind the limbward side of the optically thin magnetic flux concentration. The line of sight for the dark centerward bands is shown by the dark shaded region. Image reproduced by permission from Keller et al. (2004), copyright by AAS.
View Image Figure 24:
G-band brightness vs. magnetic field strength at continuum optical depth unity for a snapshot of magneto-convection with a unipolar magnetic field. Note that while all bright points correspond to strong magnetic fields there are many locations of strong field that appear dark in the G-band.
View Image Figure 25:
Magnetic field (filled contours at 250 G intervals from 0 G to 3500 G) and temperature (top) (1000 K intervals from 4000 K to 16,000 K), and ln ρ (bottom) (in 0.5 intervals from –2 to 4). The τ = 1 depth is shown as the thick line around z = 0 Mm. The flux concentrations are significantly cooler than their surroundings and so have a smaller scale height. The established, strong “flux tube” in the center has been evacuated and is in equilibrium. The smaller flux concentrations on either side are in the process of being evacuated, starting above the surface and piling up plasma below the surface. Image reproduced by permission from Bercik (2002); Bercik et al. (2003).
View Image Figure 26:
Image of vertical velocity (red/yellow down, blue/green up in km s–1) with magnetic field contours at 0.5 kG intervals at the surface (left) and 1.5 Mm below the surface (right). Image reproduced by permission from Bercik (2002).
View Image Figure 27:
Spontaneously formed simulated pore. Clockwise from upper left: emergent intensity, vertical magnetic field at ⟨τ⟩ = 1, horizontal magnetic field at the same level, inclination angle to the vertical. The pore is edge brightened in part of its circumference. The field is vertical in the pore interior and becomes inclined more than 45° at the pore edge.
View Image Figure 28:
Micropore formation sequence. Left panels: images of the magnetic field strength, center panels: emergent intensity, and right panels: mask showing low intensity, strong field locations. Image reproduced by permission from Bercik (2002) and Bercik et al. (2003).
Watch/download Movie Figure 29: (mpg-Movie; 24372 KB)
Movie: Time sequence of temperature and density fluctuations during pore formation viewed from below (surface is at the bottom). Note the cooler temperatures extending downward from surface, followed by lower densities. Movie produced by Sandstrom, CSC, NASA Ames Res. Ctr.
Watch/download Movie Figure 30: (mpg-Movie; 33906 KB)
Movie: Time sequence of log |B | during pore formation. The flux concentration forms first at the surface and then extends downward. Near the surface the pore’s field is filamentary, but at large depths it becomes mostly coherent. Movie produced by Sandstrom, CSC, NASA Ames Res. Ctr.
Watch/download Movie Figure 31: (mpg-Movie; 15141 KB)
Movie: Emergent intensity and |B | (kG) in opposite polarity spot pair initiated from a pair of axial symmetric, self-similar flaring magnetic field funnels. Each spot has the same flux, but the one on the left has a slightly weaker field. The simulation domain is 98 × 49 Mm by 6 Mm depth. The vertical dimension has been stretched by a factor of 2 in the bottom panel (from Rempel et al., 2009a).
View Image Figure 32:
Vertical slice through an umbral dot. Image is density fluctuation with respect to the surroundings. The solid line is Rossland optical depth unity. The dotted lines are isotherms. The arrows are velocity (longest is 2.7 km/s). Image reproduced by permission from Schüssler and Vögler (2006), copyright by AAS.
View Image Figure 33:
Penumbral field lines color coded by velocity at several locations in a penumbra. Set 1 is in the umbra just adjacent to the penumbral head. Sets 2 – 6 are at increasing radial distance in the penumbra. Velocities are 0 – 2 km/s (red), 2 – 4 km/s (yellow), 4 – 8 km/s (green), > 8 km/s (blue). The cutting plane shows the vertical field magnitude at ⟨τ⟩ = 1. Image reproduced by permission from Rempel (2011), copyright by AAS.
View Image Figure 34:
Work as a function of radius and depth in the penumbra. The contours are where the average outflow is more than 2 and 4 km/s. The Lorentz force accelerates the fluid in the Evershed flow along the penumbral filaments, while in the inner penumbra below the surface there is an approximate balance between pressure and Lorentz forces. Image reproduced by permission from Rempel (2011), copyright by AAS.