The solar surface is covered with magnetic features with spatial scales from smaller than can currently be resolved ( 70 km with the Swedish 1 m Solar Telescope) to active regions covering up to 100 Mm (Figure 1). These evolve on a correspondingly wide range of time scales, from seconds for the smallest observed features, to months for some active regions. If one counts as a single feature any contiguous collection of the same polarity with magnitude above some cutoff, then the magnetic flux distribution is a power law of slope –1.85 (Figure 2). Alternatively, if one identifies features as individual flux peaks, then the distribution is log-normal (Parnell et al., 2009; Thornton and Parnell, 2011). These power laws are featureless, they have no peaks or valleys.
The large-scale magnetic structures, sunspots, and active regions possess some well defined global properties: all active regions in a given hemisphere have the same polarities of leading/following spots, but reversed between the northern and southern hemispheres (Hale’s polarity law); the polarities reverse in a semi-periodic 22 year cycle; in each cycle spots first appear at mid latitudes and then their appearances migrate toward the equator; active regions are tilted with the leading spot closer to the equator (Joy’s law); trailing spot fields migrates toward the poles and sunspots tend to reappear at certain active longitudes (Figure 3). See review by Hathaway (2010). These properties imply the existence of a global dynamo process.
There is an excellent review of small-scale solar magnetic field observations (network and internetwork quiet Sun) by de Wijn et al. (2009). The main observational results are: strong fields tend to be vertical and weaker fields horizontal. Vertical kilogauss fields (in pressure equilibrium with their surroundings) are found in the magnetic network and as isolated, intermittent concentrations in intergranular lanes. Horizontal magnetic fields are found all over the Sun (Trujillo Bueno et al., 2004; Harvey et al., 2007), predominantly inside and near the edges of granules. They are transient, intermittent and have granule-scale sizes and lifetimes and strengths in the hectogauss range (generally less than equipartition with the convective dynamic pressure) (Ishikawa and Tsuneta, 2010). Weaker horizontal fields have no preferred orientation. Stronger ones tend to align with the active regions. The horizontal field properties are similar in the quiet Sun, plage, and polar regions (Ishikawa and Tsuneta, 2009). The spatially averaged horizontal magnetic field strength is 50 – 60 G, while the spatially averaged vertical field strength is only 11 G (Lites et al., 2008). This may be due to the larger area covered by horizontal fields compared to the isolated vertical field concentrations. There is no characteristic size or lifetime for the horizontal fields (they have an exponential distribution both in size and lifetime) (Danilovic et al., 2010). There is some question of the accuracy of Hinode determinations of quiet Sun transverse magnetic fields due to s/n problems (Borrero and Kobel, 2011).
Bright points in the G-band (dominated by CH molecular transitions) have been used as proxies for the magnetic field. At disk center small magnetic concentrations appear as bright points in the intergranular lanes, while larger concentrations are dark. The increased brightness in magnetic concentrations is due to their lower density compared with their surroundings. At a given geometric height, granules are hotter than the intergranular lanes, which are, in turn, hotter than G-band bright points. Although at a given geometric height the magnetic elements are cooler than the surrounding medium, one sees into deeper layers, to where the temperature is higher, due to the reduced opacity and to heating from the hot surrounding granules. Locations of large magnetic concentrations are cooler than even the G-band bright points because both convective heat transport and side wall heating are reduced.
The presence of strong magnetic fields enhances the pillow appearance of granules because their low density and resulting low opacity allow one to see deeper into the hot granules behind them (the “hot wall” effect Spruit, 1976, 1977; Keller et al., 2004; Shelyag et al., 2004; Carlsson et al., 2004). Where the fields are strong, the intergranular lanes are depressed up to 350 km below the mean height. Thus the surface is extremely corrugated. Toward the limb, where the surface is viewed at an angle, the low density and opacity in the strong magnetic elements allows one to see the hot granule walls behind. These are the faculae (Figure 4) (Keller et al., 2004; Carlsson et al., 2004). The excess brightness comes from a thin layer ( 30 km) of steep density gradient at the interface between the magnetic and nonmagnetic atmospheres. Typically there is a dark lane just centerward of the bright faculae. As the line of sight moves limbward from granule to faculae, it first intersects a granule top and is bright, then intersects cool material above the granule and inside the magnetic concentration, and finally intersects the hot granule wall on the far side of the magnetic concentration. Variations in the field strength produces variations in the density and opacity which leads to a striated appearance in the bright granule walls. Where the field is weaker, the density is higher, so the opacity larger. This effect is enhanced by a higher CH concentration also due to the higher density. Thus, where the magnetic field is weaker, the radiation emerges from higher, cooler layers, so these locations appear darker.
High resolution observations of solar faculae show that they have an asymmetric contrast profile, with some brightness extending up to one arcsecond in the limbward direction from their peak in brightness (Hirzberger and Wiehr, 2005). The wide contrast profile cannot be explained solely by the “hot wall” effect, as was noted by Lites et al. (2004). The works by Keller et al. (2004) and Steiner (2005) address this issues, with somewhat conflicting but broadly consistent explanations. One conclusion is that the limbward extension of brightness comes from seeing the granule behind the facular magnetic field through the rarefied facular magnetic flux concentration; a circumstance that observers suspected decades ago. The explanation is corroborated by the direct comparisons of observations and simulations by De Pontieu et al. (2006).
Three orders of magnitude more magnetic flux is observed to emerge as small scale loops in the quiet Sun than emerges in active regions (Thornton and Parnell, 2011). This new flux is first seen as horizontal field (linear polarization in Stokes spectra) inside granules followed by the appearance of vertical field at the ends of the horizontal field (circular polarized Stokes spectra) (Centeno et al., 2007; Martínez González and Bellot Rubio, 2009; Ishikawa et al., 2010; Guglielmino et al., 2012) (Figure 5).
These -loop footpoints get quickly swept into the intergranular lanes and the horizontal field to the edges of the granules. They do not show a helical structure. Transient horizontal fields also appear briefly where new downflow lanes form (Danilovic et al., 2010). The flux in these emerging bipoles is small, 1016 – few × 1017 Mx, but their rate of appearance is large, around a few × 10–10 km2 s, hence their dominant contribution to the emerging flux of the Sun (Martínez González and Bellot Rubio, 2009; Ishikawa and Tsuneta, 2009; Ishikawa et al., 2010). Most of these small loops are low lying, with only about a quarter reaching up to chromospheric heights.
Living Rev. Solar Phys. 9, (2012), 4
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