7.2 Center-to-limb behavior

As one observes towards the limb several differences in the surface appearance occur (Figure 51Watch/download Movie and Figure 11Watch/download Movie). First, the granules develop a three-dimensional pillow appearance with the granules higher than the intergranular lanes (see Figure 10View Image), with their near sides brighter than their far sides. This is partly due to the true three-dimensional structure of granulation, the granules are observed higher than the intergranular lanes. Bright granules have their continuum optical depth unity 80 km above the mean surface. Partly it is due to the near side being seen more normal to the line of sight and the far side at a more glancing angle.

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 (Figure 50View Image). At a given geometric height granules are hotter than the intergranular lanes, which are in turn hotter than G-band bright points, which are hotter than the large magnetic concentrations. Although at a given geometric height the magnetic elements are cooler than the surrounding medium, one sees into deeper layers, due to the reduced opacity, to where the temperature is higher, in part due to heating from the hot surrounding granules (Spruit, 1976Jump To The Next Citation Point1977bJump To The Next Citation PointSchüssler et al., 2003Keller et al., 2004Jump To The Next Citation PointCarlsson et al., 2004Jump To The Next Citation Point). In the G-band there is an additional, smaller, effect that the CH molecule becomes dissociated in the low density magnetic concentrations. The bottom panel of Figure 50View Image shows the temperature as function of lg τ500. The contrast in temperature between magnetic concentrations and non-magnetic areas increases with decreasing optical depth giving larger intensity contrast with increasing opacity (e.g., Ca H,K). The G-band has its mean formation height (black line in bottom panel) at lg τ500 = − 0.48 corresponding to a mean formation height 54 km above where τ500 = 1, therefore giving a larger contrast than in the continuum. The contrast enhancement by the destruction of CH is seen as a dip in the curve showing the mean formation optical depth in the bottom panel. Note also that the G-band intensity has its peak contribution at similar heights as the continuum (that is why the granulation pattern looks similar). Bright points in the G-band have been used as a proxy for magnetic field concentrations. While G-band bright points are a good proxy for strong magnetic fields, there are many more regions of strong field that appear dark in the G-band, typically because they cover a larger area (Figure 52View Image). Occasionally, especially dark micropores form at the vertices of several intergranular lanes. The contrast in the G-band has also been studied by Rutten et al. (2001), Sánchez Almeida et al. (2001), and Steiner et al. (2001).

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Figure 50: 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.

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Figure 51: mov-Movie (8726 KB) G-band images calculated from the simulation at disk center and towards the limb at μ = 0.8, 0.6, 0.4. At disk center small magnetic concentrations appear bright, while larger ones appear dark. When looking toward the limb the granulation appears hilly and one sees the bright walls of granules where the line of sight passes through a low density magnetic concentration. Movie shows time evolution. Note the formation of a micropore near the upper center (movie by Mats Carlsson).
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Figure 52: 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.
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Figure 53: Comparison of G-band intensity at viewing angle μ = 0.63 of observations (left) and at μ = 0.6 simulated (right).

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, 19761977bKeller et al., 2004Jump To The Next Citation PointShelyag et al., 2004Carlsson et al., 2004Jump To The Next Citation Point). Where the fields are strong the intergranular lanes are depressed up to 350 km below the mean height. Thus the τ = 1 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 53View Image) (Keller et al., 2004Jump To The Next Citation PointCarlsson 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 (Figure 54View Image). 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. (2004Jump To The Next Citation Point) 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).

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Figure 54: 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 (Keller et al., 2004).
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Figure 55: Emergent continuum intensity as a twisted flux tube emerges through the solar surface (Yelles Chaouche et al., 2005Jump To The Next Citation Point).

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