4.3 Small scale flux concentrations

Magnetic concentrations arise from loops emerging into the upper solar atmosphere and leaving their legs behind and from the diverging convective upflows which sweep magnetic field into the intergranular lanes and concentrate the field into sheets and at the vertices of the lanes into “tubes” of magnetic flux (Vögler et al., 2005Jump To The Next Citation Point; Schaffenberger et al., 2005; Stein and Nordlund, 2006Jump To The Next Citation Point). To maintain force balance, locations of higher field strength (higher magnetic pressure) tend to have smaller plasma density and lower gas pressure. Strong magnetic fields, through the Lorentz force, inhibit overturning convective motions and hence the transport of energy toward the surface. Radiative energy loss to space continues, so regions of strong field cool relative to their surroundings at the same geometric layer. Being cooler, these locations have a smaller scale height. Plasma drains out of the magnetic field concentrations in a process called “convective intensification” or “convective collapse” (Parker, 1978; Spruit, 1979; Unno and Ando, 1979; Nordlund, 1986; Bercik et al., 1998; Grossmann-Doerth et al., 1998; Bushby et al., 2008). This process continues until the magnetic pressure (plus a small gas pressure) inside the flux concentration approximately equals the gas pressure outside, giving rise to a field strength much greater than the equipartition value with the dynamic pressure of the convective motions.
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 (2002Jump To The Next Citation Point).

The opacity of magnetic flux concentrations is reduced, because they are evacuated, so photons escape from deeper in the atmosphere, that is, optical depth surfaces are depressed into the interior (Wilson depression, Maltby, 2000). Radiatively, they are holes in the surface. The temperature structure in these concentrations is nearly in radiative equilibrium with radiative heating from fluid flowing down along their sides and cooling from emission in vertical rays (Bercik, 2002Jump To The Next Citation Point, Figure 21View Image). Where the flux concentration is narrow, heating from the side walls raises the internal temperature at optical depth unity and the concentration appears bright (Spruit, 1976Jump To The Next Citation Point). Small magnetic flux concentrations may appear especially bright in the continuum (Bercik, 2002Jump To The Next Citation Point; Keller et al., 2004Jump To The Next Citation Point; Carlsson et al., 2004Jump To The Next Citation Point; Steiner, 2010). This enhanced brightness extends for all the sight lines that pass through the low density, optically thinner, magnetic concentration where photons escape from deeper, hotter layers (Figures 22View Image and 23View Image). Where the concentrations are wide, the side wall heating is not significant and the flux concentrations appear darker than the surroundings as pores or sunspots.

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. (2004Jump To The Next Citation Point), 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.

In the G-band there is an additional, smaller, effect – the CH molecule becomes dissociated in the low density magnetic concentrations (Steiner et al., 2001Jump To The Next Citation Point; Carlsson et al., 2004; Shelyag et al., 2004; Steiner, 2005). The bottom panel of Figure 22View Image shows the temperature as function of lgτ500. 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 lgτ500 = − 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 24View Image). In simulations, all the bright points correspond to locations of large field magnitude, but not all large field locations correspond to bright points (Vögler et al., 2005Jump To The Next Citation Point; Stein and Nordlund, 2006Jump To The Next Citation Point). Further, the field has a longer lifetime than the bright points. 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).


  Go to previous page Go up Go to next page