2 Global Magnetic Structure

In this section, we will discuss the global structure of the magnetic field vector in sunspots. Even though sunspot’s magnetic fields are organized at very small scales (see, for example, Figures 4View Image8View Image), there are many questions that can be addressed considering mainly its global structure: wave propagation (Khomenko and Collados, 2008; Moradi and Cally, 2008), helioseismology (Moradi et al., 2010Jump To The Next Citation Point; Cameron et al., 2011), extrapolations to obtain the coronal magnetic field (Schrijver et al., 2008; Metcalf et al., 2008; DeRosa et al., 2009). In the former cases, small-scale magnetic structures do not interact with typical helioseimology waves (p and f-modes) because their wavelengths are much larger than the typical sizes of the magnetic structures. In the latter case, small-scale horizontal magnetic structures do not affect the coronal magnetic structure because they produce loops that close at photospheric and chromospheric levels (Wiegelmann et al., 2010).

Other branch where observational inferences of sunspot’s global magnetic structure are needed is in theoretical modeling of sunspots (i.e., magneto-hydrostatic; Low, 1975, 1980; Osherovich and Lawrence, 1983Jump To The Next Citation Point; Pizzo, 1986Jump To The Next Citation Point, 1990Jump To The Next Citation Point; Jahn and Schmidt, 1994b). These models employ the magnetic field configuration inferred from observations as boundary conditions in their equations, as well as employing the observations to validate their final results.

The first section of this chapter will be devoted to study the magnetic field configuration as seen at a constant optical depth or τ-level, whereas the second section will study the vertical variations of the magnetic field. These two can be employed as Dirichlet or Neumann boundary conditions, respectively, in theoretical models and extrapolations. The rest of the sections in this chapter will focus on other issues such as the plasma-β, potentiality of the magnetic field, thermal-magnetic relation, and so forth.

 2.1 As seen at constant τ-level
 2.2 Vertical-τ variations
 2.3 Is the sunspot magnetic field potential?
 2.4 What is the plasma-β in sunspots?
 2.5 Sunspots’ thermal brightness and thermal-magnetic relation
 2.6 Twist and helicity in sunspots’ magnetic field

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