The existence of sunspots has been known since ancient times (Sec. 1.1), but it was only in 1908 that they were found to be the sites of very strong magnetic fields, where huge magnetic flux tubes emerge through the solar surface. In the past ten years, there has been a sea change in understanding due to high-resolution observations of their fine-scale structure from the ground and space (Figures 1.28 and 1.29), as well as an initial probing of subsurface structure by local helioseismology and an increase in computational power that has made much more realistic simulations viable.

Aspects related to sunspots that are covered in this chapter include magnetoconvection and sunspot cooling (Sec. 9.1), intense magnetic flux tubes (Sec. 9.2), magnetic buoyancy (Sec. 9.3), the global equilibrium of sunspots (Sec. 9.4), fine-scale structure of umbra and penumbra (Sec. 9.5), sunspot evolution (Sec. 9.6), and, to conclude, a numerical model that unifies many aspects of sunspots (Sec. 9.7).

In preparation, Sections 1.4.2, 1.7, and 2.9 describe the observed properties and behaviour of photospheric magnetic fields, active regions, sunspots and flux tubes. Excellent accounts can be found in the reviews by Solanki (2003), Thomas and Weiss (2008).

Magnetoconvection

Before tackling sunspots, it is worth summarising magnetoconvection (i.e., thermal convection in a magnetic field). Modelling the convection zone is a formidable task, since the convection is nonlinear, compressible, three-dimensional, unsteady, rotating and threaded by intense flux tubes, while many parameter values are far too extreme to be adopted in computations.