p-mode interaction with sunspots

This chapter brings together two of the prominent features of our star the Sun: its well-developed p-mode spectrum of global oscillations excited by near-surface convection, and its magnetic activity famously represented by sunspots. Modern developments in observations of p-mode and sunspot magnetic field interactions have helped bridge the gap between theory and observations: both the oscillations within a sunspot and in the immediate surroundings of the sunspot appear to be due to magnetohydrodynamics waves driven by p-modes with characteristic spatial patterns of frequencies intimately related to magnetic inclination and the height variation of the plasma p = 1 layer. The chapter makes the case that the behavior of waves in sunspots is dominated by four processes: the ramp effect; fast-to-slow mode conversion; fast-wave reflection; and fast-to-Alfvén mode conversion. The chapter then discusses some of the major developments in helioseismic forward and inverse modeling that have occurred over the last decade.