Jacket modes: Solar acoustic oscillations confined to regions surrounding sunspots and plage

It is demonstrated by the application of classical eigenfunction expansion techniques that the interaction of an incident solar acoustic oscillation, or p-mode, with a scattering obstacle - such as a sunspot - involves not only the scattering of the incident p-mode into other p-modes of like frequency (mode mixing), but also the generation of an acoustic halo localized like a "jacket" about the scatterer. This halo oscillates at the same frequency as the incident p-mode and is composed of a superposition of a continuous spectrum of modes referred to as jacket modes. It is pointed out that these jacket modes should appear as a broad enhancement to the background power underlying the p-mode ridges in k-ω diagrams for regions in close proximity to sunspots and the boundaries of plage. The basic results draw upon a remarkable analogy between the oscillations of an adiabatically stratified plane-parallel polytrope and the wave functions for the hydrogen atom: the laterally propagating p-modes that participate in the mode mixing correspond to the negative-energy bounds states of the hydrogen atom, while the continuous spectrum of jacket modes corresponds to the continuum of positive-energy states in which the electron is not bound to the proton.