Mixed Modes in Theory and Practice
Studies of the Sun’s interior through the analysis and interpretation of its p-mode oscillations — helioseismology — have illuminated a vast and diverse range of physical and astronomical phenomena. Aside from the Sun, measurements of solar-like p-modes are easiest for post-main-sequence stars; subgiants and red giants now constitute the majority of our seismic observations. However, foundational assumptions underlying helioseismology cease to be applicable for these evolved stars, on account of their different internal structures, rendering them impenetrable to analysis of a similar kind. Whereas the helioseismic techniques in question borrow heavily from the quantum mechanics of atomic systems, I will demonstrate that oscillations in these giants — which possess mixed p-mode and g-mode character — behave like acoustic “molecules”, rather than atoms, and therefore demand the adaptation of techniques from quantum chemistry instead. I describe two applications of this construction to constraining stellar properties by forward modelling. First, I will show that it permits the correction of systematic errors resulting from deficiencies in numerical models of stellar surfaces. I will also use it to describe the nonlinear effects of radial differential rotation on these mixed modes: left unaccounted for, these may yield erroneous diagnoses and measurements of buried magnetic fields.