Stellar Surfaces in the Frequency Domain

Abstract

The analysis and interpretation of stellar oscillations — asteroseismology — illuminates a vast and diverse range of physical and astronomical phenomena. In particular, convectively excited pressure waves (p-modes), like those seen in the Sun, permit strong constraints on both the global properties and interior structures of cool stars. However, our efforts to reconcile asteroseismic observations with astrophysical theory are hindered by methodological systematic errors, associated with deficiencies in numerical treatments of stellar surfaces — the asteroseismic "surface term". These errors must be corrected for in the process of performing such analysis. 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. I show that while different prescriptions for correcting solar-like p-modes perform similarly on Sun-like main sequence stars, they return qualitatively different characteristics when applied to these evolved stars. Moreover, foundational assumptions underlying these prescriptions cease to be applicable for these evolved stars, on account of their different internal structures, rendering them ontologically questionable. Whereas the helioseismic techniques in question borrow heavily from the quantum mechanics of atomic systems, I 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 develop a novel theoretical decomposition of the wave operator in these evolved stars, explore the properties of this new construction, and outline explicit methodological generalisations of existing asteroseismic surface-correction techniques for evolved stars that are both theoretically and numerically defensible. I demonstrate that the use of these new methods is necessary, in order to avoid systematic errors, when measuring stellar properties using mixed-mode asteroseismology.