Can Asteroseismic Structure Inversions Be Performed in Structure-Dependent Coordinates?

Yes. Unlike other applications of observational asteroseismology, "structure inversions" constrain the physical properties of stellar interiors in a model-independent fashion. However, existing techniques -- which parameterise these quantities as functions of the physical radial or mass coordinate -- break down when applied to stars which differ substantially from the Sun. These difficulties may be overcome by operating in coordinate systems that have long been known to more naturally suit the physical characteristics of the measured normal modes. We derive expressions for transforming inversion kernels in the acoustic and buoyancy radial coordinates, rather than in the physical radius, and make available a numerically performant implementation. These modified inversions directly address several specific known shortcomings of existing inversion procedures. Using the buoyancy radius in gravity-mode and mixed-mode pulsators permits meaningful comparisons of stars and models with differently-sized convective and radiative zones, which defeat standard inversions. Even in pressure-mode oscillators, inversions in the acoustic radial coordinate eliminate the methodological requirement for the mass and radius of the true star being needed to be known in advance.