Mode Mixing and Rotational Splittings. II. Reconciling Different Approaches to Mode Coupling

Abstract In the mixed-mode asteroseismology of subgiants and red giants, coupling between p- g- mode cavities must be understood well in order to derive localized estimates interior rotation from measurements multiplet rotational splittings. There exist now two different descriptions this coupling: one based on an asymptotic quantization condition, other arising matrices associated with “acoustic molecular orbitals.” We examine analytic properties both, closed-form expressions for various quantities—such as period-stretching function τ —which previously had solved numerically. Using these, we reconcile both formulations first time, deriving relations by which quantities each formulation may translated interpreted within other. This yields information criterion whether a given configuration mixed modes meaningfully constrain parameters construction, is likely not satisfied majority first-ascent giant stars our observational sample. Since construction has been already used make such examine—through hare-and-hounds exercise—whether, how, limitations affect these existing measurements. While averaged core seem fairly robust, template-matching using difficulty reliably assigning splittings individual multiplets, or estimating mixing fractions ζ most p -dominated modes, where are needed. finally discuss implications extending two-zone model radial differential rotation, e.g., via inversions, methods.