Structural and Evolutionary Diagnostics from Asteroseismic Phase Functions

In the asymptotic parameterisation of mode frequencies, the phase function $epsilon( u)$ completely specifies the detailed structure of the frequency eigenvalues. In practice, however, this function of frequency is reduced to a single scalar $epsilon$, defined, particularly by observers, as the intercept of a least-squares fit to the frequencies against radial order, or via the central value of this function. The procedure by which this is done is not unique. We derive a few simple expressions relating various observational estimators of $epsilon$ for radial modes to each other, and to the underlying theoretical object. In particular we demonstrate that a ``reduced functional parameterisation is both insensitive to mis-estimations of $Delta u$, and easy to evaluate locally in terms of both observational and theoretical quantities. It has been shown previously that such a local definition of $epsilon$ can distinguish between stars on the ascending part of the red giant branch and those in the red clump. We find that this sensitivity to evolutionary stage arises from differences in the local frequency derivative of the underlying phase function, a consequence of differences in internal structure. By constructing an HR-like diagram out of purely seismic observables, we provide a unified view of the textit{Kepler} asteroseismic sample, as well as the initial results from textit{TESS}. We investigate how various astrophysical quantities and modelling parameters affect the morphology of isochrones on this seismic diagram. We also show that $epsilon$ can be used as an independent input when deriving stellar parameters from global asteroseismic quantities.

Modeling Convective Core Overshoot and Diffusion in Procyon Constrained by Asteroseismic Data

We compare evolved stellar models, which match Procyons mass and position in the HR diagram, to current ground-based asteroseismic observations. Diffusion of helium and metals along with two conventional core overshoot descriptions and the Kuhfuss nonlocal theory of convection are considered. We establish that one of the two published asteroseismic data reductions for Procyon, which mainly differ in their identification of even versus odd l-values, is a significantly more probable and self-consistent match to our models than the other. The most probable models according to our Bayesian analysis have evolved to just short of turnoff, still retaining a hydrogen convective core. Our most probable models include Y and Z diffusion and have conventional core overshoot between 0.9 and 1.5 pressure scale heights, which increases the outer radius of the convective core by between 22% to 28%, respectively. We discuss the significance of this comparatively higher than expected core overshoot amount in terms of internal mixing during evolution. The parameters of our most probable models are similar regardless of whether adiabatic or nonadiabatic model p-mode frequencies are compared to the observations, although, the Bayesian probabilities are greater when the nonadiabatic model frequencies are used. All the most probable models (with or without core overshoot, adiabatic or nonadiabatic model frequencies, diffusion or no diffusion, including priors for the observed HRD location and mass or not) have masses that are within one sigma of the observed mass 1.497+/-0.037 Msun.