Core Overshoot: An Improved Treatment and Constraints from Seismic Data

Abstract

We present a comprehensive set of stellar evolution models for Procyon A in an effort to guide future measurements of both traditional stellar parameters and seismic frequencies toward constraining the amount of core overshoot in Procyon A and possibly other stars. Current observational measurements of Procyon A when combined with traditional stellar modeling only place a large upper limit on overshoot of αOV < 1.1. By carrying out a detailed pulsation analysis, we further demonstrate how p- and g-mode averaged spacings can be used to gain better estimates of the core size. For both p- and g-modes, the frequency spacings for models without overshoot are clearly separated from the models with overshoot. In addition, measurements of the l = 0 averaged small p-mode spacings could be used to establish Procyon A's evolutionary stage. For a fixed implementation of overshoot and under favorable circumstances, the g-mode spacings can be used to determine the overshoot extent to an accuracy of ±0.05HP. However, we stress that considerable confusion is added due to the unknown treatment of the overshoot region. This ambiguity might be removed by analyzing many different stars. A simple nonlocal convection theory developed by Kuhfuss is implemented in our stellar evolution code and contrasted with the traditional approaches. We show that this theory supports a moderate increase of the amount of convective overshoot with stellar mass of ΔαOV +0.10 between 1.5 and 15 M☉. This theory places an upper limit on Procyon A's core overshoot extent of ~0.4HP, which matches the limit imposed by Roxburgh's integral criterion.