Core Overshoot: An Improved Treatment and Constraints from Seismic Data

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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 towards 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 alphaOV < 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 +-0.05 Hp. 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 non-local 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 Delta(alphaOV) = +0.10 between 1.5 Msun and 15 Msun. This theory places an upper limit on Procyon A's core overshoot extent of ~0.4 Hp which matches the limit imposed by Roxburgh's integral criterion.
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