Core Overshoot: An Improved Treatment and Constraints from Seismic Data

We present a comprehensive set of stellar evolution models for Procyon A inan effort to guide future measurements of both traditional stellar parametersand seismic frequencies towards constraining the amount of core overshoot inProcyon A and possibly other stars. Current observational measurements ofProcyon A when combined with traditional stellar modeling only place a largeupper limit on overshoot of alphaOV < 1.1. By carrying out a detailed pulsationanalysis, we further demonstrate, how p- and g-mode averaged spacings can beused to gain better estimates of the core size. For both p- and g-modes, thefrequency spacings for models without overshoot are clearly separated from themodels with overshoot. In addition, measurements of the l=0 averaged smallp-mode spacings could be used to establish Procyon A's evolutionary stage. Fora fixed implementation of overshoot and under favorable circumstances, theg-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 theunknown treatment of the overshoot region. This ambiguity might be removed byanalyzing many different stars. A simple non-local convection theory developedby Kuhfuss is implemented in our stellar evolution code and contrasted with thetraditional approaches. We show that this theory supports a moderate increaseof 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 onProcyon A's core overshoot extent of ~0.4 Hp which matches the limit imposed byRoxburgh's integral criterion.Comment: 45 pages, 26 figures, accepted in Ap