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Kepler Eclipsing Binaries with $δ$ Scuti/$γ$ Doradus Pulsating Components 1: KIC 9851944

KIC 9851944 is a short period ($P=2.16$ days) eclipsing binary in the {\it Kepler} field of view. By combining the analysis of {\it Kepler} photometry and phase resolved spectra from Kitt Peak National Observatory and Lowell Observatory, we determine the atmospheric and physical parameters of both stars. The two components have very different radii ($2.27R_{\odot}$, $3.19R_{\odot}$) but close masses ($1.76 M_{\odot}$, $1.79M_{\odot}$) and effective temperatures ($7026$K, $6902$K), indicating different evolutionary stages. The hotter primary is still on the main sequence (MS), while the cooler and larger secondary star has evolved to post-MS, burning hydrogen in a shell. A comparison with coeval evolutionary models shows that it requires solar metallicity and a higher mass ratio to fit the radii and temperatures of both stars simultaneously. Both components show $δ$ Scuti type pulsations which we interpret as p-modes and p and g mixed modes. After a close examination of the evolution of $δ$ Scuti pulsational frequencies, we make a comparison of the observed frequencies with those calculated from MESA/GYRE.