KIC 12268220: A $\delta$ Scuti Pulsating Star and an Active Protohelium White Dwarf in an Eclipsing Binary System

We present a photometric, spectroscopic, asteroseismic, and evolutionary analysis of the Algol-type eclipsing binary KIC 12268220. We find the O'Connell effect and anticorrelated eclipse timing variations in the Kepler light curve, revealing the presence of large starspots. Radial velocities and atmospheric parameters are obtained from ground-based spectroscopic observations. Combined with the radial velocity measurements and Gaia-derived total luminosity, our light-curve modeling yields the solution of the physical parameters for both the primary and secondary components. We find 14 independent frequencies arising from the $\delta$ Scuti primary, and the observed frequencies agree with the frequency range of unstable modes from nonadiabatic calculations. Based on the conclusion from previous literature, we run a grid of models to study the evolution process of our system. The evolutionary tracks of our model suggest that the low-mass ($\sim 0.23\,M_\odot$) evolved secondary shows a similar evolutionary state to the R CMa-type system, which might evolve to an EL CVn system.