Abstract

Post-common-envelope binaries (PCEBs) have been frequently used to observationally constrain models of close-compact-binary evolution, in particular common-envelope (CE) evolution. However, recent surveys have detected PCEBs consisting of a white dwarf (WD) exclusively with an M dwarf companion. Thus, we have been essentially blind with respect to PCEBs with more massive companions. Recently, the second PCEB consisting of a WD and a G-type companion, the spectacularly self-lensing binary KOI-3278, has been identified. This system is different from typical PCEBs not only because of the G-type companion, but also because of its long orbital period. Here we investigate whether the existence of KOI-3278 provides new observational constraints on theories of CE evolution. We reconstruct its evolutionary history and predict its future using BSE, clarifying the proper use of the binding energy parameter in this code. We find that a small amount of recombination energy, or any other source of extra energy, is required to reconstruct the evolutionary history of KOI-3278. Using BSE we derive progenitor system parameters of M-1, = 2.450 M-circle dot, M-2,M-1 = 1.034 M-circle dot, and P-orb, similar to 1300 d. We also find that in similar to 9 Gyr the system will go through a second CE phase leaving behind a double WD, consisting of a C/O WD and a He WD with masses of 0.636 M-circle dot and 0.332 M-circle dot, respectively. After IK Peg, KOI-3278 is the second PCEB that clearly requires an extra source of energy, beyond that of orbital energy, to contribute to the CE ejection. Both systems are special in that they have long orbital periods and massive secondaries. This may also indicate that the CE efficiency increases with secondary mass.