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Post-common-envelope binaries (PCEBs) have been frequently used toobservationally constrain models of close-compact-binary evolution, inparticular common-envelope (CE) evolution. However, recent surveys havedetected PCEBs consisting of a white dwarf (WD) exclusively with an M dwarfcompanion. Thus, we have been essentially blind with respect to PCEBs with moremassive companions. Recently, the second PCEB consisting of a WD and a G-typecompanion, the spectacularly self-lensing binary KOI-3278, has been identified.This system is different from typical PCEBs not only because of the G-typecompanion, but also because of its long orbital period. Here we investigatewhether the existence of KOI-3278 provides new observational constraints ontheories of CE evolution. We reconstruct its evolutionary history and predictits future using BSE, clarifying the proper use of the binding energy parameterin this code. We find that a small amount of recombination energy, or any othersource of extra energy, is required to reconstruct the evolutionary history ofKOI-3278. Using BSE we derive progenitor system parameters of M1,i = 2.450Msun, M2,i = 1.034 Msun, and Porb,i ~ 1300 d. We also find that in ~9 Gyr thesystem will go through a second CE phase leaving behind a double WD, consistingof a C/O WD and a He WD with masses of 0.636 Msun and 0.332 Msun, respectively.After IK Peg, KOI-3278 is the second PCEB that clearly requires an extra sourceof energy, beyond that of orbital energy, to contribute to the CE ejection.Both systems are special in that they have long orbital periods and massivesecondaries. This may also indicate that the CE efficiency increases withsecondary mass.

The evolution of the self-lensing binary KOI-3278: evidence of extra energy sources during CE evolution