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 M1,i = 2.450
Msun, M2,i = 1.034 Msun, and Porb,i ~ 1300 d. We also find that in ~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 Msun and 0.332 Msun, 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.Comment: Accepted for publication in A&A Letters, 4 pages, 2 figure
