filled their Roche lobes until the time their envelopes were totally eroded. This strongly supports the hypothesis that KOI-71 and KOI-81 are end-states of stable mass-transfer. We note here, however, that Kepler can also discover binaries in which the mass of the core is too large for the donor to have been filling its Roche lobe while in its current orbit. This would be a signature that the binary was a common-envelope survivor. We could then use the current values of the orbital separation and masses to constrain the parameters of the common envelope evolution [Equation (1)]. 

For KOI-74b and KOI-81b, however, there may be reason to suggest that the actual masses are smaller than the values associated with stable mass transfer. R2010 place lower limits on the masses that extend into the brown dwarf regime. In addition, for KOI-74, there is only marginal overlap between R2010 and the stable mass transfer model presented in the last section. It is therefore worth seriously considering that the mass of one or both of these cores may be in the brown dwarf regime. Here we use KOI-74 as an illustrative example. We will show that a value of the core mass smaller than expected from stable mass transfer may be a signal that there was a common envelope, but that the orbit was eccentric at the time the primary filled its Roche lobe. This is expected in some triple systems. It therefore seems inevitable that, whatever the history of KOI-74 and KOI-81, binaries in which the core mass is too low will eventually be found, and the scenario we present below will apply. 

First we note that, even if the core mass of KOI-74 is small, formal solutions to the stable- mass transfer equations exist, predicting 0 . 005 M ⊙ < M$_{c}$ < 0 . 018 M ⊙ and 1 . 2 M ⊙ < M 1 < 2 M ⊙ at the time of Roche-lobe filling. These solutions are not viable, however, because the equilibrium radius of a low-core-mass primary would decline as mass was donated in a steady, stable manner. The second term in Equation (1) would contribute little, and, although the first term might not apply exactly throughout the evolution, the trend of smaller radius with decreasing mass would be followed during phase 2. The orbital period would have to be much smaller than 5 . 2 days. 

If, therefore, KOI-74b is a low-mass stellar core, the binary likely passed through a com- mon envelope phase. Using Equation (2) we find that a$_{i}$ > M 1 /M$_{c}$. Furthermore, dynamical instability requires M 1 be larger than roughly (1 . 3 − 1 . 5) × (2 . 2 M ⊙ ) . This predicts an initial separation so large that the primary could not have filled its Roche lobe. 

This may indicate that the initial orbit was highly eccentric and that a dynamical instability was triggered during periastron. During the common envelope, the eccentricity was eliminated while the semimajor axis became smaller. Such a high eccentricity is not generally expected in a binary in which one companion is poised to fill its Roche lobe, because tidal effects will tend to circularize the orbit. If, however, KOI-74 is a triple, the Lidov-Kozai (Lidov 1961; Kozai 1962) mechanism could have produced the extreme eccentricity that led 

