the post-CE core is an important problem in itself. We should stress that there is no strong constraint from either observations or theory which dictates that the post-CE remnant immediately after the dynamical event will have the exact same mass as the WD companion that is observed much later. As such, the mass of a post-CE remnant could be anywhere between our minimum and maximum core-mass definitions. A stronger constraint on the post-CE core mass is proposed in [@IvaCha09; @Ivanova10].

The solid line in Fig.\[alpha\] represents the *closest possible orbit* from Roche-radius considerations: only the states below the solid line are possible, and the actual state depends on the degree of the post-CE detachment. Only the strip bounded from above by the thick solid line and lying within the shaded region is permitted for a self-consistent final post-CE binary. We note from the Fig \[alpha\] that, depending on the choice of the post-CE remnant mass, the minimum possible semi-major axis of the post-CE binary can vary by a factor of 30.

The post-CE binary can not have more energy than the initial binary and still satisfy conservation of energy (see dashed-dotted green line on Fig. \[alpha\]), since some energy must 