Common envelope events with low-mass giants: understanding the energy budget

Common envelope events are important interactions between two binary stars that lead to the formation of close binary systems. We present here a systematic three-dimensional study in which we model common envelope events with low-mass giant donors. The results allow us to revise the energy formalism that is usually used to determine common envelope event outcomes. We show that the energy budget for this type of system should include the recombination energy, and that it also must take into account that a significant fraction of the released orbital energy is taken away by the ejecta. We provide three ways in which our results can be used by binary population synthesis studies: a relation that links the observed post-common envelope binary with the initial binary parameters, a fitting formula for the $\alpha_{\rm ce}\lambda$ parameter of the standard energy formalism, and a revised energy formalism that takes into account both the recombination energy and the energy that is taken away by the ejecta.