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We present a three-dimensional (3D) study of common envelope events (CEEs) toprovide a foundation for future one-dimensional (1D) methods to model theself-regulated phase of a CEE. The considered CEEs with a low-mass red giantend with one of three different outcomes -- merger, slow spiral-in, or promptformation of a binary. To understand which physical processes determinedifferent outcomes, and to evaluate how well 1D simulations model theself-regulated phase of a CEE, we introduce tools that map our 3D models to 1Dprofiles. We discuss the differences in the angular momentum and energyredistribution in 1D and 3D codes. We identified four types of ejectionprocesses: the pre-plunge-in ejection, the outflow during the plunge-in, theoutflow driven by recombination, and the ejection triggered by a contraction ofthe circumbinary envelope. Significant mass is lost in all cases, including themergers. Therefore a self-regulated spiral-in can start only with a stronglyreduced envelope mass. We derive the condition to start a recombinationoutflow, which can proceed either as a runaway or a stationary outflow. We showthat the way the energy of the inspiraling companion is added to the envelopein 1D studies intensifies the envelope's entropy increase, alters the start ofthe recombination outflow, and leads to different outcomes in 1D and 3Dstudies. The steady recombination outflow may dispel most of the envelope inall slow spiral-in cases, making the existence of a long-term self-regulatedphase debatable, at least for low-mass giant donors.

Common envelope events with low-mass giants: understanding the transition to the slow spiral-in