Common-envelope phases are decisive for the evolution of many binary systems. Of particular interest are cases with asymptotic giant branch (AGB) primary stars, because they are thought to be progenitors of various astrophysical transients. In three-dimensional hydrodynamic simulations with the moving-mesh code AREPO, we study the common-envelope evolution of a $1.0,M_{odot}$ early-AGB star with companions of different masses. Although the stellar envelope of the AGB star is less tightly bound than that of a red giant, we find that the release of orbital energy of the core binary is insufficient to eject more than about twenty percent of the envelope mass. Ionization energy released in the expanding envelope, however, can lead to complete envelope ejection. Because recombination proceeds largely at high optical depths in our simulations, it is likely that this effect indeed plays a significant role in the considered systems. The efficiency of mass loss and the final orbital separation of the core binary system depend on the mass ratio between the companion and the primary star. Our results suggest a linear relation between the ratio of final to initial orbital separation and this parameter.
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