Common envelope binary interactions: how much does the orbit shrink?

The common envelope binary interaction takes place when an expanding giant engulfs its companion. The result is dramatic orbital shrinkage, which may bring the two stars to merge. However, if enough energy is transferred to the envelope, sufficient gas is ejected from the system that the core of the giant and the companion survive as a compact binary. This mechanism results in the formation of cataclysmic variables, the progenitor of type Ia supernovae, compact neutron star and black hole binaries and more. Critical to our understanding of these compact binaries and their merger rates (SN Ia rates, gravitational wave event rates...) is how much orbital shrinkage takes place. A prediction of this quantity has eluded us, despite increased efforts. We present 3D hydrodynamic simulations with improved physics (addition of recombination energy and dust) and, following the technique of Iaconi and De Marco (2019), we remark on what this new generation of simulations conveys on the topic if the common envelope efficiency parameter, which is traditionally used to parametrise the interaction and determine the final post-CE separation. Finally we revise the technique to determine the orbital shrinkage from observations of binary central stars of planetary nebulae, something that, hand in hand with simulations can provide some constraints.