Close double neutron stars have been observed as Galactic radio pulsars, while their mergers have been detected as gamma-ray bursts and gravitational-wave sources. They are believed to have experienced at least one common-envelope episode during their evolution prior to double neutron star formation. In the last decades there have been numerous efforts to understand the details of the common-envelope phase, but its computational modelling remains challenging. We present and discuss the properties of the donor and the binary at the onset of the Roche-lobe overflow leading to these common-envelope episodes as predicted by rapid binary population synthesis models. These properties can be used as initial conditions for detailed simulations of the common-envelope phase. There are three distinctive populations, classified by the evolutionary stage of the donor at the moment of the onset of the Roche-lobe overflow: giant donors with fully-convective envelopes, cool donors with partially-convective envelopes, and hot donors with radiative envelopes. We also estimate that, for standard assumptions, tides would not circularise a large fraction of these systems by the onset of Roche-lobe overflow. This makes the study and understanding of eccentric mass-transferring systems relevant for double neutron star populations.
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