Formation of long-period post-common-envelope binaries I. No extra energy is needed to explain oxygen-neon white dwarfs paired with AFGK-type main-sequence stars

In this first in a series of papers related to long-period post-common-envelope (CE) binaries, we investigated whether extra energy is required or not to explain the currently known post-CE binaries with sufficiently long orbital periods consisting of oxygen-neon white dwarfs with AFGK-type main-sequence star companions. We carried out binary population simulations with the BSE code and searched for their formation pathways. Unlike what has been claimed for a long time, we show that all such post-CE binaries can be explained by assuming inefficient CE evolution, which is consistent with results achieved for the remaining post-CE binaries. There is therefore no need for an extra energy source. We also found that for CE efficiency close to 100 post-CE binaries hosting oxygen-neon white dwarfs with orbital periods as long as a thousand days can be explained. For all known systems we found formation pathways consisting of CE evolution triggered when a highly evolved (i.e. the envelope mass being comparable to the core mass) thermally-pulsing asymptotic giant branch star fills its Roche lobe at an orbital period of several thousand days. Due to the sufficiently low envelope mass and sufficiently long orbital period, the resulting post-CE orbital period can easily be several tens of days. We conclude that the known post-CE binaries with oxygen-neon white dwarfs and AFGK-type main-sequence stars can be explained without invoking any energy source other than orbital and thermal energy. Our results strengthen the idea that the most common formation pathway of the overall population of post-CE binaries hosting white dwarfs is through inefficient CE evolution.