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

Context. It has been claimed for more than a decade that energies other than orbital and thermodynamic internal are required to explain post-common envelope (CE) binaries with sufficiently long orbital periods (greater than or similar to 1 d) hosting AFGK-type main-sequence stars (similar to 0.5 - 2.0 M-circle dot) paired with oxygen-neon white dwarfs (greater than or similar to 1.1 M-circle dot). This would imply a completely different energy budget during CE evolution for these post-CE binaries in comparison to the remaining systems hosting M dwarfs and/or less massive white dwarfs. Aims. In this first in a series of papers related to long-period post-CE binaries, we investigated whether extra energy is required 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. Methods. We carried out binary population simulations with the BSE code adopting empirically derived inter-correlated main-sequence binary distributions for the initial binary population and assuming that the only energy, in addition to orbital, that help to unbind the CE is thermal energy. We also searched for the formation pathways of the currently known systems from the zero-age main-sequence binary to their present-day observed properties. Results. 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 one thousand days can be explained. For all known systems we found formation pathways consisting of CE evolution triggered when a highly evolved (i.e. when the envelope mass is 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. Conclusions. 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.