Post-common envelope evolution of helium-core white dwarfs⋆

Context. Helium-core white dwarfs (He WDs) from the common envelope (CE) channel offer insights into binary evolution and compact remnant formation. Their cooling rates influence their detectability and affect age estimates of close binaries. Compared with those from stable Roche-lobe overflow (SRLOF), CE He WDs experience a distinct mass-loss history, leading to fundamental differences in the post-CE evolution of the resulting WDs.Aims. We investigate how the H-envelope mass (M_{H) affects the cooling evolution of CE He WDs. In particular, we analyze how the bifurcation point, which separates the degenerate He core from the envelope, determines the remaining MH and the presence of residual H burning.Methods. We computed evolutionary sequences for He WDs of 0.20 M⊙ to 0.42 M⊙, from a 1 M⊙ progenitor on the red giant branch. Using the La Plata stellar evolution code (LPCODE), we followed their evolution from the post-CE phase to the cooling track, identifying two pathways depending on the remaining H: (i) non-flashing sequences, in which WDs cool without prior nuclear burning, and (ii) flashing sequences, in which H shell flashes reshape the envelope before cooling.Results. CE He WDs with minimal MH cool rapidly after formation, with negligible residual H burning. For a sample with Teff between 12 000 and 27 000 K, our models predict ages of 5–130 Myr, increasing to slightly above 300 Myr for Teff<10 000 K, which is much younger than those from SRLOF sequences. In contrast, WDs with more MH sustain residual nuclear burning, delaying cooling. At Teff<10 000 K, these models predict ages of several Gyr, far exceeding those from SRLOF and minimal-envelope sequences. Flashing sequences significantly extend the pre-WD phase compared to non-flashing sequences, but this phase remains much shorter than in SRLOF evolution. The amount of MH also affects mass and surface gravity estimates, introducing systematic differences from SRLOF WDs at a given Teff.Conclusions. The evolutionary paths of CE He WDs differ significantly from those of SRLOF-produced WDs. Minimal-envelope CE WDs cool rapidly and merge at lower temperatures, while those with sustained H burning remain bright for longer and merge at higher temperatures. These differences with SRLOF WDs are critical for understanding the evolutionary history and final fate of He WDs in compact binaries.}