Two hot pre-white dwarfs inside the red giant branch planetary nebula Pa 13. Double-core evolution or common-envelope-induced rejuvenation

The close binary central stars of planetary nebulae (PNe) offer a unique window for investigating the conditions that immediately follow the ejection of a common envelope (CE). Double-eclipsing and double-lined double systems are particularly valuable as they provide minimally model-dependent constraints on fundamental binary parameters. In this context, we report that the nucleus of Pa 13 (P=0. 3988, d) belongs to this rare class of systems and we present a comprehensive analysis of its double-degenerate binary. We performed a two-component nonlocal thermodynamic equilibrium spectral analysis based on phase-resolved X-shooter spectroscopy, multiband light-curve modeling, spectral energy distribution fitting, and a kinematic analysis. Both stars are found to be hot pre-white dwarfs, with Star 1 being cooler but larger (, R=0. 40 50. 0 than Star 2 (, R=0. 16 75. 0 The weakness of the spectral lines of Star 2 made both the atmospheric and radial velocity (RV) analyses challenging, and we uncovered a strong sensitivity of the assumed surface ratio to its derived RV curve. However, the RV curve and Kiel mass of Star 1 (M₁=0. 41 could be determined precisely, which allowed for a dynamical mass determination of Star 2 (M₂=0. 39 Moreover, we uncovered that Pa 13 exhibits a small but significant orbital eccentricity (e = 0. 02. Since the mass ratio of Pa 13 is close to unity, the system may have formed through double-core CE evolution. Alternatively, there must exist an efficient CE-induced rejuvenation mechanism capable of reheating the cool white dwarf in the binary, as already indicated by the Hen 2-428 system. which makes it only the second post-CE binary central star with a measured eccentricity. Our kinematic analysis shows that Pa 13 belongs to the Galactic halo, implying a system age of ≈ 11, Gyrs. We conclude that Pa 13 provides the strongest evidence so far that PNe can be observed around post-red giant branch stars. Immediately after the CE ejection, Star 1 likely still filled its Roche lobe, which suggests that Pa 13 is a more evolved, detached descendant of over-contact double-degenerate systems such as Hen 2-428