Modelling the impact of circumbinary disk accretion on post-AGB binary evolution and surface chemistry

Abstract Post-asymptotic giant branch (post-AGB) binaries are surrounded by dusty circumbinary disks and exhibit unexpected orbital properties resulting from poorly understood binary interaction processes. Re-accreted gas from the circumbinary disk alters the photospheric chemistry of the post-AGB star, producing a characteristic underabundance of refractory elements that correlates with condensation temperature – a phenomenon known as chemical depletion. This work investigates how re-accretion from a disk drives chemical depletion, and the impact accreted matter has on post-AGB evolution. We used the MESA code to evolve 0.55 and 0.60 M $_{\odot}$ post-AGB stars with the accretion of refractory element-depleted gas from a circumbinary disk. Our study adopts observationally-constrained initial accretion rates and disk masses to reproduce the chemical depletion patterns of six well-studied post-AGB binary stars: EP Lyr, HP Lyr, IRAS 17038-4815, IRAS 09144-4933, HD 131356, and SX Cen. We find high accretion rates ( $\gt 10^{-7}$ M $_{\odot}\,\mathrm{yr}^{-1}$ ) and large disk masses ( $\gtrsim10^{-2}$ M $_{\odot}$ ) necessary to reproduce observed depletion, particularly in higher-mass, hotter post-AGB stars ( $T_{\textrm{eff}}\gtrsim$ 6 000 K). A slower evolution (lower core mass) is required to reproduce cooler ( $T_{\textrm{eff}}\lesssim$ 5 000 K) depleted post-AGB stars. Rapid accretion significantly impacts post-AGB evolution, stalling stars at cooler effective temperatures and extending post-AGB lifetimes by factors of around 3 to 10. Despite this, extended post-AGB timescales remain within or below the planetary nebula visibility timescale, suggesting accretion cannot account for the observed lack of ionised PNe in post-AGB binaries. Our findings constrain accretion-flow parameters and advance our understanding of disk-binary interactions in post-AGB systems.