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

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 $\unicode{x2013}$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 ($>\,$10$^{-7}$ M$_{\odot}$yr$^{-1}$) and large disk masses ($\geq\,$10$^{-2}$ M$_{\odot}$) necessary to reproduce observed depletion, particularly in higher-mass, hotter post-AGB stars (T$_{\textrm{eff}}\geq$ 6000 K). A slower evolution (lower core mass) is required to reproduce cooler (T$_{\textrm{eff}}\leq$ 5000 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 (PN) 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.