Modelling depletion by re-accretion of gas from a dusty disc in post-AGB stars

Many disc-type post-asymptotic giant branch (post-AGB) stars are chemically peculiar, showing underabundances of refractory elements in their photospheres that correlate with condensation temperature. The aim of this paper is to investigate how accretion from a circumbinary disc can cause this phenomenon of depletion and how this impacts the evolution of post-AGB stars. We used the \texttt{MESA} code to evolve stars in the post-AGB phase, while including accretion of metal-poor gas. We compared the models to a sample of 58 observed disc-type post-AGB stars with chemical abundance data. For each of these stars, we estimated the luminosity and the mass using the Gaia distance. We modelled the accretion rate onto the binary from a viscously evolving disc for a range of initial accretion rates and disc masses. We find that large initial accretion rates ($\gtrsim 3\times10^{-7}$ $M_\odot$/yr) and large initial disc masses ($\sim10^{-2}$ $M_\odot$) are needed to reproduce the observed depleted post-AGB stars. Based on these high accretion rates, the evolution timescale of post-AGB stars can be significantly extended by a factor between two and five. We distinguish depletion patterns that are unsaturated (plateau profile) from those that are saturated, and we expect that post-red giant branch (post-RGB) stars are much more likely to show an unsaturated abundance pattern compared to post-AGB stars. Finally, because of the slower evolution of the low-mass post-RGB stars, we find that these systems can become depleted at lower effective temperatures ($< 5000$ K). We conclude that accretion from a circumbinary disc successfully accounts for the chemical peculiarity of post-AGB stars.