Backflow in post-asymptotic giant branch stars

We derive the conditions for a backflow toward the central star(s) of circumstellar material to occur during the post-asymptotic giant branch (post-AGB) phase. The backflowing material may be accreted by the post-AGB star and/or its companion, if such exists. Such a backflow may play a significant role in shaping the descendant planetary nebula, by, among other things, slowing down the post-AGB evolution, and by forming an accretion disc which may blow two jets We consider three forces acting on a slowly moving mass element: the gravity of the central system, radiation pressure, and fast wind ram pressure. We find that for a significant backflow to occur, a slow dense flow should exist, such that the relation between the total mass in the slow flow, M_i, and the solid angle it covers Ω, is given by (M_i/β) ≳ 0.1 M_⊙, where β ≡ Ω/4π. The requirement for both a high mass-loss rate per unit solid angle and a very slow wind, such that it can be decelerated and flow back, probably requires close binary interaction, hence this process is rare.