No evidence for a strong decrease of planetesimal accretion in old white dwarfs

A large fraction of white dwarfs are accreting or have recently accreted rocky material from their planetary systems, thereby `polluting' their atmospheres with elements heavier than helium. In recent years, the quest for mechanisms that can deliver planetesimals to the immediate vicinity of their central white dwarfs has stimulated a flurry of modelling efforts. The observed time evolution of the accretion rates of white dwarfs through their multi-Gyr lifetime is a crucial test for dynamical models of evolved planetary systems. Recent studies of cool white dwarf samples have identified a significant decrease of the mass accretion rates of cool, old white dwarfs over Gyr time-scales. Here, we revisit those results using updated white dwarf models and larger samples of old polluted H- and He-atmosphere white dwarfs. We find no compelling evidence for a strong decrease of their time-averaged mass accretion rates for cooling times between 1 and 8 Gyr. Over this period, the mass accretion rates decrease by no more than a factor of the order of 10, which is one order of magnitude smaller than the decay rate found in recent works. Our results require mechanisms that can efficiently and consistently deliver planetesimals inside the Roche radius of white dwarfs over at least 8 Gyr.