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Recent observations of a large number of DA and DB white dwarfs show evidenceof debris disks, which are the remnants of old planetary systems. The infraredexcess detected with \emph{Spitzer} and the lines of heavy elements observed intheir atmospheres with high-resolution spectroscopy converge on the idea thatplanetary material accretes onto these stars. Accretion rates have been derivedby several authors with the assumption of a steady state between accretion andgravitational settling. The results are unrealistically different for DA and DBwhite dwarfs. When heavy matter is accreted onto stars, it induces an inverse$\mu$-gradient that leads to fingering (thermohaline) convection. The aim ofthis letter is to study the impact of this specific process on the derivedaccretion rates in white dwarfs and on the difference between DA and DB. Wesolve the diffusion equation for the accreted heavy elements with atime-dependent method. The models we use have been obtained both with the IRAPcode, which computes static models, and the La Plata code, which computesevolutionary sequences. Computations with pure gravitational settling arecompared with computations that include fingering convection. The mostimportant result is that fingering convection has very important effects on DAsbut is inefficient in DBs. When only gravitational settling is taken intoaccount, the time-dependent computations lead to a steady state, as postulatedby previous authors. When fingering convection is added, this steady stateoccurs much later. The surprising difference found in the past for theaccretion rates derived for DA and DB white dwarfs disappears. The derivedaccretion rates for DAs are increased when fingering convection is taken intoaccount, whereas those for DBs are not modified. More precise and developedresults will be given in a forthcoming paper.

Accretion from debris disks onto white dwarfs : Fingering (thermohaline) instability and derived accretion rates