Dilution of accreted planetary matter in hot DA white dwarfs according to their mass

Context. A large proportion of observed white dwarfs show evidence of debris disks, remnants of the former planetary systems, and/or signatures of heavy elements in their atmospheres, induced by the accretion of planetary matter onto their surfaces. The observed abundances are the result of the balance between the accretion flux and the dilution of this planetary material by internal transport processes. A recent study showed that more massive DA white dwarfs are less polluted than smaller mass ones. It was suggested that the reason could be related to the formation of planetary systems when these stars were on the main sequence. Aims. The aim of this work is to test how internal dilution processes, including thermohaline convection, change with white dwarf masses, and whether such an effect could account for variations in the observed pollution. Methods. We computed the efficiency of atomic diffusion and thermohaline convection after the accretion of heavy elements onto white dwarfs using static DA models with various masses, effective temperatures, and hydrogen contents. Results. We confirm that thermohaline convection is always more efficient in diluting accreted elements than atomic diffusion, as previously shown in the literature. However, we find that element dilution by thermohaline convection is less efficient in massive white dwarfs than in smaller mass ones, due to their larger internal density. Conclusions. We showed that the differences in observed heavy element pollution in white dwarfs according to their masses cannot be explained by the dilution induced by atomic diffusion and thermohaline mixing alone. Indeed, the pollution by planetary system accretion should be more easily detectable in massive white dwarfs than in low-mass ones. We discuss other processes that should be taken into account before drawing any conclusion about the occurrences of planetary systems according to the mass of the star on the main sequence.