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

TL;DR

The paper investigates how internal dilution processes, especially thermohaline convection, affect the surface pollution of hot DA white dwarfs by accreted planetary matter across a range of masses and effective temperatures. Using static DA WD models, it compares atomic diffusion and thermohaline mixing under two accretion scenarios, finding that thermohaline convection dominates diffusion but becomes less efficient in more massive WDs due to higher internal densities. Consequently, dilution alone cannot explain the observed trend of lower pollution in more massive WDs; other physical processes or formation histories must contribute. The work highlights the need for time-dependent accretion modeling and consideration of additional mixing channels to reliably connect WD pollution levels with planetary system occurrences and progenitor masses.

Abstract

A large proportion of observed white dwarfs (WDs) 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 WDs 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. The aim of this work is to test how internal dilution processes, including thermohaline convection, change with WD masses, and whether such an effect could account for variations in the observed pollution. We computed the efficiency of atomic diffusion and thermohaline convection after the accretion of heavy elements onto WDs using static DA models with various masses, effective temperatures, and hydrogen contents. 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 WDs than in smaller mass ones, due to their larger internal density. We showed that the differences in observed heavy element pollution in WDs 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 WDs 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.

Figures (3)

• Figure 1: Mass fraction profiles of accreted Mg (left panels) and mean molecular weight gradients' profiles (right panels) for the M06T25H-4, M08T25H-4, and M10T25H-4 models, as a function of the outer mass normalised to the total mass of the white dwarf model. The top panels correspond to case 1 (the same value for $\sigma$ for all models), the bottom panels to case 2 (a different value for $\sigma$ so that the $\mu$ gradients' profiles would be the same for all models). All cases were computed with the same total accreted mass ($10^{16}$g).
• Figure 2: Diffusion coefficient for atomic diffusion (dashed lines) and thermohaline convection (solid lines) for different white dwarf masses and effective temperatures with $\log(M_\mathrm{H}/M_\mathrm{WD})=-4$. Cases 1 and 2 are presented in the top and bottom panels, respectively. The grey areas represent the region of mass $M_\mathrm{mix}$ where the composition was initially fully mixed (the same region was plotted for each model for clarity).
• Figure 3: Ratio between accretion rates determined assuming gravitational settling and thermohaline convection as dilution processes ($\dot{M}_\mathrm{g+th}$) and accretion rates determined assuming gravitational settling only ($\dot{M}_\mathrm{g}$), for models of different masses and effective temperatures (listed in Tab. \ref{['tab:mod']}). See the text for more details.