Exogeological inferences from white dwarf pollutants: the impact of stellar physics

TL;DR

This work studies how stellar atmospheric physics biases the geological inferences drawn from metals polluted onto white dwarfs. Using a Bayesian forward model (PyllutedWD) with multiple sinking-time grids (Koester, STELUM, and 3D overshoot variants S3D/SV) and a thermohaline mixing scheme, the authors quantify how convective overshoot and mixing alter inferred core–mantle differentiation and incomplete condensation, across a large sample from PEWDD. They introduce a discrepancy metric $M_{a,b}$ to predict when changing diffusion grids will meaningfully affect results, and identify both full-sensitivity cases (where interpretations shift) and robust systems (where conclusions hold across assumptions). The study finds that in H-dominated WDs, overshoot effects are most pronounced in the $T_{ m eff}\approx 12{,}000$–$18{,}000$ K range, generally lowering inferred Fe and O in accreted material, while thermohaline mixing tends to raise inferred accretion rates and can suppress differential sinking. The results underscore the need to model multiple physical inputs and propagate these uncertainties when interpreting WD pollution, and they demonstrate four systems with robust geological histories, informing future large-scale surveys of polluted white dwarfs.

Abstract

Many white dwarfs have accreted material from their own planetary systems. These objects can be used to infer the composition of exoplanetary material and identify evidence for key geological processes. However, the white dwarf atmospheric physics distorts the inferred material composition away from the true composition, mainly through differential atomic diffusion of the accreted metals. Correcting for this effect is essential, but is dependent on various physical assumptions associated with the white dwarf itself. We first focus on the effect of assumptions related to convective overshoot and thermohaline mixing on the atomic diffusion timescales. For white dwarfs with H-dominated atmospheres between 12000 K and 18000 K, we find that including a complete treatment of convective overshoot decreases the inferred Fe and O abundances in accreted material. For these white dwarfs, we also find that including thermohaline mixing decreases Fe and O abundances. For He-dominated systems, the effect of convective overshoot is comparatively minor. We then explore the overall effect of other physical assumptions by comparing publicly available grids of diffusion timescales. We find that the choice of model grid can have a large impact for white dwarfs with He-dominated atmospheres, notably on the inferred core to mantle ratio of accreted material. We identify several systems for which the geological interpretation is robust against these systematics. We also present a `discrepancy metric' which can be used to estimate the potential impact of changing the stellar physics without requiring detailed modelling.

Figures (19)

• Figure 1: The change in relative sinking timescales for H-dominated white dwarfs when including 3D convective overshoot, compared to no overshoot, as a function of effective temperature ($x$ axis) and surface gravity ($y$ axis). The colour scale shows the change in the Fe/Mg sinking timescale ratio, on a log scale (base 10). Under the assumption of steady state accretion, the change in this ratio equals the change in the inferred Fe/Mg abundance ratio in the pollutant. The ratio is therefore significant when its absolute value is greater than the approximate uncertainty of metal abundances, typically 0.1 to 0.2 dex. The crosses indicate our sample of H-dominated white dwarfs which were modelled individually with these different treatments of overshoot (Test 1). The grey dots show all other H-dominated white dwarfs in PEWDD. Points may overlap when an individual white dwarf has multiple entries in PEWDD. For example, the Gaia J0611$-$6931 (Phot) point corresponds to two entries (both listed explicitly in Table \ref{['tab:sample']}). The vertical dashed lines indicate the temperature range where convective overshoot has been explored with 3D simulations (as in the S3D grid). Outside of this range, we use the SV grid.
• Figure 2: The geological interpretation of the metals accreted by GD 56 changes when convective overshoot is taken into account. The black data points, with 1 sigma error bars, show the abundances of metals in the photosphere of GD 56 on a log scale relative to Mg, and scaled to solar. The solid blue line shows the inferred composition of the accreted material when modelling the data without convective overshoot. The shaded blue region is a 1 sigma confidence interval. Our Bayesian framework finds (weak) evidence for core-mantle differentiation, with the best model invoking a core-rich composition. This composition should not be directly compared to the data points, because differential sinking causes the accreted and detected compositions to differ. The dashed blue line accounts for this correction, and may be compared with the data. For visual clarity, the 1 sigma confidence interval is omitted in this case. The red lines show the equivalent results when including convective overshoot using results from detailed 3D simulations. When taking this effect into account, the best model does not find any evidence of core-mantle differentiation. The compositions without overshoot (blue lines) predict negligible quantities of C and N, so these are not shown.
• Figure 3: The geological interpretation of the metals accreted by WD 0310$-$688 changes when convective overshoot is taken into account (red). The interpretation of the plot features is similar to Figure \ref{['fig:GD56']}, but the abundances are scaled to the dominant photospheric element, in this case H, rather than Mg. We choose this scaling in cases where one or more of the fits does not replicate the Mg abundance particularly well, such that scaling to Mg results in a non-representative illustration of the overall quality of that fit. For the accreted compositions, the vertical position is arbitrary, so we fix the Mg abundance to match the detected abundance (and therefore there is no uncertainty on the Mg abundance for the accreted compositions). Our Bayesian framework finds (weak) evidence for incomplete condensation only when including convective overshoot.
• Figure 4: The geological interpretation of the metals accreted by GD 424 changes depending on whether convective overshoot is neglected (blue) or included (red). The plot features are similar to Figure \ref{['fig:GD56']}.
• Figure 5: The susceptibility of H-dominated white dwarfs to a change in geological interpretation when including a full treatment of convective overshoot, compared to no overshoot, as a function of effective temperature and surface gravity. We show this in terms of the mean value of our discrepancy metric (see Section \ref{['sec:overshoot_overview']}) for randomly generated synthetic white dwarfs. The metric does not take into account the specific abundances (and errors) of detected metals, which is important for predicting whether any particular polluted white dwarf will be susceptible. The metric is inversely proportional to the uncertainty on abundances - here we assume 0.2 dex errors. The sample used for Test 1 is shown with black crosses. The black circles show the subset of those systems for which the geological interpretation does actually change when using a full 3D parametrisation of convective overshoot. The grey dots show all other H-dominated white dwarfs in PEWDD.