Polluted White Dwarfs: Mixing Regions and Diffusion Timescales

Abstract

Many isolated white dwarfs (WDs) show spectral evidence of atmospheric metal pollution. Since heavy element sedimentation timescales are short, this most likely indicates ongoing accretion. Accreted metals encounter a variety of mixing processes at the WD surface: convection, gravitational sedimentation, overshoot, and thermohaline instability. We present MESA WD models that explore each of these processes and their implications for inferred accretion rates. We provide diffusion timescales for many individual metals, and we quantify the regimes in which thermohaline mixing dominates over gravitational sedimentation in setting the effective settling rate of the heavy elements. We build upon and confirm earlier work finding that accretion rates as high as $10^{13} \, \rm g \, s^{-1}$ are needed to explain observed pollution in DA WDs for $T_{\rm eff} > 15,000 \, \rm K$, and we provide tabulated results from our models that enable accretion rate inferences from observations of polluted DA WDs. If these rates are representative of young WDs, we estimate that the total mass of planetesimal material accreted over a WD lifetime may be as high as $10^{28} \, \rm g$, though this estimate is susceptible to potential selection biases and uncertainties about the nature of disk processes that supply accretion to the WD surface. We also find that polluted DB WDs experience much less thermohaline mixing than DA WDs, and we do not expect thermohaline instability to be active for polluted DB WDs with $T_{\rm eff} < 18,000 \, \rm K$.