Accretion Rates and Thermohaline Convection in Polluted White Dwarfs
Abstract
Polluted white dwarfs provide a unique window into the composition of exoplanetary material, but interpreting their surface abundances requires a quantitative understanding of the mixing processes in their envelopes. Accretion of metal-rich debris onto hydrogen-rich white dwarfs drives thermohaline (fingering) convection in the underlying radiative zone. Previous studies have modeled this as enhanced diffusive transport, often inferring mass accretion rates, Ṁacc, that exceed constraints from X-ray observations. Here we develop a time-dependent model that treats thermohaline mixing as a propagating front whose evolution is coupled self-consistently to the surface abundance of heavy elements. We perform hydrodynamical simulations which demonstrate that thermohaline mixing drives the composition gradient towards marginal stability. Using this condition, we derive analytic solutions in shallow and deep stratification regimes, finding that the mixed layer depth, h, and surface abundance, Xsurf, both scale as t1/2 at early times, transitioning to h ∝ t4/27 and Xsurf ∝ t10/27 at later times. The mixed layer reaches depths of only ∼ 100 km over 105 yr and, without gravitational settling, never reaches a steady state. Including settling leads to an equilibrium surface abundance scaling as Xsurf, eq ∝ Ṁacc30/43. Applied to G 29--38, the model matches the observed heavy-element abundance for Ṁacc ∼ 2× 109--4× 109 g s−1, in better agreement with X-ray constraints than prior estimates incorporating thermohaline mixing. We also present a general scaling relation for inferring accretion rates directly from observed surface abundances and stellar properties, giving a practical prescription for other polluted white dwarfs.
Versions
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BibTeX
@misc{fuentes2026accretion,
title = {{Accretion Rates and Thermohaline Convection in Polluted White Dwarfs}},
author = {J. R. Fuentes and Matias Castro-Tapia and Jim Fuller and Marcus King},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.31110},
eprint = {2608.31110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31110},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Accretion Rates and Thermohaline Convection in Polluted White Dwarfs
AU - J. R. Fuentes
AU - Matias Castro-Tapia
AU - Jim Fuller
AU - Marcus King
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2608.31110
UR - https://arxiv.org/abs/2608.31110
AB - Polluted white dwarfs provide a unique window into the composition of exoplanetary material, but interpreting their surface abundances requires a quantitative understanding of the mixing processes in their envelopes. Accretion of metal-rich debris onto hydrogen-rich white dwarfs drives thermohaline (fingering) convection in the underlying radiative zone. Previous studies have modeled this as enhanced diffusive transport, often inferring mass accretion rates, Ṁ_acc, that exceed constraints from X-ray observations. Here we develop a time-dependent model that treats thermohaline mixing as a propagating front whose evolution is coupled self-consistently to the surface abundance of heavy elements. We perform hydrodynamical simulations which demonstrate that thermohaline mixing drives the composition gradient towards marginal stability. Using this condition, we derive analytic solutions in shallow and deep stratification regimes, finding that the mixed layer depth, h, and surface abundance, X_surf, both scale as t^1/2 at early times, transitioning to h ∝ t^4/27 and X_surf ∝ t^10/27 at later times. The mixed layer reaches depths of only ∼ 100 km over 10^5 yr and, without gravitational settling, never reaches a steady state. Including settling leads to an equilibrium surface abundance scaling as X_surf, eq ∝ Ṁ_acc^30/43. Applied to G 29--38, the model matches the observed heavy-element abundance for Ṁ_acc ∼ 2× 10^9--4× 10^9 g s^−1, in better agreement with X-ray constraints than prior estimates incorporating thermohaline mixing. We also present a general scaling relation for inferring accretion rates directly from observed surface abundances and stellar properties, giving a practical prescription for other polluted white dwarfs.
ER -