污染白矮星中的吸积率与热盐对流
Accretion Rates and Thermohaline Convection in Polluted White Dwarfs
- California Institute of Technology（加州理工学院）
- McGill University（麦吉尔大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出时变热盐混合模型，模拟污染白矮星中吸积驱动的指状对流，匹配G 29--38的丰度并给出吸积率推断公式。
AI中文摘要：
污染白矮星为研究系外行星物质的组成提供了独特的窗口，但解释其表面丰度需要定量理解其包层中的混合过程。富含金属的碎片吸积到富氢白矮星上，会在其下方的辐射区驱动热盐（指状）对流。以往的研究将此建模为增强的扩散输运，通常推断出的质量吸积率 $\dot{M}_{\rm acc}$ 超过了X射线观测的约束。在此，我们开发了一个时变模型，将热盐混合视为一个传播前沿，其演化与重元素表面丰度自洽耦合。我们进行了流体动力学模拟，证明热盐混合使成分梯度趋向于边际稳定。利用这一条件，我们在浅层和深层分层状态下推导了解析解，发现混合层深度 $h$ 和表面丰度 $X_{\rm surf}$ 在早期均按 $t^{1/2}$ 标度，后期转变为 $h \propto t^{4/27}$ 和 $X_{\rm surf} \propto t^{10/27}$。混合层在 $10^5$ 年内仅达到约 $\sim 100$ km 的深度，且在没有重力沉降的情况下，永远不会达到稳态。考虑沉降后，平衡表面丰度标度为 $X_{\rm surf, eq} \propto \dot{M}_{\rm acc}^{30/43}$。应用于 G 29--38 时，该模型在 $\dot{M}_{\rm acc} \sim 2\times 10^9$--$4\times 10^{9}~\mathrm{g~s^{-1}}$ 时与观测到的重元素丰度匹配，与包含热盐混合的先前估计相比，与X射线约束更一致。我们还提出了一个通用标度关系，可直接从观测表面丰度和恒星性质推断吸积率，为其他污染白矮星提供了实用方法。
英文摘要：
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, $\dot{M}_{\rm acc}$, 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, $X_{\rm surf}$, both scale as $t^{1/2}$ at early times, transitioning to $h \propto t^{4/27}$ and $X_{\rm surf} \propto t^{10/27}$ at later times. The mixed layer reaches depths of only $\sim 100$ km over $10^5$ yr and, without gravitational settling, never reaches a steady state. Including settling leads to an equilibrium surface abundance scaling as $X_{\rm surf, eq} \propto \dot{M}_{\rm acc}^{30/43}$. Applied to G 29--38, the model matches the observed heavy-element abundance for $\dot{M}_{\rm acc} \sim 2\times 10^9$--$4\times 10^{9}~\mathrm{g~s^{-1}}$, 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.
