[论文解读] On the filtering and processing of dust by planetesimals 1. Derivation of collision probabilities for non-drifting planetesimals

T. Guillot, Shigeru Ida+1 more|arXiv (Cornell University)|Sep 25, 2014

Astrophysics and Star Formation Studies参考文献 76被引用 45

一句话总结

本论文推导了在原行星盘中受气体阻力影响漂移的尘埃颗粒与非漂移行星esimal之间的碰撞概率，计算了在几何、Safronov、settling（沉降）和流体动力学四种物理 regime 下的过滤效率。研究发现，在湍流较强的盘中（α = 10⁻²），尘埃过滤效率低下；但在弱湍流盘中（α = 10⁻⁴），仅当行星esimal 尺寸较小（<10 km）或胚胎较大（>1000 km）时，过滤才变得高效，且其径向依赖关系存在差异：几何 regime 下为 r⁻⁷/⁴，沉降 regime 下为 r⁻¹/⁴ 至 r¹/⁴。

ABSTRACT

Context. Circumstellar disks are known to contain a significant mass in dust ranging from micron to centimeter size. Meteorites are evidence that individual grains of those sizes were collected and assembled into planetesimals in the young solar system. Aims. We assess the efficiency of dust collection of a swarm of non-drifting planetesimals { ev with radii ranging from 1 to $10^3$\,km and beyond. Methods. We calculate the collision probability of dust drifting in the disk due to gas drag by planetesimal accounting for several regimes depending on the size of the planetesimal, dust, and orbital distance: the geometric, Safronov, settling, and three-body regimes. We also include a hydrodynamical regime to account for the fact that small grains tend to be carried by the gas flow around planetesimals. Results. We provide expressions for the collision probability of dust by planetesimals and for the filtering efficiency by a swarm of planetesimals. For standard turbulence conditions (i.e., a turbulence parameter $\alpha=10^{-2}$), filtering is found to be inefficient, meaning that when crossing a minimum-mass solar nebula (MMSN) belt of planetesimals extending between 0.1 AU and 35 AU most dust particles are eventually accreted by the central star rather than colliding with planetesimals. However, if the disk is weakly turbulent ($\alpha=10^{-4}$) filtering becomes efficient in two regimes: (i) when planetesimals are all smaller than about 10 km in size, in which case collisions mostly take place in the geometric regime; and (ii) when planetary embryos larger than about 1000 km in size dominate the distribution, have a scale height smaller than one tenth of the gas scale height, and dust is of millimeter size or larger in which case most collisions take place in the settling regime. These two regimes have very different properties: we find that the local filtering efficiency $x_{filter,MMSN}$ scales with $r^{-7/4}$ (where $r$ is the orbital distance) in the geometric regime, but with $r^{-1/4}$ to $r^{1/4}$ in the settling regime. This implies that the filtering of dust by small planetesimals should occur close to the central star and with a short spread in orbital distances. On the other hand, the filtering by embryos in the settling regime is expected to be more gradual and determined by the extent of the disk of embryos. Dust particles much smaller than millimeter size tend only to be captured by the smallest planetesimals because they otherwise move on gas streamlines and their collisions take place in the hydrodynamical regime. Conclusions. Our results hint at an inside-out formation of planetesimals in the infant solar system because small planetesimals in the geometrical limit can filter dust much more efficiently close to the central star. However, even a fully-formed belt of planetesimals such as the MMSN only marginally captures inward-drifting dust and this seems to imply that dust in the protosolar disk has been filtered by planetesimals even smaller than 1 km (not included in this study) or that it has been assembled into planetesimals by other mechanisms (e.g., orderly growth, capture into vortexes). Further refinement of our work concerns, among other things: a quantitative description of the transition region between the hydro and settling regimes; an assessment of the role of disk turbulence for collisions, in particular in the hydro regime; and the coupling of our model to a planetesimal formation model.

研究动机与目标

• 本论文旨在量化不同尺寸的非漂移行星esimal 在原行星盘中对向内漂移尘埃的过滤效率。
• 解决长期以来关于早期太阳系中尘埃如何在气体阻力导致的快速向内漂移下仍能被保留的难题。
• 研究聚焦于在多种物理 regime 下，尘埃颗粒与行星esimal 之间的碰撞概率。
• 旨在通过尘埃捕获机制解释陨石组分（如球粒和钙铝钙钛矿）的观测尺寸分布与成分特征。
• 目标包括识别行星esimal 群体能高效过滤尘埃的条件，特别是在最小质量太阳星云（MMSN）背景下的情形。

提出的方法

• 作者基于行星esimal 尺寸、尘埃尺寸、轨道距离和气体性质，推导了在四种 regime（几何、Safronov、沉降和三体）下的碰撞概率。
• 引入流体动力学 regime 以模拟小颗粒如何随气体流场绕行星esimal 流动，从而降低碰撞概率。
• 利用尘埃颗粒的阻尼时间与行星esimal 穿越时间的比值来定义不同 regime 的过渡条件。
• 通过局部过滤效率 x_filter,MMSN 和积分过滤效率 X_filter 计算过滤效率，同时考虑径向分布与盘的湍流程度。
• 模型假设行星esimal 的典型密度为 1 g cm⁻³，并通过 α 参数考虑湍流变化的影响。
• 该框架应用于 MMSN 盘模型，轨道距离范围为 0.1 AU 至 35 AU，尘埃尺寸从亚微米至米量级。

实验结果

研究问题

• RQ1 在原行星盘中，不同尺寸与轨道 regime 下，尘埃颗粒与非漂移行星esimal 的碰撞概率如何？
• RQ2 盘的湍流程度（以 α 参数量化）如何影响行星esimal 对尘埃的过滤效率？
• RQ3 在何种条件下尘埃过滤才变得高效——特别是对于小行星（<10 km）或大胚胎（>1000 km）？
• RQ4 几何与沉降 regime 下，过滤效率的径向依赖关系有何差异？
• RQ5 行星esimal 周围的流体动力学流场在降低小尘埃颗粒碰撞概率方面起到何种作用？

主要发现

• 在湍流较强的盘中（α = 10⁻²），MMSN 行星esimal 带对尘埃的过滤效率低下，1 AU 处对毫米至米量级尘埃的局部过滤效率 x_filter,MMSN 仅约 1%。
• 在弱湍流盘中（α = 10⁻⁴），当行星esimal 尺寸小于 ∼10 km 时，过滤效率变得高效，此时碰撞概率随轨道距离按 r⁻⁷/⁴ 变化。
• 在沉降 regime 中，大胚胎（>1000 km）的过滤效率高效，且随距离按 r⁻¹/⁴ 至 r¹/⁴ 变化，表明其在更广的径向范围内实现渐进、持续的尘埃过滤。
• 小尘埃颗粒（亚毫米级）因流体动力学效应而难以捕获，其流场会将其绕过行星esimal，从而降低碰撞概率。
• 在沉降 regime 中，过滤效率与行星esimal 密度无关，而几何 regime 中则有关，表明其捕获机制具有根本性差异。
• 结果表明，行星esimal 的形成可能遵循“由内而外”的演化路径：靠近恒星的小行星可高效过滤尘埃，而大胚胎则可在更广的径向范围内实现尘埃过滤。