We present results of a detailed study of the rate of the accretion of planetesimals by a growing proto-Jupiter in the core-accretion model. Using a newly developed code, we accurately combine a detailed three-body trajectory calculation with gas drag experienced during the passage of planetesimals in the protoplanet's envelope. We find that the motion of planetesimals is excited to the extent that encounters with the proto-planetary envelope become so fast that ram pressure breaks up the planetesimals in most encounters. As a result, the accretion rate is largely independent of the planetesimal size and composition. For the case we explored of a planet forming at 5.2 AU from the Sun in a disk with a solid surface density of 6 g/cm^2 (Lozovsky et al. 2017) the accretion rate we compute differs in several respects from that assumed by those authors. We find that only 4-5 M_Earth is accreted in the first 1.5x10^6 years before the onset of rapid gas accretion. Most of the mass, some 10 M_Earth, is accreted simultaneously with this rapid gas accretion. In addition, we find that the mass accretion rate remains small, but non-zero for at least a million years after this point, and an additional 0.3-0.4 M_Earth is accreted during that time. This late accretion, together with a rapid infall of gas could lead to the accreted material being mixed throughout the outer regions, and may account for the enhancement of high-Z material in Jupiter's envelope.

中文翻译：

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核-吸积模型中小行星吸积效率的详细计算

我们展示了对核心吸积模型中不断增长的原木星的小行星吸积率的详细研究结果。使用新开发的代码，我们准确地将详细的三体轨迹计算与小行星在原行星包层中通过时经历的气体阻力相结合。我们发现小行星的运动被激发到与原行星包络相遇的程度，以至于在大多数相遇中撞击压力会破坏小行星。因此，吸积率在很大程度上与行星的大小和组成无关。对于我们探索的行星在距太阳 5.2 天文单位的情况下形成的盘状固体表面密度为 6 g/cm^2 (Lozovsky et al. 2017）我们计算的吸积率在几个方面与这些作者假设的不同。我们发现在气体快速吸积开始前的前 1.5x10^6 年中只有 4-5 个 M_Earth 被吸积。大部分质量，大约 10 M_Earth，与这种快速气体吸积同时吸积。此外，我们发现质量吸积率仍然很小，但在此之后至少一百万年不为零，并且在此期间又吸积了 0.3-0.4 M_Earth。这种较晚的吸积，加上气体的快速流入，可能导致吸积的物质在整个外部区域混合，并可能解释木星包层中高 Z 物质的增强。与这种快速气体吸积同时吸积。此外，我们发现质量吸积率仍然很小，但在此之后至少一百万年不为零，并且在此期间又吸积了 0.3-0.4 M_Earth。这种较晚的吸积，加上气体的快速流入，可能导致吸积的物质在整个外部区域混合，并可能解释木星包层中高 Z 物质的增强。与这种快速气体吸积同时吸积。此外，我们发现质量吸积率仍然很小，但在此之后至少一百万年不为零，并且在此期间又吸积了 0.3-0.4 M_Earth。这种较晚的吸积，加上气体的快速流入，可能导致吸积的物质在整个外部区域混合，并可能解释木星包层中高 Z 物质的增强。