Dependence of a planet's chaotic zone on particle eccentricity: the shape of debris disc inner edges
Dependence of a planet's chaotic zone on particle eccentricity: the shape of debris disc inner edges
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行星混沌带对粒子偏心率的依赖性：碎片盘内边缘的形状
DOI：
10.1111/j.1365-2966.2011.19948.x
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发表时间：
2011
影响因子：
4.8
通讯作者：
M. Wyatt
中科院分区：
文献类型：
--
作者：
A. Mustill;M. Wyatt
行星的轨道被一个混沌带所包围，其中附近粒子的轨道是混沌和不稳定的。wise表明混沌是由平均运动共振的重叠驱动的，发生在距离（δa/a）混沌≈1.3μ^2/7的行星轨道范围内。然而，平均运动共振的宽度随着粒子偏心距的增大而增大，这将增加高偏心距时混沌区的宽度。在这里，我们使用迭代相遇映射和n体积分来研究混沌区的宽度。我们发现，智慧的经典处方对低偏心率轨道上的粒子很有效。然而，在临界偏心率以上，依赖于行星的质量，混沌带的宽度随着偏心率的增加而增加。然后，对Wisdom的分析论点进行扩展，表明在临界偏心率以上，混沌区宽度由（δa/a）chaos≈1.8e^1/5μ^1/5给出，这与相遇图的结果非常吻合。临界偏心率由ecrit≈0.21μ^3/7给出。当一颗行星雕刻由偏心星子组成的碎片盘的内缘时，这个扩展的混沌区就会产生一个更大的清理区域。因此，从经典混沌带估计的行星质量可能是错误的。我们将这一结果应用于HR 8799系统，结果表明，根据圆盘的截短推断出的HR 8799 b的质量可能会根据圆盘粒子的偏心率变化高达50%。在圆盘边缘为90au的情况下，如果圆盘粒子的离心率较低（> 0.02），则行星b的质量为8-10倍木星质量，而如果圆盘粒子的离心率较高，则只有4-8倍木星质量。我们的结果还暗示了行星向内部系统提供物质的能力，这一过程可以解释白矮星大气中的金属污染。(少)
The orbit of a planet is surrounded by a chaotic zone wherein nearby particles' orbits are chaotic and unstable. It was shown by Wisdom that the chaos is driven by the overlapping of mean motion resonances which occurs within a distance (δa/a)chaos≈ 1.3μ^2/7 of the planet's orbit. However, the width of mean motion resonances grows with the particles' eccentricity, which will increase the width of the chaotic zone at higher eccentricities. Here we investigate the width of the chaotic zone using the iterated encounter map and N-body integrations. We find that the classical prescription of Wisdom works well for particles on low-eccentricity orbits. However, above a critical eccentricity, dependent upon the mass of the planet, the width of the chaotic zone increases with eccentricity. An extension of Wisdom's analytical arguments then shows that, above the critical eccentricity, the chaotic zone width is given by (δa/a)chaos≈ 1.8e^1/5μ^1/5, which agrees well with the encounter map results. The critical eccentricity is given by ecrit≈ 0.21μ^3/7. This extended chaotic zone results in a larger cleared region when a planet sculpts the inner edge of a debris disc composed of eccentric planetesimals. Hence, the planet mass estimated from the classical chaotic zone may be erroneous. We apply this result to the HR 8799 system, showing that the mass of HR 8799 b inferred from the truncation of the disc may vary by up to 50 per cent depending on the disc particles' eccentricities. With a disc edge at 90 au, the necessary mass of planet b to cause the truncation is 8-10 Jovian masses if the disc particles have low eccentricities (≲0.02), but only 4-8 Jovian masses if the disc particles have higher eccentricities. Our result also has implications for the ability of a planet to feed material into an inner system, a process which may explain metal pollution in white dwarf atmospheres. (Less)