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arXiv 2104.02072astro-ph.EP
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约束星子搅动：碎片盘边缘有多锋利？

Constraining planetesimal stirring: how sharp are debris disc edges?

Sebastian Marino

备注：
Accepted for publication in MNRAS. 15 ppages, 11 figures
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摘要：

微行星的研磨碰撞在碎片盘中产生尘埃，需要搅动它们的轨道。然而，搅拌水平在很大程度上仍然不受约束，因此搅拌机制也不受约束。这项工作显示了如何锋利的外边缘的光盘可以用来约束搅拌水平。也就是说，边缘越尖锐，偏心距分散必须越低。对于瑞利分布的偏心率（$e$），我发现，光盘表面密度的外缘附近可以参数化为$\tanh[(r_{\max}-r)/l_{\rm out}]$，其中$r_{\max}$近似的最大半长轴和$l_{\rm out}$定义的边缘平滑度。如果半长轴分布具有尖锐边缘，则$e_\mathrm{rms}$大致为$1.2 l_{\rm out}/r_{\max}$，或者如果半长轴由于自搅拌而扩散，则为$e_\mathrm{rms}=0.77 l_{\rm out}/r_{\max}$。用该模型对HD 107146、HD 92945、HD 206893、AU Mic和HR 8799等5个宽盘的ALMA数据进行了拟合。结果表明，HD 107146、HD 92945和AU Mic具有最尖锐的外缘，对应于$0.121\pm0.05$、$0.15^{+0.07}_{-0.05}$和$0.10\pm0.02$的$e_\mathrm{rms}$值，如果它们的圆盘是自搅拌的，这表明存在嵌入圆盘中的冥王星大小的物体。尽管这些搅拌值大于通常假设的值，但HD 92945的径向搅拌与受圆盘高度限制的垂直搅拌非常一致。另一方面，HD 206893和HR~8799有平滑的外边缘，这表明分散的盘，因为这两个系统都有大量的内伴星。

英文摘要：

The dust production in debris discs by grinding collisions of planetesimals requires their orbits to be stirred. However, stirring levels remain largely unconstrained, and consequently the stirring mechanisms as well. This work shows how the sharpness of the outer edge of discs can be used to constrain the stirring levels. Namely, the sharper the edge is the lower the eccentricity dispersion must be. For a Rayleigh distribution of eccentricities ($e$), I find that the disc surface density near the outer edge can be parametrised as $\tanh[(r_{\max}-r)/l_{\rm out}]$, where $r_{\max}$ approximates the maximum semi-major axis and $l_{\rm out}$ defines the edge smoothness. If the semi-major axis distribution has sharp edges $e_\mathrm{rms}$ is roughly $1.2 l_{\rm out}/r_{\max}$, or $e_\mathrm{rms}=0.77 l_{\rm out}/r_{\max}$ if semi-major axes have diffused due to self-stirring. This model is fitted to ALMA data of five wide discs: HD 107146, HD 92945, HD 206893, AU Mic and HR 8799. The results show that HD 107146, HD 92945 and AU Mic have the sharpest outer edges, corresponding to $e_\mathrm{rms}$ values of $0.121\pm0.05$, $0.15^{+0.07}_{-0.05}$ and $0.10\pm0.02$ if their discs are self-stirred, suggesting the presence of Pluto-sized objects embedded in the disc. Although these stirring values are larger than typically assumed, the radial stirring of HD 92945 is in good agreement with its vertical stirring constrained by the disc height. HD 206893 and HR~8799, on the other hand, have smooth outer edges that are indicative of scattered discs since both systems have massive inner companions.

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