Fomalhaut b could be massive and sculpting the narrow, eccentric debris disc, if in mean-motion resonance with it

The star Fomalhaut hosts a narrow, eccentric debris disc, plus a highly eccentric companion Fomalhaut b. It is often argued that Fomalhaut b cannot have significant mass, otherwise it would quickly perturb the disc. We show that material in internal mean-motion resonances with a massive, coplanar Fomalhaut b would actually be long-term stable, and occupy orbits similar to the observed debris. Furthermore, millimetre dust released in collisions between resonant bodies could reproduce the width, shape and orientation of the observed disc. We first re-examine the possible orbits of Fomalhaut b, assuming that it moves under gravity alone. If Fomalhaut b orbits close to the disc midplane then its orbit crosses the disc, and the two are apsidally aligned. This alignment may hint at an ongoing dynamical interaction. Using the observationally allowed orbits, we then model the interaction between a massive Fomalhaut b and debris. Whilst most debris is unstable in such an extreme configuration, we identify several resonant populations that remain stable for the stellar lifetime, despite crossing the orbit of Fomalhaut b. This debris occupies low-eccentricity orbits similar to the observed debris ring. These large bodies would have a clumpy distribution, but dust released in collisions between them would form a narrow, relatively smooth ring similar to observations. We show that if Fomalhaut b has a mass between those of Earth and Jupiter then, far from removing the observed debris, it could actually be sculpting it through resonant interactions.

恒星北落师门（Fomalhaut）拥有一个狭窄且偏心率较高的残骸盘（debris disc），同时还伴随一颗偏心率极高的伴星北落师门b（Fomalhaut b）。学界普遍认为北落师门b的质量不应过大，否则会快速扰动该残骸盘。我们的研究表明，若北落师门b具有一定质量且轨道与残骸盘共面，那么与它处于内部平动共振（mean-motion resonances）的残骸物质实际上可长期保持稳定，且其轨道与观测到的残骸轨道特征一致。此外，共振天体之间碰撞产生的毫米级尘埃（millimetre dust），可完美复刻观测到的残骸盘的宽度、形态与取向。我们首先仅考虑引力作用，重新分析了北落师门b的可能轨道。若北落师门b的轨道接近残骸盘的主平面，则其轨道会穿过残骸盘，且二者的拱线相互对齐。这种拱线对齐现象，或许暗示二者目前正处于动态相互作用中。基于观测允许的轨道参数，我们随后对具有一定质量的北落师门b与残骸物质之间的相互作用进行了建模。尽管在这种极端构型下，绝大多数残骸物质都会处于不稳定状态，但我们仍识别出了若干共振族群——即使它们的轨道会穿过北落师门b的轨道，却可在恒星的整个生命周期内保持稳定。这些稳定的残骸物质拥有低偏心率轨道，与观测到的残骸环特征一致。这些大质量残骸天体的分布会呈现成团特征，但它们之间碰撞产生的尘埃，会形成一个狭窄且相对平滑的环结构，与观测结果相符。我们的研究证实，若北落师门b的质量介于地球与木星之间，那么它非但不会驱散观测到的残骸物质，反而可通过平动共振作用塑造该残骸盘的结构。