Interactions between planets and debris disks

构成碎片盘的微行星受到系统中任何行星的动态扰动;这些扰动影响了盘的结构。通过观察~mm大小的尘埃颗粒（由较大的天体碰撞和研磨而产生，因此有望追踪微行星的分布），我们因此可以推断具有碎片盘的恒星的行星系统。例如，太阳系历史的一些最好的证据来自于研究太阳小行星和埃奇-柯伊伯带的结构。首先，该项目关注的是HD 107146，一颗约1亿年前的太阳型星星，它拥有一个相对较宽的碎片盘，从约30到150 AU延伸。最近的阿尔马观测表明，在大约80天文单位的地方，星子的表面密度有一个耗尽。一个可能的解释是，有一颗质量只有几个地球的行星在大约80天文单位的圆形轨道上，它正在清除它周围的星子。然而，耗尽的确切形状并没有得到很好的限制：从径向密度分布图和观测值得到了很好的拟合，径向密度分布图随距离增加，但在~ 80 AU处有一个完整的间隙（如果有一颗行星处于耗尽状态，这是可以预期的），以及一个双幂律分布图，显示了在更广泛的范围内的部分耗尽，这就需要其他的解释了。另一种观点认为，一颗行星是在偏心轨道上分散到圆盘中的，而观测到的结构是行星轨道与圆盘相互作用时圆形化的结果。然而，当行星与行星盘之间的距离很大，并且碎片盘被探测到时，行星盘似乎已经几乎完全耗尽，而HD 107146则相对较小，因此应该考虑其他情况。在这个项目中，我们将考虑多行星系统如何塑造盘;具体来说，我们将研究长期共振的影响。当行星的岁差率与盘中的微行星的岁差率相等时，就会发生这种现象，并在很长的时间尺度上激发这些微行星的离心率。在偏心轨道上的天体大部分时间都在不等于其半长轴的距离上;因此，如果在~ 80天文单位处存在长期共振，这可能会导致HD 107146系统中所见的那种耗尽。我们将开始提出一个双行星系统，并旨在约束参数空间（包括行星的质量和距离），以尽可能大的程度上考虑所观察到的磁盘结构和长期相互作用的时间尺度的要求。N体动力学模拟将用于研究行星的各种组合所产生的盘结构。这些模拟的输出也将经过后处理，以包括灾难性碰撞造成的盘损耗的影响，灾难性碰撞将微行星磨成小颗粒，这些小颗粒被辐射压力吹出系统，在研究了HD 107146的具体例子之后，我们的目标是将这种长期分析扩展到显示损耗的其他碎片盘;从长远来看，我们还将更普遍地考虑其他类型的行星-盘相互作用的可观察效应。

The planetesimals which make up debris disks are dynamically perturbed by any planets that are present in the system; these perturbations influence the disk structure. By observing ~mm sized dust grains (which result from larger bodies colliding and grinding themselves down, and thus are expected to trace out the distribution of planetesimals) we can therefore make inferences about the planetary systems of stars with debris disks. For example, some of the best evidence for the history of our Solar System comes from studying the structure of the Sun's Asteroid and Edgeworth-Kuiper belts.In the first instance this project is focusing on HD107146, a ~100Myr old solar-type star which hosts a relatively wide debris disk, extending from ~30 to 150AU. Recent ALMA observations of the disk suggest that there is a depletion in the surface density of planetesimals at around 80AU. One possible explanation is that there is a planet of a few Earth masses on a circular orbit at ~80AU which is clearing the region immediately surrounding it of planetesimals. The exact shape of the depletion is not well-constrained, however: good fits to the observations are obtained from both a radial density profile that increases with distance but has a complete gap at ~80AU (as would be expected if there is a planet at the depletion), and a double-power-law profile that shows a partial depletion over a much broader range, which would require some other explanation.Another idea that has been proposed is that a planet was scattered out into the disk on an eccentric orbit, and the observed structure is a result of the way the planet's orbit was circularised as it interacted with the disk. However, in cases where planets at large separations are seen and the debris disk is detected, the planet appears to have depleted the disk almost completely, in contrast to the relatively small depletion seen for HD107146; other scenarios should therefore be considered.In this project we will consider how a multi-planet system would shape the disk; specifically, we will examine the effect of secular resonances. These occur where the precession rate of the planets equals that of the planetesimals in the disk, and act over long timescales to excite the eccentricities of these planetesimals. Objects on eccentric orbits will spend the majority of their time at distances not equal to their semi-major axis; this could therefore give rise to a depletion of the kind seen in the HD107146 system if there is a secular resonance at ~80AU. We will begin by proposing a two-planet system, and aim to constrain the parameter space (consisting of the planet masses and distances) to as great an extent as possible by considering the requirements imposed by the observed disk structure and the secular interaction timescale. N-body dynamical simulations will then be used to investigate the disk structures that would arise from various combinations of planets. The output from these simulations will also be post-processed to include the effect of disk depletion due to catastrophic collisions, which grind planetesimals into small particles which are blown out of the system by radiation pressure.Having examined the specific example of HD107146, we aim to extend this secular analysis to other debris disks which show depletions; in the longer term we will also be considering more generally the observable effects of other types of planet-disk interaction.