Interactions between planets and debris disks

组成碎片盘的行星体受到系统中存在的任何行星的动态扰动；这些扰动影响着盘的结构。因此，通过观察~mm大小的尘埃颗粒(由较大的天体碰撞和研磨产生的尘埃颗粒，因此有望追踪到行星体的分布)，我们可以对具有碎片盘的恒星的行星系统做出推断。例如，太阳系历史的一些最好的证据来自于对太阳小行星和Edgeworth-Kuiper带结构的研究。首先，这个项目关注的是HD107146，一颗大约100 Myr的太阳型恒星，它拥有一个相对较宽的碎片盘，从~30延伸到150AU。ALMA最近对该圆盘的观测表明，在大约80AU处，小行星的表面密度已经耗尽。一种可能的解释是，有一颗几个地球质量的行星在大约80AU的圆形轨道上，它正在清除它周围紧邻的区域的小行星。然而，耗尽的确切形状并没有很好的限制：从径向密度分布和双幂定律分布都可以很好地符合观测结果，径向密度分布随着距离的增加而增加，但在~80AU处有一个完全的缺口(如果有行星处于耗尽状态，预计会出现这种情况)，这需要一些其他的解释。另一个提出的想法是，一颗行星在偏心轨道上散布到圆盘中，观察到的结构是行星与圆盘相互作用时轨道循环的结果。然而，在大间隔行星和碎片盘被探测到的情况下，行星似乎几乎完全耗尽了盘，而HD107146的消耗相对较小；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将如何塑造盘；具体地说，我们将检查长期共振的影响。当行星的进动速度等于盘中的小行星的进动速度时，就会发生这种情况，并在长时间尺度上激发这些小行星的偏心率。偏心轨道上的天体大部分时间将在与其半长轴不同的距离处度过；因此，如果在~80AU处存在长期共振，这可能会导致HD107146系统中看到的那种损耗。我们将首先提出一个双行星系统，目标是通过考虑所观察到的盘结构和长期相互作用时间尺度施加的要求，尽可能地限制参数空间(由行星质量和距离组成)。然后将使用N体动力学模拟来研究由各种行星组合产生的盘状结构。这些模拟的输出也将被后处理，以包括由于灾难性碰撞而导致的盘片耗尽的影响，这是将行星体研磨成被辐射压力吹出系统的小粒子。在研究了HD107146的具体例子之后，我们的目标是将这种长期分析扩展到其他显示耗尽的碎片盘；在更长的时间内，我们还将更广泛地考虑其他类型的行星-盘相互作用的可观察到的影响。

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.