Astrophysical dynamics

我计划探索从行星到星系暗晕的天体物理系统的行为。由于这些系统受重力的支配，重力是无标度的，类似的理论工具可以用来研究所有这些系统。-在弦理论的推动下，宇宙暗物质的一个很有希望的候选者是一种非常轻的轴子状粒子，有时被称为“模糊暗物质”。在最有趣的质量范围内，德布罗意波长相当于一个星系的大小。在其他新的效应中，(I)暗物质中波动的干涉图案导致晕中的热力学平衡松弛，以及(Ii)在星系中心形成致密的玻色-爱因斯坦凝聚体或孤子。我计划研究孤子的形成以及在模拟中发现的孤子质量和晕质量之间的关系。-星系中心的超大质量黑洞被致密的星团包围。它们应该处于亚稳态热平衡状态，即受恒星轨道半长轴冻结约束的最大熵态。我们已经证明了这些平衡在球形组态和不平衡组态之间呈现出相变。我计划通过模拟来探索这一转变，并调查在不平衡状态下发生瞬变的比率，例如潮汐扰乱事件和黑洞合并。-许多恒星是在由两颗接近的双星围绕其共同的质心运行的四星系中发现的。在某些情况下，双星在潮汐摩擦的作用下演化时，被捕获到相互的轨道共振中。作为恒星性质和轨道参数函数的共振系统的丰富性，为双星中潮汐摩擦的机制提供了新的限制，我计划对此进行研究。-动力天文学的主要任务之一是从示踪物(例如球状星系团或附近的卫星星系)的相混合群体的运动学快照估计系统的引力势(例如银河系的暗晕)。我已经得出了一种新的估计器，它的精确度比它的竞争对手高出几倍，并计划将其应用于使用盖亚任务高精度运动学星表的各种系统。-GAIA星表使我们能够详细地探索太阳附近恒星的相空间分布。我曾预测，从被破坏的双星产生的星-星关联函数应该可以检测到100个分秒左右的距离，并计划测量这一点。-有几种说法表明，在~700个已知的多行星系统中的行星在质量和半径上表现出强烈的相似性，这意味着相邻行星的形成是相关的。如果是真的，这一结果将给行星形成的物理学带来意想不到的限制。我计划使用一个更可信的零假设和借用宇宙学的更敏锐的统计检验来调查这一说法。

I plan to explore the behaviour of astrophysical systems ranging from planets to the dark halos of galaxies. Since these systems are governed by gravity, which is scale-free, similar theoretical tools can be used to study all of them. - a promising candidate for cosmological dark matter, motivated by string theory, is a very light axion-like particle, sometimes called "fuzzy dark matter". In the most interesting mass range the de Broglie wavelength is comparable to the size of a galaxy. Among other novel effects, (i) fluctuating interference patterns in the dark matter lead to relaxation towards thermodynamic equilibrium in the halo, and (ii) a compact Bose-Einstein condensate or soliton forms at the centre of the galaxy. I plan to investigate the formation of the soliton and the relation between soliton mass and halo mass found in simulations. - supermassive black holes at the centres of galaxies are surrounded by dense star clusters. These should be in metastable thermal equilibria, i.e., maximum-entropy states subject to the constraint that the semimajor axes of the stellar orbits are frozen. We have shown that these equilibria exhibit a phase transition between spherical and lopsided configurations. I plan to explore this transition with simulations, and to investigate the rate of transients such as tidal disruption events and black-hole mergers in the lopsided state. - many stars are found in quadruple systems consisting of two close binaries orbiting their common centre of mass. In some cases the binaries have been captured into mutual orbital resonances as they evolve by tidal friction. The abundance of resonant systems as a function of stellar properties and orbital parameters provides novel constraints on the mechanism of tidal friction in binary stars, which I plan to investigate. - one of the main tasks of dynamical astronomy is to estimate the gravitational potential of a system (e.g., the Galaxy's dark halo) from a kinematic snapshot of a phase-mixed population of tracers (e.g., globular clusters or nearby satellite galaxies). I have derived a novel estimator that is several times more accurate than its competitors, and plan to apply this to a variety of systems using high-accuracy kinematic catalogues from the Gaia mission. - the Gaia catalogues allow us to explore in detail the phase-space distribution of stars in the solar neighbourhood. I have predicted that the star-star correlation function arising from disrupted binary stars should be detectable out to separations of a hundred parsecs or so and plan to measure this. - there are several claims that the planets in the ~700 known multi-planet systems exhibit strong similarities in mass and radius, implying that the formation of adjacent planets is correlated. If true, this result places unexpected constraints on the physics of planet formation. I plan to investigate this claim using a more plausible null hypothesis and sharper statistical tests borrowed from cosmology.