Astrophysical dynamics

我计划探索天体物理系统的行为，从行星到星系的暗晕。由于这些系统是由重力控制的，而重力是无标度的，所以类似的理论工具可以用来研究所有这些系统。宇宙暗物质的一个很有希望的候选者，由弦理论驱动，是一种非常轻的类轴子粒子，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。在其他新效应中，(i)暗物质的波动干涉模式导致晕中的热力学平衡松弛，以及（ii）在星系中心形成紧凑的玻色-爱因斯坦凝聚体或孤子。我计划研究在模拟中发现的孤子的形成和孤子质量与光晕质量之间的关系。星系中心的超大质量黑洞被密集的星团包围。它们应该处于亚稳态热平衡，即在恒星轨道半长轴冻结的约束下的最大熵状态。我们已经证明，这些平衡表现出球形和不平衡构型之间的相变。我计划通过模拟来探索这种转变，并研究不平衡状态下潮汐破坏事件和黑洞合并等瞬态的速率。许多恒星都是在四重系统中被发现的，四重系统由两个紧密的双星围绕它们共同的质量中心运行。在某些情况下，双星在潮汐摩擦的作用下演变成相互的轨道共振。共振系统的丰度作为恒星特性和轨道参数的函数，为双星潮汐摩擦的机制提供了新的约束，这是我计划研究的。动态天文学的主要任务之一是通过相位混合的示踪物质（如球状星团或附近的卫星星系）的动态快照来估计一个系统（如银河系的暗晕）的引力势。我已经推导出一种新颖的估计器，它比它的竞争对手精确几倍，并计划将其应用于使用来自盖亚任务的高精度运动学目录的各种系统。盖亚星表使我们能够详细地探索太阳附近恒星的相空间分布。我曾预言，从被破坏的双星中产生的星-星相关函数应该可以探测到100秒差距左右的距离，并计划测量它。有几种说法认为，在大约700个已知的多行星系统中，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。如果这是真的，这个结果将给行星形成的物理学带来意想不到的限制。我打算用一个更合理的零假设和借鉴宇宙学的更清晰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.