Hawking - How massive are debris discs? Weighing a fundamental component of planetary systems

我们的太阳系包含大量的“碎片”，它指的是任何比行星小的固体物体：小行星、彗星、尘埃和矮行星（如冥王星）都是碎片。太阳系中的大部分碎片集中在小行星带和柯伊伯带，它们通常被称为“碎片盘”。这样的圆盘包含了大小不一的碎片，从微小的尘埃颗粒一直到小行星和矮行星。令人惊讶的是，我们也可以在其他恒星周围看到碎片盘；现代仪器可以看到太阳系外碎片盘中的尘埃，尽管目前的技术无法探测到较大的天体（小行星和矮行星）。这就导致了一个问题：我们不知道碎片盘的质量有多大，因为它们的质量主要是由看不见的大天体组成的。这些碎片盘看起来与我们自己的小行星和柯伊伯带非常不同，确定它们的质量将真正帮助我们了解行星系统是如何形成的，它们是如何演变的，系外行星的轨道，以及我们的太阳系有多典型（或不寻常）。我提出的研究将全新的动力学理论与詹姆斯·韦伯太空望远镜（JWST）的前沿数据结合起来，首次测量了碎片盘的质量。这是通过考虑系外行星在靠近碎片盘的轨道上发生的相互作用来完成的。这些相互作用既影响盘的形状，也影响系外行星的轨道，并取决于碎片盘的质量；我会用这些相互作用来直接测量碎片盘的质量。这种新方法的优点是，与以前的技术不同，它不需要对未知量进行大量假设。具体来说，我确定了两种已知的碎片盘，它们特别容易用这种方法来测量它们的质量：第一种是既窄又椭圆的碎片盘，第二种是既宽又含有间隙的碎片盘。我是几个JWST项目的成员，该项目将在奖学金开始之前寻找这些圆盘附近的系外行星；作为一名研究员，我将把这些观测结果与新的动力学理论结合起来，测量出碎片盘的质量。然后，这些质量将用于确定位于圆盘内的最大碎片体（小行星或矮行星）的大小；最后，这些碎片大小将用于测试碎片理论和系统形成模型的关键方面。在进行科学研究的同时，我还计划了一个大型的公众参与项目，以提高人们对数学对当今人们所依赖的几乎所有产品和服务的重要性的认识。没有数学，我们就无法设计飞机、制造手机、进行医学扫描或理解宇宙，但对许多人来说，数学可能是无聊、烦人甚至可怕的。我的目的是向年轻人展示，数学有许多迷人的应用，超出了大多数人在日常生活中所经历的；例如，试着在没有数学的情况下建造一座城市或向火星发射火箭。我建议开发有趣的交互式计算机软件，向小学生展示数学的多样化和令人兴奋的应用，使他们尽早认识到数学具有超越人们日常经验的巨大潜力。目的不是教数学，而是为教师提供一个辅助工具，让他们展示数学可以解决的惊人问题，帮助他们证明为什么数学很重要，值得学习。最终，它甚至可以激励下一代STEM学生。

Our Solar System contains lots of 'debris', which refers to any solid object smaller than a planet: asteroids, comets, dust and dwarf planets (like Pluto) are all debris. Much of the debris in the Solar System is concentrated in the Asteroid and Kuiper Belts, which are more generally referred to as 'debris discs'. Such discs contain debris with a huge range of sizes, from tiny dust grains all the way up to asteroids and dwarf planets. Surprisingly, we can see debris discs around other stars too; modern instruments can see the dust in extrasolar debris discs, although the larger bodies (asteroids and dwarf planets) cannot be detected with current technology. This leads to a problem: we do not know how massive debris discs are, because their masses are dominated by the unseen large bodies. These debris discs look very different to our own Asteroid and Kuiper Belts, and establishing their masses would really help us to understand how planetary systems form, how they evolve, where exoplanets orbit, and how typical (or unusual) our Solar System is.My proposed research combines brand new dynamical theory with cutting-edge data from the James Webb Space Telescope (JWST), to measure debris-disc masses for the first time. This is done by considering the interactions that occur when an exoplanet orbits close to a debris disc. These interactions affect both the disc shape and the exoplanet orbit, and depend on the debris-disc mass; I would use these interactions to measure debris-disc masses directly. This new method has the advantage that, unlike previous techniques, it does not require a lot of assumptions about unknown quantities. Specifically, I identify two types of known debris disc that are particularly susceptible to having their masses measured in this way: first, discs that are both narrow and elliptical in shape, and second, discs that are both wide and contain a gap. I am a member of several JWST programmes, which will look for exoplanets near these discs before the fellowship starts; as a fellow I would then measure the debris-disc masses by combining these observations with new dynamical theory. These masses would then be used to determine the sizes of the largest debris bodies (asteroids or dwarf planets) that lie within the discs; finally, these debris sizes would be used to test key aspects of debris theory and system-formation models.In parallel to my scientific research, I also plan a large public-engagement programme to raise awareness of how vital mathematics is to almost all products and services that people rely on today. Without maths we could not design aeroplanes, build mobile phones, perform medical scans or understand the universe, but to many people maths can be boring, annoying or even scary. My aim is to show to young people that mathematics has many fascinating applications beyond what most people experience in their everyday lives; for example, try building a city or launching a rocket to Mars without maths. I propose to build fun, interactive computer software that demonstrates the diverse and exciting applications of mathematics to primary school pupils, to foster an early understanding that maths has enormous potential beyond people's day-to-day experiences. The aim is not to teach maths, but to provide a supplementary tool for teachers to show the amazing things that maths can tackle, to help demonstrate why maths is important and worth learning. Ultimately, it could even inspire the next generation of STEM students.