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”，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，这两个带更普遍地被称为“碎片盘”。这样的圆盘含有大小不一的碎片，从微小的尘埃颗粒一直到小行星和矮行星。令人惊讶的是，我们也可以看到其他恒星周围的碎片盘；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，因为它们的质量由看不见的大天体主导。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，建立它们的质量将真正帮助我们了解行星系统是如何形成的，它们是如何演化的，系外行星在哪里运行，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来自詹姆斯·韦伯太空望远镜(JWST)的尖端数据相结合，首次测量碎片盘质量。这是通过考虑系外行星在接近碎片盘的轨道上运行时发生的相互作用来实现的。这些相互作用影响着行星盘形状和系外行星轨道，并取决于碎片-盘质量；我会使用这些相互作用来直接测量碎片-盘质量。这种新方法的优点是，与以前的技术不同，它不需要对未知量做很多假设。具体地说，我确定了两种类型的已知碎片盘，它们特别容易被用这种方式测量其质量：第一，形状既窄又椭圆形的盘；第二，既宽又包含间隙的盘。我是几个JWST计划的成员，这些计划将在联谊会开始之前寻找这些圆盘附近的系外行星；作为研究员，我会通过将这些观测与新的动力学理论相结合来测量碎片-圆盘的质量。然后，这些质量将被用来确定位于圆盘内的最大碎片天体(小行星或矮行星)的大小；最后，这些碎片大小将被用来测试碎片理论和系统形成模型的关键方面。在我进行科学研究的同时，我还计划实施一个大型公共参与方案，以提高人们对数学对于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，数学可能是枯燥、恼人甚至可怕的。我的目标是向年轻人展示，数学有许多令人着迷的应用，超出了大多数人在日常生活中的经历；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、交互式的计算机软件，向小学生展示数学的各种和令人兴奋的应用，以促进早期理解，即数学具有超越人们日常经验的巨大潜力。其目的不是教授数学，而是为教师提供一个辅助工具，展示数学可以解决的令人惊叹的事情，帮助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.