Collaborative Research: Dynamical Tides in Close Stellar Binaries and Exoplanetary Systems

潮汐在许多天体物理环境中都是一个重要的因素。潮汐可以影响生命，就像地球上的潮汐周期一样；它们可以影响地质学，比如木星对木卫一的强烈潮汐引力；甚至可以影响双星的演化。麻省理工学院（MIT）和弗吉尼亚大学（UVA）之间的一项研究合作将分析恒星-恒星和恒星-行星双星中的潮汐摩擦，并评估这些系统中非线性流体动力学对潮汐的重要性。流体动力学是研究气体和液体如何流动的科学，而非线性系统是指输出的变化与输入的变化具有复杂的（不是简单的线性）数学关系的系统。主要研究人员已经发展了研究弱和强非线性潮汐流体动力学的基本理论和计算方法。所提出的计算将推动目前的技术水平，以便为一系列恒星类型、演化阶段和潮汐非线性程度的潮汐摩擦提供基于物理的处方。详细的计算和数值模拟将被提炼成简单的公式，这可能对天体物理学家未来的研究有用。麻省理工学院PI每年将在麻省理工学院夏季研究计划（MSRP）中为一名学生担任潮汐研究的研究导师。MSRP最初是麻省理工学院的一项倡议，旨在解决非裔美国人、墨西哥裔美国人、美洲原住民和波多黎各人在美国工程和科学领域代表性不足的问题。它旨在从美国院校中寻找有才华的本科生，这些学生是代表性不足的少数民族，他们可能会从在麻省理工学院（MIT）的一个研究小组度过一个夏天（9周）中受益。弗吉尼亚大学的PI将指导弗吉尼亚-北卡罗来纳州路易斯·斯托克斯少数民族参与联盟的本科生参与者，该联盟旨在扩大代表性不足的少数民族在STEM学科中的参与。提出了三个项目：(1)弱非线性波波相互作用驱动的热木星轨道衰变。先前对类太阳恒星的研究将扩展到一系列恒星质量和进化状态。(2)强非线性极限中的圆化和轨道衰减，即引力波发生破波的极限。同样，目标是将先前的计算扩展到观测到的主序星，以及亚巨星和红巨星分支星的范围。(3)高偏心率行星迁移过程中，非线性波相互作用对恒星和行星涨潮的影响。对于每个项目，将进行理论预测与现有数据的详细比较。这包括紧密的双星，围绕着各种主序星的热木星和海王星，以及有亚恒星伴星的进化恒星。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Tides are an important factor in many astrophysical settings. Tides can affect life, like tidal cycles on Earth; they can affect geology, as in the intense tidal pull of Jupiter on Io; and can even influence the evolution of stars in binary pairs. A research collaboration between Massachusetts Institute of Technology (MIT) and the University of Virginia (UVA) will analyze tidal friction in close star-star and star-planet binaries and assess the importance of nonlinear fluid dynamics on tides in these systems. Fluid dynamics is the science of how gases and liquids flow, and a nonlinear system is one in which the change in the output has a complicated (not simply linear) mathematical relationship with a change in the input. The principal investigators (PIs) have developed the basic theory and computational methods to study both weakly and strongly nonlinear tidal fluid dynamics. The proposed calculations will advance the state of the art in order to provide physics-based prescriptions for tidal friction over a range of stellar types, evolutionary stages, and degree of nonlinearity of the tide. The detailed calculations and numerical simulations will be distilled into simple prescriptions which may be useful for future investigations by astrophysicists. The MIT PI will serve as a research mentor in the study of tides to a student each year in the MIT Summer Research Program (MSRP). MSRP began as an MIT initiative to address the issue of underrepresentation of African Americans, Mexican Americans, Native Americans and Puerto Ricans in engineering and science in the US. It seeks to identify talented undergraduate students from US institutions who are underrepresented minorities and might benefit from spending a summer (nine weeks) at MIT working in a research group. The UVA PI will mentor undergraduate participants in the Virginia-North Carolina Louis Stokes Alliance for Minority Participation, which seeks to broaden participation of underrepresented minority populations in STEM disciplines.Three projects are proposed: (1) Orbital decay of hot Jupiters driven by weakly nonlinear wave-wave interactions. Previous work on solar-type stars will be expanded to include a range of stellar masses and evolutionary states. (2) Circularization and orbital decay in the strongly nonlinear limit, where wave breaking occurs for gravity waves. Again the goal is to expand previous calculations to the observed range of main sequence stars, as well as sub-giant and red giant branch stars. (3) Nonlinear wave interaction effects on the tide raised in the star and in the planet during high eccentricity planet migration. For each project, a detailed comparison of theoretical predictions to available data will be carried out. This includes close stellar binaries, the hot Jupiters and Neptunes around a variety of main sequence stars, and evolved stars with substellar companions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.