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

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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.