| Abstract: |
| A classic dynamical problem is to find the tidal equilibrium states for astrophysical systems containing both self-gravity and angular momentum. This type of constrained optimization procedure is sometimes known as a Darwin Problem (dating to its first implementation in 1880 regarding the Earth-moon system). Dissipation causes physical systems to evolve toward lower energy states, so that the lowest energy state is the preferred configuration. These states are often called tidal equilibrium states because tidal interactions cause the dissipation in many astrophysical systems of interest. In binary star systems with both orbital and spin angular momentum, for example, the equilibrium state corresponds to aligned angular momentum vectors and synchronous rotational frequencies. This talk discusses several generalizations to previous incarnations of the Darwin problem. Specifically, we include the quadrupole moment of the central star in two-body systems, add a third body in hierarchical star-planet-moon systems, and allow for mass transfer in multi-planet systems. In general, these tidal equilibrium states exist for only a portion of parameter space, which is delineated through this work. |
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