Inverse problems based on seismology and magnetohydrodynamics of solar system gas giants

Revealing the interiors, and constraining the equations of state (describing how materials behave under realistic pressure and temperature conditions), of gas giant planets in the solar system have been important objectives in planetary science, even more so since the detection of many gaseous exoplanets. These exoplanets are being examined to learn more about how the solar system came to be, and to compare the formation of our solar system to those planetary systems. Seismology has been playing a role in obtaining (instantaneous) models of gas giant planets, including their layering and equations of state, while planetary magnetic fields have been informing one further about their interior properties and thermal evolution. This project involves a novel mathematical framework to facilitate gaining new insights in the (new class of) inverse problems associated with seismology and magnetohydrodynamcs describing the generation of magnetic fields through dynamos. The project offers, via collaborations, a unique interdisciplinary educational experience for the students giving them a much broader appreciation of the importance of novel techniques and implications in space exploration. The principal investigator will study inverse problems for revealing the interiors of gas giant planets, that is, Saturn and Jupiter, in the solar system, pertaining to seismology and magnetohydrodynamics. Both are mathematically fundamentally distinct from their treatments on Earth and raise intriguing challenges in their analyses. These inverse problems are defined through systems of linear(ized) partial differential equations describing acoustic-gravitational oscillations and nonlinear partial differential equations describing magnetohydrodynamics (in the Boussinesq approximation) as well as edge operators. The project is foundational, but its significance extends to the data that have and will become available from NASA's Cassini and Juno missions; the investigator collaborates with members of the Science Team of the second mission. The results will contribute to discerning limits and possibilities, including guarantees of reliability or lack thereof. 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.