Ring and Doppler Imaging Seismology from a Uranus Orbiter: Promise and Challenges
Authors: Mankovich Christopher , Friedson Jim , Parisi Marzia , Hofstadter Mark , Markham Stephen , Hedman Matthew 
Published: July 2024

The detection of Uranus normal mode oscillations would provide hugely valuable diagnostics for ice giant interior structure. Since oscillation modes are generally sensitive to fluid stability, and low angular degree modes reach deep into the interior, their frequencies can deliver powerful information independent of that from the improved gravity field measurements we expect from radio tracking of the spacecraft1. Here we explore two methodologies for seismology of Uranus by an orbiting spacecraft.
First, ring seismology uses stellar occultation or imaging data to uncover resonances between non-radial planetary normal modes and ring orbits. This has been successful at Saturn, where the planet's oscillating gravity field generates waves near epicyclic (Lindblad) or vertical resonances2-8. For Uranus's system of predominantly narrow (1-10 km scale) rings, ring seismology would entail the search for m-lobed standing patterns on Uranus's narrow rings that betray the influence of gravitational forcing near a resonance. The resonant shepherding of the Epsilon ring by the moons Cordelia and Ophelia is a striking example of confinement of a narrow Uranian ring9, but the mechanism confining up to 8 other rings is unknown10, and a rich spectrum of Uranian oscillations may be partly responsible.
Uranus interior models that satisfy all available data predict that the narrow rings overlap with Uranian fundamental modes and internal gravity modes11, as well as inertial modes. We model the mode spectrum in a set of new Uranus interior models to quantify the constraining power than one or two ring seismology detections in the Uranian rings would have for Uranus interior structure.
Second, Doppler imaging seismology would produce a time series of radial velocity maps of the Uranian photosphere, from which frequencies of normal modes could be extracted. The radial velocity signal is likely dominated by the higher frequency pressure (p) modes, i.e., trapped sound waves, the type of mode responsible for the 5-minute oscillation in the sun. We show how frequency measurements for a set of p modes with consecutive radial order can be used to construct an &#233;chelle diagram, where deviations from constant frequency spacing are sensitive diagnostics of composition or sound speed interfaces in the planetary interior.
The modest requirements of ring seismology stand in contrast to Doppler imaging's requirement for dedicated instrumentation (in the form of an interferometer or magneto-optical filter design) and more substantial payload. This will need to be weighed against the advantage that p modes offer for localizing features in the planetary interior (especially when combined with inversion techniques12) and synergies with other science areas, especially atmospheric dynamics13.
Further insights into the Uranian normal mode spectrum may be obtainable from direct gravitational seismology, i.e., the detection of modes through their gravitational influence on the trajectory of the spacecraft itself14,15. This builds on the tentative evidence for Jupiter and Saturn seismicity in the Doppler tracking of the Juno and Cassini spacecraft16,17.
&#160;References:[1] Parisi et al. 2024, PSJ; doi:10.3847/PSJ/ad4034
[2] Marley &amp; Porco 1993, Icarus; doi:10.1006/icar.1993.1189
[3] Hedman &amp; Nicholson 2013, AJ; doi:10.1088/0004-6256/146/1/12
[4] Hedman &amp; Nicholson 2014, MNRAS; doi:10.1093/mnras/stu1503
[5] French et al. 2019, Icarus; doi:10.1016/j.icarus.2018.10.013
[6] Hedman et al. 2019, AJ; doi:10.3847/1538-3881/aaf0a6
[7] French et al. 2021, Icarus; doi:10.1016/j.icarus.2021.114660
[8] Hedman et al. 2022, PSJ; doi:10.3847/PSJ/ac4df8
[9] Porco &amp; Goldreich 1987, AJ; doi:10.1086/114354
[10] French et al. 2024, Icarus; doi:10.1016/j.icarus.2024.115957
[11] A'Hearn et al. 2022; doi:10.3847/PSJ/ac82bb
[12] Jackiewicz et al. 2012, Icarus; doi:10.1016/j.icarus.2012.06.028
[13] Schmider et al. 2024, PSJ; doi:10.3847/PSJ/ad3066
[14] Friedson 2020, Ph. Tr. R. Sc. A; doi:10.1098/rsta.2019.0475
[15] Parisi et al. 2024, in preparation
[16] Durante et al. 2022, Nat. Co.; doi:10.1038/s41467-022-32299-9
[17] Markham et al. 2020, PSJ; doi:10.3847/PSJ/ab9f21