# DDA 2015 – Saturn Ring Seismology – How ring dynamics reveal the internal structure of the planet

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Jim Fuller (CalTech)

#### Abstract

Seismology allows for direct observational constraints on the interior structures of stars and planets. Recent observations of Saturn’s ring system have revealed the presence of density waves within the rings excited by oscillation modes within Saturn, allowing for precise measurements of a limited set of the planet’s mode frequencies. Additional ring waves are created at Lindblad resonances with density inhomogeneities in the planet, allowing for measurements of internal differential rotation. I construct interior structure models of Saturn, compute the corresponding mode frequencies, and compare them with the observed mode frequencies. The observed modes, some of which are finely split in frequency, can only be reproduced in models containing gravity modes that propagate in a stably stratified region of the planet. The stable stratification must exist deep within the planet near the large density gradients between the core and envelope. The planetary oscillation modes may in turn influence the evolution of the rings by depositing angular momentum at Lindblad resonances. In particular, the Maxwell gap is likely opened due to a resonance with Saturn’s $l=m=2$ fundamental mode.

#### Notes

• Internal structures of giant planets  poorly constrained
• Haven’t been able to do seismology…until Cassini @ Saturn
• Consider just the C ring spiral density waves.
• Pattern speed & pattern number: diagnostics.
• $m(\Omega – \Omega_p) = \kappa$
• $\Omega_p = -\sigma_\alpha/m$
• Very tiny perturbations cause these density waves.
• mode periods: ~hours
• mode amplitudes (inside Saturn): ~1 m
• Planet model:
• inner core, stable outer core, g-mode cavity, f-mode cavity, convective outer envelope
• resonances with $l=m$ f modes
• unexpected: frequency fine-splitting! (Maxwell Gap)
• new: implies stable stratification region
• generates families of g modes ($2^{nd}$ order)
• fast rotation $\rightarrow$ mode mixing
• mess!
• analogous to hydrogen atom in strong electromagnetic field
• strongest mixing near f-mode freq’s
• $\rightarrow$ lots of modes generated in the rings that are currently to “faint” to see
• Conclusions:
• Evidence for stable stratification (non-adiabatic interior) of Saturn
• Helium rain, core erosion, both, something else?
• Missing ingredient: differential rotation?
• Some evidence for density inhomogeneities within Saturn