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\begin{document}

\title{Nonradial Oscillations of Saturn: Forcing of the Slowest Spiral Density
Waves in the C Ring by I-modes and R-modes and the Implications for the
Internal Structure}



\author[1]{Andrew Friedson}%
\author[2]{Katie Broad}%
\affil[1]{Jet Propulsion Laboratory}%
\affil[2]{Purdue University}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\begin{abstract}
It is now known that many spiral density waves in Saturn's C ring are
forced by resonant gravitational interactions with the planet's
nonradial oscillations. Observations of their periods have the power to
reveal new information concerning subtle aspects of the planet's
internal structure. The properties of a certain class of nonradial
oscillations, consisting of the inertial and rotational normal modes
(i-modes and r-modes), are particularly sensitive to small departures of
the internal density stratification from adiabatic, and may be
especially useful in revealing such departures and their implications
for any compositional gradients residing inside Saturn. We calculate the
frequencies and eigenfunctions (shapes) of the i-modes and r-modes for a
given suite of internal structure models and determine the Lindblad
resonance locations and periods of the density waves they excite in the
C ring. We find that for reasonable models of Saturn's internal
structure, the i-mode and r-mode frequencies overlap the range of
frequencies of the slowest density waves observed in the C ring, that
is, those having pattern speeds similar to Saturn's rotation rate. In
addition, the presence of observable density waves forced by r-modes
requires Saturn to possess (at least) two statically stable
(non-convective) regions, one in the deep interior and the other in the
outer molecular hydrogen envelope. The inner zone is most likely
stabilized by a significant compositional gradient, the outer zone by a
compositional gradient, by baroclinic processes, or both. Unresolved
questions remain. Currently, the model predicts that if energy is
equipartitioned among the i-modes, then some slow density waves should
be detectable at radii inside \textasciitilde{}84500 km in the C ring.
None have been observed inside this radius. In addition, the source of
excitation of the normal modes remains to be identified. We are
currently exploring whether they can draw their energy from baroclinic
instability in the outer stable zone. These questions will be addressed
at length at the meeting. This work is supported by the NASA SSW
program.%
\end{abstract}%



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