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\begin{document}

\title{Io's Long-Wavelength Topography as a Probe for a Subsurface Magma Ocean}



\author[1]{Szilárd Gyalay}%
\author[1]{Francis Nimmo}%
\affil[1]{University of California, Santa Cruz}%


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  \date{June 18, 2024}


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\begin{abstract}
We investigate how spatial variations in tidal heating affect Io's
isostatic topography at long wavelengths. The difference between the
hydrostatic shape implied by Io's gravity field and its observed global
shape is less than the latter's 0.3 km uncertainty. Assuming Airy
isostasy, degree-2 topography \textless{}300 m amplitude is only
possible if surface heat flux varies spatially by \textless{}17\% of the
mean value. This is consistent with Io's volcano distribution and is
possible if tidal heat is generated within a convecting layer underneath
the lithosphere. However, that layer would require a viscosity
\textless{}10\textsuperscript{10} Pa s. A magma ocean would have low
enough viscosity but would not generate enough tidal heat internally.
Conversely, assuming Pratt isostasy, we find \textasciitilde{}150 m
degree-2 topography is easily achievable. If a magma ocean was present,
Airy isostasy would dominate; we therefore conclude that Io is unlikely
to possess a magma ocean.%
\end{abstract}%



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