The promise and limitations of improved-accuracy gravity field measurements for Uranus and Neptune

Uranus and Neptune present unique challenges to planetary modelers. The
composition of the so-called ice giants is very uncertain, even more so than the
composition of the gas giants. For instance, it is far from clear that either
planet's composition is dominated by water. Instead, the composition of Uranus and
Neptune likely includes water and other refractory elements in large quantities as
well as a substantial H/He envelope. Furthermore, formation models also predict
that composition gradients are likely in the interiors of these planets, rather
than a neat differentiation into layers of homogeneous composition. (See Helled
and Fortney 2020 and references within.)

A key question that impacts the science case for a potential orbiting mission to
Uranus or Neptune is how will more precise measurements of the gravitational field
better constrain either planet's interior density profile and composition.
Surprisingly, there is yet no published answer to this question.  Here, we present
new work that explores this issue, using a Bayesian framework that allows
exploration of a wide range of interior density profiles.

Our approach, which builds off our previous work for Saturn (Movshovitz et al.,
2020) and that of others  (e.g. Marley et al., 1995, Helled et al., 2011) takes a
relatively unbiased view of the interior structure by employing so-called
empirical density profiles. A parameterization is applied to the density profiles
directly (via mathematical base functions) instead of to an assumed layered
composition (H/He, water, rocks). While some of these empirical density profiles
may imply unrealistic compositions, they can also probe solutions that would be
missed by the standard layered-composition approach.

Here we will present models of Uranus and Neptune constructed with this approach,
and ask two questions: 1) How large is the space of possible solutions today? 2)
How much will it be reduced should a future mission to Uranus and Neptune improve
the precision on their gravity field measurements by several orders of magnitude,
to the level now available for Jupiter and Saturn?