Constraints on the Moment of Inertia of Jupiter via Interior Models

Details Constraints on the Moment of Inertia of Jupiter via Interior Models Constraints on the Moment of Inertia of Jupiter via Interior Models

Sep 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006dps....38.1107c&link_type=abstract

American Astronomical Society, DPS meeting #38, #11.07; Bulletin of the American Astronomical Society, Vol. 38, p.496

Statistics

Computation

Scientific paper

It has long been known that there is no one-to-one correspondence between the measured J2/q (gravitational response to a prescribed uniform rotation) and C/MR2 (non-dimensionalized moment of inertia) of a planet, despite the Radau-Darwin formula. Here, q is the ratio of centrifugal acceleration to direct gravity at the equator and other symbols have their usual meanings. J2/q is quite precisely known for Jupiter but C/MR2 has not been measured. Standard Jupiter models typically give a moment of inertia factor C/MR2 0.25 or more, suggesting little or no core, but a recently proposed value (Ward & Canup 2006), based on dynamical considerations, is 5 to 10% smaller. Is it possible to reconcile the claimed value of C with the observed value of J2? This is difficult to assess through the traditional computationally intensive approaches. In order to evaluate a very large number of possible models, we make use of the well known analytical solutions for the n=1 polytrope (with and without a simple modification to include a zero pressure density) to construct piecewise continuous models of density containing multiple adjustable parameters that can mimic more realistic equations of state. Our results at constant J2 indicate that the C/MR2 may vary up to as much as 13% less than the value typically predicted for Jupiter from the Radau-Darwin formula. Nevertheless, we show that incorporating the criteria of Jupiter's observed J4 value along with a set of physical constraints (density and compressibility of possible materials) further restricts the allowed range of C/MR2. Many and perhaps all of the most extreme models can be eliminated, suggesting a difficulty in fitting the value suggested by Ward & Canup (2006) and supporting the usual inferences about Jupiter's putative core. This approach can also be used for the other giant planets.

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