A complete study of the precision of the concentric MacLaurin spheroid method to calculate Jupiter's gravitational moments

TL;DR

This study evaluates the precision of the concentric MacLaurin spheroid method for calculating Jupiter's gravitational moments, emphasizing the need for many spheroids and proper outer layer modeling to meet Juno mission accuracy.

Contribution

It provides a detailed analysis of the errors in the CMS method and offers guidelines for achieving the required precision in Jupiter modeling with Juno data.

Findings

Using at least 1500 spheroids improves accuracy.

Proper outer layer modeling is crucial for precise results.

Errors in outermost layer treatment limit the method's ultimate precision.

Abstract

A few years ago, Hubbard (2012, 2013) presented an elegant, non-perturbative method, called concentric MacLaurin spheroid (CMS), to calculate with very high accuracy the gravitational moments of a rotating fluid body following a barotropic pressure-density relationship. Having such an accurate method is of great importance for taking full advantage of the Juno mission, and its extremely precise determination of Jupiter gravitational moments, to better constrain the internal structure of the planet. Recently, several authors have applied this method to the Juno mission with 512 spheroids linearly spaced in altitude. We demonstrate in this paper that such calculations lead to errors larger than Juno's error bars, invalidating the aforederived Jupiter models at the level required by Juno's precision. We show that, in order to fulfill Juno's observational constraints, at least 1500 spheroids must be used with a cubic, square or exponential repartition, the most reliable solutions. When using a realistic equation of state instead of a polytrope, we highlight the necessity to properly describe the outermost layers to derive an accurate boundary condition, excluding in particular a zero pressure outer condition. Providing all these constraints are fulfilled, the CMS method can indeed be used to derive Jupiter models within Juno's present observational constraints. However, we show that the treatment of the outermost layers leads to irreducible errors in the calculation of the gravitational moments and thus on the inferred physical quantities for the planet. We have quantified these errors and evaluated the maximum precision that can be reached with the CMS method in the present and future exploitation of Juno's data.