In this article, a Markov chain Monte Carlo (MCMCMC) exploration of the possible interior density profiles of a giant planet is presented, which is not tied to assumed composition, thermal state, or material equations of state.
Abstract:
The gravity field of a giant planet is typically our best window into its interior structure and composition. Through comparison of a model planet's calculated gravitational potential with the observed potential, inferences can be made about interior quantities, including possible composition and the existence of a core. Necessarily, a host of assumptions go into such calculations, making every inference about a giant planet's structure strongly model dependent. In this work, we present a more general picture by setting Saturn's gravity field, as measured during the Cassini Grand Finale, as a likelihood function driving a Markov Chain Monte Carlo exploration of the possible interior density profiles. The result is a posterior distribution of the interior structure that is not tied to assumed composition, thermal state, or material equations of state. Constraints on interior structure derived in this Bayesian framework are necessarily less informative, but are also less biased and more general. These empirical and probabilistic constraints on the density structure are our main data product, which we archive for continued analysis. We find that the outer half of Saturn's radius is relatively well constrained, and we interpret our findings as suggesting a significant metal enrichment, in line with atmospheric abundances from remote sensing. As expected, the inner half of Saturn's radius is less well constrained by gravity, but we generally find solutions that include a significant density enhancement, which can be interpreted as a core, although this core is often lower in density and larger in radial extent than typically found by standard models. This is consistent with a dilute core and/or composition gradients.
TL;DR: In this article , a turbulent high-resolution dynamo simulation in a spherical shell that produces these features simultaneously for the first time is reported. But the simulation is limited to the case of Saturn.
TL;DR: The emcee algorithm as mentioned in this paper is a Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010).
TL;DR: This document introduces a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010).
TL;DR: A family of Markov chain Monte Carlo methods whose performance is unaffected by affine tranformations of space is proposed, and computational tests show that the affine invariant methods can be significantly faster than standard MCMC methods on highly skewed distributions.
TL;DR: All of the methods in this work can fail to detect the sorts of convergence failure that they were designed to identify, so a combination of strategies aimed at evaluating and accelerating MCMC sampler convergence are recommended.
Q1. What contributions have the authors mentioned in the paper "Saturn’s probable interior: an exploration of saturn’s potential interior density structures" ?
In this work, the authors present a more general picture by setting Saturn ’ s gravity field, as measured during the Cassini Grand Finale, as a likelihood function driving a Markov Chain Monte Carlo exploration of the possible interior density profiles. Constraints on interior structure derived in this Bayesian framework are necessarily less informative, but are also less biased and more general. The authors find that the outer half of Saturn ’ s radius is relatively well constrained, and they interpret their findings as suggesting a significant metal enrichment, in line with atmospheric abundances from remote sensing. As expected, the inner half of Saturn ’ s radius is less well constrained by gravity, but the authors generally find solutions that include a significant density enhancement, which can be interpreted as a core, although this core is often lower in density and larger in radial extent than typically found by standard models.
Q2. What are the future works mentioned in the paper "Saturn’s probable interior: an exploration of saturn’s potential interior density structures" ?
In this paper, the authors presented an empirical approach to using gravity data to explore the interior structures of fluid planets and applied it to Saturn using data from Cassiniʼs Grand Finale orbits. Here the authors wish to summarize their findings for Saturn, and about planetary interior modeling in general, and to consider the strengths and weaknesses of their “ density first ” approach, versus traditional, composition-based modeling. The great variety of density profiles included in their sample may seem surprising and counterintuitive, but it is an unavoidable consequence of using an integrated quantity, in this case the external potential, to study the spatial distribution of local quantities, in this case the interior density and all properties of the planet that derive from it. As a result, the main finding the authors can report on, with respect to Saturn, is to confirm the well-known but often underappreciated suspicion that solutions to Saturn ’ s gravitational potential field exist that do not conform to a simple model of a few compositionally homogeneous and thermally adiabatic layers.