Study of Jupiter’s Interior with Quadratic Monte Carlo Simulations

Abstract

We construct models for Jupiter’s interior that match the gravity data obtained by the Juno and Galileo spacecraft. To generate ensembles of models, we introduce a novel quadratic Monte Carlo technique, which is more efficient in confining fitness landscapes than the affine invariant method that relies on linear stretch moves. We compare how long it takes the ensembles of walkers in both methods to travel to the most relevant parameter region. Once there, we compare the autocorrelation time and error bars of the two methods. For a ring potential and the 2d Rosenbrock function, we find that our quadratic Monte Carlo technique is significantly more efficient. Furthermore, we modified the walk moves by adding a scaling factor. We provide the source code and examples so that this method can be applied elsewhere. Here we employ our method to generate five-layer models for Jupiter’s interior that include winds and a prominent dilute core, which allows us to match the planet’s even and odd gravity harmonics. We compare predictions from the different model ensembles and analyze how much an increase in the temperature at 1 bar and ad hoc change to the equation of state affect the inferred amount of heavy elements in the atmosphere and in the planet overall.

Relation of Gravity, Winds, and the Moment of Inertia of Jupiter and Saturn

“…To construct EOSs for models in this article, we start from the ab initio EOS that Militzer & Hubbard (2013) computed for one hydrogen-helium mixing ratio. With these calculations, absolute entropies (Militzer 2013) were derived that implicitly set the temperature profiles in our models. We use our helium EOS from Militzer (2006Militzer ( , 2009 to perturb helium fraction in our H-He EOS as we detailed in Hubbard & Militzer (2016b).…”

“…With these calculations, absolute entropies (Militzer 2013) were derived that implicitly set the temperature profiles in our models. We use our helium EOS from Militzer (2006Militzer ( , 2009 to perturb helium fraction in our H-He EOS as we detailed in Hubbard & Militzer (2016b). We also follow this article when we introduce heavily elements into our models.…”

“…For our Monte Carlo calculations of Jupiter's interior (Militzer 2023), we vary the beginning and end pressure of the helium rain layer but apply constraints so that they remain compatible with H-He phase diagram as derived by Morales et al (2009). We also vary a parameter α that controls the shape of the helium profile in this layer, as we explain in Militzer et al (2022).…”