Evolution of Semiconvective Staircases in Rotating Flows: Consequences for Fuzzy Cores in Giant Planets

Abstract

Recent observational constraints on the internal structure of Jupiter and Saturn suggest that these planets have “fuzzy” cores, i.e., gradients of the concentration of heavy elements that might span a large fraction of the planet’s radius. These cores could be composed of a semiconvective staircase, i.e., multiple convective layers separated by diffusive interfaces arising from double-diffusive instabilities. However, to date, no study has demonstrated how such staircases can avoid layer mergers and persist over evolutionary timescales. In fact, previous work has found that these mergers occur rapidly, leading to only a single convective layer. Using 3D simulations, we demonstrate that rotation prolongs the lifetime of a convective staircase by increasing the timescale for both layer merger and erosion of the interface between the final two layers. We present an analytic model for the erosion phase, predicting that rotation increases the erosion time by a factor of approximately Ro ^−1/2 , where Ro is the Rossby number of the convective flows (the ratio of the rotation period to the convective turnover time). For Jovian conditions at early times after formation (when convection is vigorous enough to mix a large fraction of the planet), we find the erosion time to be roughly 10 ^9 yr in the nonrotating case and 10 ^11 yr in the rotating case. If these timescales are confirmed with a larger suite of numerical simulations, the existence of convective staircases within the deep interiors of giant planets is a strong possibility, and rotation could be an important factor in the preservation of their fuzzy cores.

Keywords

• Jupiter
• Saturn
• Solar system gas giant planets
• Extrasolar gaseous giant planets
• Planetary interior
• Hydrodynamical simulations