On the Radius Anomaly of Hot Jupiters: Reexamination of the Possibility and Impact of Layered Convection

TL;DR

This study reevaluates whether layered convection caused by compositional inhomogeneity can explain hot Jupiters' large radii, finding limited impact under realistic conditions and questioning its role as the primary cause.

Contribution

It provides a detailed evolutionary analysis showing layered convection's limited effect on hot Jupiter radii and challenges previous assumptions about compositional inhomogeneity's role.

Findings

Layered convection is absent for the first 1 Gyr after formation.

Increased heavy element mass offsets the radius contraction delay.

Artificial layered convection requires extremely thin layers, whose stability is uncertain.

Abstract

Observations have revealed that a significant number of hot Jupiters have anomalously large radii. Layered convection induced by compositional inhomogeneity has been proposed to account for the radius anomaly of hot Jupiters. To reexamine the impact of the compositional inhomogeneity, we perform an evolutionary calculation by determining convection regime at each evolutionary time step according to the criteria from linear analyses. It is shown that the impact is limited in the case of the monotonic gradient of heavy element abundance. The layered convection is absent for the first 1 Gyr from the formation of hot Jupiters and instead overturning convection develops. The super-adiabaticity of the temperature gradient is limited by the neutrally stable state for the Ledoux stability criterion. The effect of the increased mass of heavy elements essentially compensates the effect of the delayed contraction on the planetary radius caused by compositional inhomogeneity. In addition, even in the case where the layered convection is artificially imposed, this mechanism requires extremely thin layers (~ 10^1-10^3 cm) to account for the observed radius anomaly. The long-term stability of such thin layers remains to be studied. Therefore, if the criteria adopted in this paper are adequate, it might be difficult to explain the inflated radii of hot Jupiters by monotonic gradient of heavy element abundance alone.