Influence of a thermal boundary layer on the thermal evolution of Uranus and Neptune

It has been a long-standing challenge to reconcile the perceived similarities of Uranus and Neptune with their highly different intrinsic heat fluxes. Previous evolution calculations using the conventional assumption of an adiabatic interior yield too high present-day luminosities or - equivalently - too long cooling times for Uranus  (e.g. [1,2]). For Neptune, however, we found that similar assumptions yield too short cooling times [3].
One proposed mechanism for reproducing the observed brightness is a conducting interface between the hydrogen- and helium-rich outer part and the ice-rich inner part that would inhibit efficient energy transport across it [4]. In this work, we use our recently developed tool for modelling giant planets based on the Henyey-method for stellar 
evolutions [5] to investigate such a conducting interface in the planet's interior, examining the influence of parameters such as assumed layer thickness and thermal conductivity on the cooling behaviour. 
We find that even a thin conductive interface of a few kilometers has significant influence on the planetary cooling. Initially, the presence of such a boundary layer speeds up cooling, while after about 0.1-0.5 Gyr the cooling is slowed down drastically compared to the adiabatic case, similar to what was found for Saturn previously [6]. Our preferred solutions for Uranus suggest equilibrium evolution with the solar incident flux, while for Neptune, we find that plateaus in T_eff(t) near its observed value require fine-tuned combinations of layer thickness and thermal conducitivity. 

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