Impact of compressibility on heat transport characteristics of large terrestrial planets

Abstract

We present heat transport characteristics for mantle convection in large terrestrial exoplanets (M⩽8M⊕). Our thermal convection model is based on a truncated anelastic liquid approximation (TALA) for compressible fluids and takes into account a selfconsistent thermodynamic description of material properties derived from mineral physics based on a multi-Einstein vibrational approach. We compare heat transport characteristics in compressible models with those obtained with incompressible models based on the classical- and extended Boussinesq approximation (BA and EBA respectively). Our scaling analysis shows that heat flux scales with effective dissipation number as Nu∼Dieff -0.71 and with Rayleigh number as Nu∼Raeff 0.27. The surface heat flux of the BA models strongly overestimates the values from the corresponding compressible models, whereas the EBA models systematically underestimate the heat flux by ∼10%–15% with respect to a corresponding compressible case. Compressible models are also systematically warmer than the EBA models. Compressibility effects are therefore important for mantle dynamic processes, especially for large rocky exoplanets and consequently also for formation of planetary atmospheres, through outgassing, and the existence of a magnetic field, through thermal coupling of mantle and core dynamic systems.