Tidal dissipation within Earth’s solidifying magma ocean: II. Atmospheric blanketing and its constraint on tidal heating

The early orbital evolution of the Earth–Moon system is strongly coupled with the thermal evolution of Earth’s magma ocean formed after the Moon-forming giant impact. The thermal budget of the magma ocean is dominated by the balance between tidal heating and the surface heat flux of the magma ocean. The former is effectively limited by the latter, because the magma ocean would stop cooling as soon as tidal heating is large enough to match the surface heat flux. One of the key factors controlling the magma ocean surface heat flux is the temperature difference at the surface, which is regulated by the thermal structure of the coexisting atmosphere. To evaluate the impact of tidal dissipation on the evolution of the Earth–Moon system, therefore, it becomes essential to understand how the cooling efficiency of Earth’s magma ocean is regulated by the thermal blanketing effect of the coexisting atmosphere, which is in turn affected by the degassing history of the magma ocean. In this work, we couple a comprehensive atmospheric model with a realistic mantle phase diagram to quantify how the surface heat flux from a magma ocean would change during the course of its solidification. Our results show that gray and nongray treatments result in about one order of magnitude difference in heat flux and that likely uncertainties in Earth’s volatile budget as well as degassing efficiency have a limited influence on magma ocean heat flux. Most importantly, the magnitude of tidal heating can be comparable to or even greater than magma ocean heat flux for a range of early Earth conditions, highlighting the fundamental role of atmospheric blanketing in the tidal evolution of the Earth–Moon system.