Variation in the balance of forces that drive and resist tectonic plate motions allows small terrestrial planet to cooler slower than larger ones. Given that interior cooling affects surface environment, through volcanic/geologic activity, this indicates that small planets should not be down-weighted in the search for life beyond Earth.
Mantle convection and, by association, plate tectonics is driven by the transport of heat from a planetary interior. This heat comes from the internal energy of the mantle and from heat flowing into the base of the mantle from the core. Past investigations of such mixed mode heating have revealed unusual behavior that confounds our intuition based on end?member cases. In particular, increased internal heating leads to a decrease in convective velocity. We investigate this behavior using a suite of numerical experiments and develop a scaling for velocity in the mixed heating case. We identify a planform transition, as internal heating increases, from sheet?like to plume?like downwellings that impacts heat flux and convective velocities. More significantly, we demonstrate that increased internal heating leads not only to a decrease in internal velocities but also a decrease in the velocity of the upper thermal boundary layer (a model analog of the Earth’s lithosphere). This behavior is connected to boundary layer interactions and is independent of any particular rheological assumptions. In cases with a temperature?dependent viscosity and weak plate margin analogs, increased internal heating does not cause an absolute decrease in surface velocity but does cause a decrease relative to purely bottom or internally heated cases as well as a transition to rigid?lid behavior at high heating rates. The differences between a mixed system and end?member cases have implications for understanding the connection between plate tectonics and mantle convection and for planetary thermal history modeling.
Paleo?temperature data indicates that the Earth’s mantle has not cooled at a constant rate. The data show slow cooling from 3.8 to 2.5?Ga followed by more rapid cooling until the present. This has been argued to indicate a transition from a single plate mode to a plate tectonics. However, a tectonic change may not be necessary. Multistage cooling can result from deep water cycling coupled to mantle convection. Melting and volcanism removes water from the mantle (degassing). Dehydration tends to stiffen the mantle, which slows convective vigor and plate velocities causing mantle heating. Higher mantle temperature tends to lower mantle viscosity and increase plate velocities. If these two tendencies are in balance, then mantle cooling can be weak. Breaking this balance, via a switch to net mantle rehydration, can cool the mantle more rapidly. We use coupled water cycling and mantle convection models to test the viability of this hypothesis. Within model and data uncertainty, the hypothesis that deep water cycling can lead to a multi?stage Earth cooling is consistent with data constraints. Probability distributions, for successful models, indicate that plate and plate margin strength play a minor role for resisting plate motions relative to the resistance from interior mantle viscosity.
Multiple hypotheses/models have been put forward regarding Earth’s cooling history. Searching for life beyond Earth has brought these models into a new light as they connect to an energy source that life can tap. Discriminating between different cooling models and adapting them to aid in the assessment of planetary habitability has been hampered by a lack of uncertainty quantification. Here, we provide an uncertainty quantification that accounts for a range of interconnected model uncertainties. This involved calculating over a million individual model evolutions to determine uncertainty metrics. Accounting for uncertainties means that model results must be evaluated in a probabilistic sense, even though the underlying models are deterministic. The uncertainty analysis was used to quantify the degree to which different models can satisfy observational constraints on the Earth’s cooling. For the Earth’s cooling history, uncertainty leads to ambiguitymultiple models, based on different hypotheses, can match observations. This has implications for using such models to forecast conditions for exoplanets that share Earth characteristics but are older than the Earth, i.e., ambiguity has implications for modeling the long-term life potential of terrestrial planets. Even for the most earthlike planet we know of, the Earth itself, model uncertainty and ambiguity leads to large forecast spreads. Given that Earth has the best data constraints, we should expect larger spreads for models of terrestrial planets, in general. The uncertainty analysis provided here can be expanded by coupling planetary cooling models to climate models and propagating uncertainty between them to assess habitability from a probabilistic view.