Constraints on plate tectonics initiation from scaling laws for single-cell convection

•A method is developed to apply the scaling laws of critical yield stress for single-cell convection to multi-cell time-dependent convection.•Lithospheric failure on terrestrial planets require a very low yield stress of the lithosphere.•The aspect ratio of a sub-cell defined by the lid relief in a multi-cell convective system is the key in the application of the critical yield stress scaling laws. The Earth is the only planet known to have plate tectonics, while other planets are covered with a stagnant lid. On the Earth, the initiation of subduction, which is thought to be the fundamental process for plate tectonics initiation, is caused not only by the negative buoyancy of the lithosphere but also by the forces from plate motions. However, for planets which do not have plate tectonics, the very first episode of lithospheric failure has to be caused by forces other than plate motions. Sublithospheric convection has been proposed as a possible mechanism that provides lithospheric instability through inducing stresses in the lithosphere, and lithospheric failure can occur when the yield stress is below a critical value. We test the applicability of scaling laws for the critical yield stress obtained in single-cell convection simulations to strongly time-dependent multi-cell systems. We show that with an appropriate choice of characteristic aspect ratio for the convective system, the scaling laws from single-cell simulations can be used to evaluate the conditions on the terrestrial planets in the inner Solar System for plate tectonics to exist. In agreement with previous studies, the estimated values for critical yield stress and coefficient of friction are much lower than the expected values for the Earth’s lithosphere.