Panel A: surface temperature evolution of magma ocean planets with different radii and atmospheric emissivities (or steam atmosphere). The horizontal dashed black line denotes the rheological transition (RT), below which a magma ocean may not be detectable due to a cold rigid lid forming at the surface. Hence, the RT criterion gives the minimum lifetime of a magma ocean that is likely to be detectable. Panel B: magma ocean lifetimes Δt_MO obtained for the gray atmosphere model (black circles) and the 2D surface fit for 0.1 R_⊕ ≤ R ≤ 1 R_⊕ and 0.01 ≤ ϵ ≤ 1.