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Table 1 The values of the temperature gradient \(|{\text{d}}\overline{T}/{\text{d}}r|_{r=r_\text {min}}\) at the bottom of the fluid layer of 3D spherical shell of \(r_\text {min}/r_\text {max}=0.5\) calculated with several values of \(r_k=k_\text {bot}/k_\text {top}\), the threshold values of dissipation number \({\text{Di}}_\text {thres}\) and planetary mass \(M_\text {thres}\) divided by the Earth’s mass \(M_\text {E}\) above which regions of stable thermal stratification occur at the bottom of the fluid layer

From: Linear analysis on the onset of thermal convection of highly compressible fluids with variable viscosity and thermal conductivity in spherical geometry: implications for the mantle convection of super-Earths

\(r_k\) \(\left| {\text{d}}\overline{T}/{\text{d}}r\right| _{r=r_\text {min}}\) \({\text{Di}}_\text {thres}\) \(M_\text {thres}/M_\text {E}\)
1 2.000 26.14 83.34
3 1.246 16.28 45.43
10 0.6593 8.616 20.09
24.24 0.3826 5 10
30 0.3327 4.348 8.360
100 0.1429 1.867 2.829