Table 1: Parameter values for the evolution model for mantle temperature and water.
Parameter Value Unit Description
  $1~M_\oplus$ $5~M_\oplus$ $8~M_\oplus$    

$d_{{\rm bas}}$
$5\times 10^3$ $5\times 10^3$ $5\times 10^3$ m average thickness of the basalt layer
$f_{{\rm bas}}$ 0.03 0.03 0.03 ... mass fraction of water in the basalt layer
$f_{\rm w}$ 0.194 0.194 0.194 ... degassing fraction of water
$d_{\rm m}$ $40\times 10^3$ $40\times 10^3$ $40\times 10^3$ m melting depth
k 4.2 4.2 4.2 J s-1 m-1 K-1 thermal conductivity
$M_{\rm w}(0)$ $4.2\times 10^{21}$ $2.1\times 10^{22}$ $5.36\times 10^{22}$ kg initial amount of mantle water
$R_{\rm c}$ $3471\times 10^3$ $5360\times 10^3$ $6085\times 10^3$ m inner radius of the mantle
$R_{\rm m}$ $6271\times 10^3$ $9684\times 10^3$ $10~994\times 10^3$ m outer radius of the mantle
$T_{\rm m}(0)$ 3000 3000 3000 K initial mantle temperature
$\kappa$ 10-6 10-6 10-6 m2 s-1 thermal diffusivity
$\rho_{{\rm bas}}$ 2950 4005 4,379 kg m-3 density of the basalt
$\rho c$ $4.2\times 10^6$ $4.2\times 10^6$ $4.2\times 10^6$ J m-3 K-1 density $\times$ specific heat
$R_{\rm T}$ $29.8\times 10^{-5}$ $29.8\times 10^{-5}$ $29.8\times 10^{-5}$ K-1 temperature dependence of regassing ratio
$\alpha$ $3\times 10^{-5}$ $3\times 10^{-5}$ $3\times 10^{-5}$ K-1 coefficient of thermal expansion
$\beta$ 0.3 0.3 0.3 ... empirical constant in Eq. (12)
${\rm Ra}_{\rm {crit}}$ 1,100 1,100 1,100 ... critical Rayleigh number
$\lambda$ 0.34 0.34 0.34  Gyr-1 decay constant of radiogenic heat
E0 $1.46\times 10^{-7}$ $1.46\times 10^{-7}$ $1.46\times 10^{-7}$ J s-1 m-3 initial heat generation per time and volume
g 9.81 20.6 25.5 m s-2 gravitational acceleration


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