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Table 1

Input parameters for thermal evolution modeling.

Parameter Value Description
Material properties
ρgra (kg m−3) 2300 Average graphite density (Sect. 2.1)
ρsil (kg m−3) 3300 Average enstatite density (Sect. 2.1)
ρiron (kg m−3) 9000 Average iron density (Sect. 2.1)
CP,gra (J K−1 kg−1) 700 Specific heat of graphite (Boylan 1996)
CP,sil (J K−1 kg−1) 1250 Specific heat of silicate (Schubert et al. 2001)
CP,iron (J K−1 kg−1) 550 Specific heat of iron (Schubert et al. 2001)
αgra (K−1) 3 × 10−5 Thermal expansivity of graphite (Morgan 1972)
αsil (K−1) 3 × 10−5 Thermal expansivity of silicate (Schubert et al. 2001)
kgra(T) (W m−1 K−1) 42327T−1.035 + 0.00103T Thermal conductivity of graphite (Hofmeister et al. 2014, Graphite AXM, Table 1)
ksil (W m−1 K−1) 5 Thermal conductivity of silicate (Schubert et al. 2001)
Egra (kJ mol−1) 209 Activation energy of graphite (Wagner & Driesner 1959)
Esil (kJ mol−1) 300 Activation energy of silicate (Schubert et al. 2001)
Agra,min. (109 Pa s) 5.3 Rheology prefactor for graphite (min. shear modulus, Cost et al. 1968)
Agra,max. (109 Pa s) 185 Rheology prefactor for graphite (max. shear modulus, Min & Aluru 2011)
Asil (109 Pa s) 160 Rheology prefactor for silicate (assuming η (1600 K) = 1021 Pa s)

Model properties
Tsurf (K) 700 Planet surface temperature (Kepler-37b, Barclay et al. 2013)
T0,lid-bot (K) 1700 Initial temperature at the bottom of the lid
T0,man (K) 2000 Initial mantle temperature
T0,core (K) 3000 Initial core temperature
H0 (10−12 W kg−1) 34.5 Initial internal heating rate of the mantle (Turcotte & Schubert 2002)
τ (Gyr) 2.95 Characteristic decay time of radioactive (Turcotte & Schubert 2002)

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