Table 1.
Model Constants
| Symbol | Value | Units | Reference |
|---|---|---|---|
| Aν | 3 × 105 | J mol−1 | Viscosity activation energy in (6) |
| Aμ | 2 × 105 | J mol−1 | Nominal shear modulus activation energy in (7) |
| Asol | −1.160 × 10−16 | K m−3 | Solidus coefficient in (29) (ET08) |
| α | 3 × 10−5 | K−1 | Thermal expansivity of mantle |
| αc | 1 × 10−5 | K−1 | Thermal expansivity of core |
| B | 2.5 | nd | Melt fraction coefficient in (8) |
| Bsol | 1.708 × 10−9 | K m−2 | Solidus coefficient in (29), calibrated |
| β | 1/3 | nd | Convective cooling exponent in (25) |
| βst | 1.71 × 104 | GPa | Effective mantle stiffness, calibrated in Section 2.1 |
| cm | 1,265 | J kg−1 K−1 | Specific heat of mantle |
| cc | 840 | J kg−1 K−1 | Specific heat of core |
| Csol | −9.074 × 10−3 | K m−1 | Solidus coefficient in (29), calibrated |
| D | 2,891 | km | Mantle depth |
| DFe | 7,000 | km | Iron solidus length scale |
| DN | 6,340 | km | Core adiabatic length scale |
| Dsol | 1.993 × 104 | K | Solidus coefficient in (29), calibrated |
| δph | 6 | nd | Rheology phase coefficient in (8, 9) |
| EG | 3 × 105 | J kg−1 | Gravitational energy density release at the ICB |
 UM
|
0.7 | nd | Upper mantle adiabatic temperature drop |
 LM
|
1.3 | nd | Lower mantle adiabatic temperature jump |
 c
|
0.8 | nd | Average core to CMB adiabatic temperature drop |
| φ* | 0.8 | nd | Rheology phase coefficient in (8, 9) |
| gUM | 9.8 | m s−2 | Upper mantle gravity |
| gLM | 10.5 | m s−2 | Lower mantle gravity |
| gc | 10.5 | m s−2 | CMB gravity |
| γcore | 1.3 | nd | Core Gruneisen parameter |
| γdip | 0.2 | nd | Magnetic dipole intensity coefficient in (35) |
| γph | 6 | nd | Rheology phase coefficient in (8, 9) |
| kUM | 4.2 | W m−1 K−1 | Upper mantle thermal conductivity |
| kLM | 10 | W m−1 K−1 | Lower mantle thermal conductivity |
| κ | 106 | m2 s−1 | Mantle thermal diffusivity |
| LFe | 750 | kJ kg−1 | Latent heat of inner core crystallization |
| Lmelt | 320 | kJ kg−1 | Latent heat of mantle melting |
| Lc | 2.5 × 10−8 | WΩK−1 | Lorentz number |
| L* | 3.09 × 1023 | W | Stellar luminosity for M* = 0.1Msun (B13) |
| Mm | 4.06 × 1024 | kg | Mantle mass |
| Mc | 1.95 × 1024 | kg | Core mass |
| μref | 6.24 × 104 | Pa | Reference shear modulus in (7) |
| μ0 | 4π × 10−7 | H m−1 | Magnetic permeability |
| ν0 | 6 × 107 | m2 s−1 | Reference viscosity |
| νLM/νUM | 2 | nd | Viscosity jump from upper to lower mantle |
| Qrad,0 | 60 | TW | Initial mantle radiogenic heat flow (J07) |
| R | 6,371 | km | Surface radius |
| Rc | 3,480 | km | Core radius |
| Rm | 4,925 | km | Radius to average mantle temperature Tm |
| Rac | 660 | nd | Critical Rayleigh number |
| ρc | 11,900 | kg m−3 | Core density |
| ρic | 13,000 | kg m−3 | Inner core density |
| ρm | 4,800 | kg m−3 | Mantle density |
| ρmelt | 2,700 | kg m−3 | Mantle melt density |
| ρsolid | 3,300 | kg m−3 | Mantle upwelling solid density |
| Δρχ | 700 | kg m−3 | Outer core compositional density difference |
| σc | 10 × 105 | S m−1 | Core electrical conductivity |
| TFe,0 | 5,600 | K | Iron solidus coefficient in (23) |
| τrad | 2.94 | Gyr | Mantle radioactive decay timescale |
| τrad,c | 1.2 | Gyr | Core radioactive decay timescale |
| ξ | 5 × 10−4 | nd | Rheology phase coefficient in (8, 9) |