Extended Data Figure 6. Equilibrium Mg and MgO concentration in the core as a function of CMB temperature.

This is obtained by rewriting $\log K_{Mg}=1.23-\frac{18816}{T}=2\log x_{Mg}-\log x_{MgO}$ into $\log X_{Mg}=\frac{1}{2}\left(1.23-\frac{18816}{T}+\log X_{MgO}\right)$ with X_MgO=0.5 (pyrolitic mantle). This curve (red for MgO, blue for Mg) allows determining magnesium saturation in the core at a given temperature. This threshold is important to (i) estimate the present-day MgO content of the core, and hence how much MgO was lost by exsolution over geologic time (Extended Data Fig. 4), and to (ii) estimate the temperature at which MgO exsolution started after core formation (Extended Data Fig. 5). For instance, for a core containing 2.9 wt.% MgO (for a Mars-sized impact, see Extended Data Fig. 3), exsolution is not bound to occur until the temperature at the CMB cools below 5030 K. Moreover, if the present-day CMB temperature is 4100 K, the MgO saturation in the present-day core is 1.1 wt.%, so that the total amount of MgO that can be exsolved from the core isn’t the total initial MgO content, but that amount minus the present-day saturation value.