Fig. 2

The reference model. a The plot of radius changes against time, b temperature profile as a function of time, and the evolution of the distribution of c temperature, d internal heating rate, e melt-content, and f bulk composition \(\xi_{{\text{b}}}\). The assumed parameter values are \(T_{{\text{M}}} = 1550\,{\text{K}}, \,M^{*} = 28, \,F_{{{\text{crst}}}}^{*} = 8, \,L^{*} = 1/5.5\). In a the green and light blue lines indicate the contribution of thermal expansion and melting, respectively, to the total radius change (the purple line). In b the gray and light-gray areas are the temperature distributions in today’s lunar mantle inferred by Khan et al. (2006) and Khan et al. (2014), respectively; the gray lines are those estimated by Karato (2013) under the assumption that the mantle consists of dry olivine (the solid line) and that containing or wet olivine with the H₂O-content of 100 ppm (the dash line). In c, the contour lines show the distribution of melt-content with the contour interval of 0.05 starting from 0 (indicated by the dashed line); in e the contour lines show the distribution of temperature