JOURNAL OF GEOPHYSICAL RESEARCH

Supporting Information for “The Volcanic and2 Radial Expansion/Contraction History of the Moon
3 Simulated by Numerical Models of Magmatism in
4 the Convective Mantle”
1Ken’yo U1 , Masanori Kameyama2 , and Masaki Ogawa1
51 Department of Earth Sciences and Astronomy, The University of Tokyo, Komaba, Meguro, Japan

62 Geodynamics Research Center, Ehime University, Matsuyama, Japan

S1.

Supplement 1

7This section contains an illustration of the average magma flux (ur ϕ) at 30km and 60 km

8plotted against time (Figure S1), and the captions for the animations of Case Ref (Movie S1-5)

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and Case vl-change (Movie S6-10); animations are uploaded as separate files.

Figure S1. The average magma flux (ur ϕ) at 30km (the blue line) and 60 km (the red line) in
the reference case (Case Ref) plotted against time.

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X-2:S1.1. Captions for animations
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Movie S1.

An animation of the distributions of temperature T calculated in the reference

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model (Case Ref).

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Movie S2.

An animation of the distributions of melt-content ϕ calculated in the reference

14model (Case Ref).

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Movie S3.

An animation of the distributions of internal heating rate q calculated in the17reference model (Case Ref).

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Movie S4.

An animation of the distributions of composition ξb calculated in the reference

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model (Case Ref). The blue color stands for the IBC components, while the red color for the21olivine-rich end-member.

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Movie S5.

An animation of the distributions of total density ρ calculated in the reference

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model (Case Ref).

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Movie S6.

An animation of the distributions of temperature T calculated in Case vl-change.

Movie S7.

An animation of the distributions of melt-content ϕ calculated in Case vl-change.

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:30

Movie S8.

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vl-change.

X-3

An animation of the distributions of internal heating rate q calculated in Case

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Movie S9.

An animation of the distributions of composition ξb calculated in Case vl-change.

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The blue color stands for the IBC components, while the red color for the olivine-rich end-35

member.

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Movie S10.

An animation of the distributions of total density ρ calculated in Case vl-change.

38S2.
3940

Supplement 2

This section contains snapshots of Case M20 and M50 (Figure S2), Ra2.15e5 and Ra7.15e5(Figure S3). See Table 3 in the main article for the case numbers.

Figure S2.

Snapshots of the distributions of melt-content ϕ calculated in Case (a) M20 and(b) M50. In (b), melt-fingers develop along the top of the partially molten region at a depth.

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X-4:Figure S3.

Snapshots of the distributions of melt-content ϕ calculated in Case (a) Ra2.15e5and (b) Ra7.15e5. In (b), partially molten plumes develop after the fingertip of melt-fingers
reaches the uppermost mantle.
S3.

Supplement 341

In the main article, we assumed that the thickness of the thermal boundary layer in the initial42

condition rl is 550 km (see Figure 1d and Eq. B3). However, rl is not well-constrained from43

earlier modeling studies. In this section, we examine this effect.
S3.1. The effects of the initial temperature distribution in the deep mantle

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In Case Ref and other cases described in the main article, the thickness of the thermal boundary

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layer in the initial condition rl is fixed at 550 km (see Figure 1d and Eq. B3). We calculated

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Case rl-100km where the thickness of the thermal boundary layer rl is 100 km to see how the47

numerical results depend on this parameter.

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As shown in Figure S4, the reduction in rl does not influence the overall features of mantle

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evolution. The radial expansion/contraction history of Case rl-100km is almost the same as that50

in Case Ref except for the first 100 Myr: the Moon contracts by −2 km for the first 100 Myr,

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expands by 2.5 km from 100 to 700 Myr and then contracts at the rate of around −1.2 km Gyr−1

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:Figure S4.

X-5

The same as Figure 4 but for Case melt-dep. The blue and red lines indicate

the contribution of thermal expansion/contraction and melting, respectively, to the total radiuschange (the black line).
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until the end of the calculated history (Figure S4). The early contraction is caused by a rapid

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cooling of the core (see Eq. 12), which occurs because the reduction in rl enhances the heat54

flow at the core-mantle boundary. As for magmatism, we observed the same history as that55

observed in Case Ref: melt-fingers grow first, then partially molten plumes grow and ascend

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to the uppermost mantle until 0.7 Gyr, and eventually the activity of plumes decline owing to57

cooling of the mantle.

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