# The 21st century Moon

## Contents

<table><tr><td>8.1 Summary</td><td>97</td></tr><tr><td>8.1.1 Mantle thermal state</td><td>98</td></tr><tr><td>8.1.2 Core properties</td><td>98</td></tr><tr><td>8.2 Perspectives</td><td>99</td></tr></table>

## 8.1 Summary

In the last chapters we have seen that, from a cold, primordial remnant of Solar System formation, the Moon has become an active and still mysterious body. Thanks to the Apollo/Luna missions, it is the only body for which we have samples of known origin. Added to that, the numerous missions of the last decade made it the body, except for the Earth, for which we have the most data. As such, it provides an excellent first step in comparative planetology.

The beauty with lunar science in comparison to other planetary bodies is that the wide range of datasets allows us to try and provide a self-consistent picture of its present state and evolution. The existence of the almost pure anorthositic crust suggests differentiation from a large pool of magma, probably from re-accretion after giant impact. However such a large scale differentiation also implies an unstable density stratification in the lunar mantle that can be dynamically modeled. The results of such dynamical models drive the heat sources distribution in the planet and thus, its entire thermochemical evolution. In this work, we took results of magma ocean related processes as initial conditions for our thermochemical models.

Finding a self-consistent story of lunar evolution will provide information on early Earth evolution and the environment in which it evolved, thus maybe shedding light on Solar System formation and the origin of life. Through this project, we studied part of that problem by investigating how heat sources distribution in the lunar mantle influences its evolution and therefore how numerical simulations could help constrain the initial amount and distribution of radioactive elements in the Moon. We then used that knowledge and a model of core evolution to put constraints on core composition and inner core growth.
### 8.1.1 Mantle thermal state

In the first part of this thesis, we demonstrated that a subcrustal enrichment in heat sources in the Procellarum KREEP Terrane leads to thermal consequences that are consistent with current observations. Contrary to standard thermal evolution models where melting is mostly caused by adiabatic decompression, it is triggered by the high concentration of heat sources that we impose below the crust. Convection also plays a role, especially on the farside, but much smaller than usually. Overall depletion in heat sources in the mantle leads to a strong asymmetry in volcanic production rate between near and farside, in agreement with observations.

Our results also imply that a large temperature anomaly is still present in that region today. This leads to an asymmetric density distribution, which would have a large influence on crustal thickness models. We showed that the present density distribution and dynamic topography produce a strong negative gravity signal in the center of the PKT. As this signal is not observed in recent gravity data, it suggest that there are other features in or below the crust that are not taken into account in our models. Plausible options are either a crust that is thinner on average in this region or that the nearside mantle is slightly denser than the farside. Finally, from a simple core cooling model, we noted that the core will probably be partially solidified and that a chemical dynamo could therefore be the cause of the paleomagnetic measurements, as a thermal one cannot explain a field that laster longer than a few hundred million years.

### 8.1.2 Core properties

In the second part of the thesis, we studied how the observed paleomagnetic history of the Moon could be explained by a chemical dynamo. We have shown that after a short period of thermal dynamo, inner core crystallisation could sustain dynamo activity by chemical buoyancy. However once crystallisation starts, core cooling becomes less efficient and most cases we tested predict a magnetic field up to the present day. This is because the liquidus at the inner core boundary is not expected to decrease by a large amount until the inner core reaches about 80% of the core radius. Therefore the core-mantle boundary heat flow remains large enough to power a chemical dynamo for a long period of time.

We argued that this could potentially be avoided either by a transition to the iron-snow regimes of core crystallisation when the inner core radius reaches a certain threshold, or by a failure of the magnetic scaling laws once the thickness of the convecting shell is too small. However this was not modeled in the framework of this project. Two major conclusions can be made from that part: if an inner core is present today, its growth most probably generated enough buoyancy to sustain a long lasting magnetic field, but a process then has to be found to explain the lack of magnetic field today. The existence of such a process will surely constrain the type and amount of light element in the core and therefore the formation scenario.
## 8.2 Perspectives

During this project we have shown how rich lunar problems are and worked towards solving some. From the mantle simulations, we have made predictions on the present day mantle thermo-chemical state that can be used to improve current crustal thickness models. If discrepancies arise by using our predictions, it may imply that such a heat source distribution is inconsistent with observations and thus that an other set of initial conditions have to be used. Such mantle state predictions from other thermal models can also be used to test them and discriminate between the different classes of models.

The two types of evolution models have diametrically opposite assumptions on the heat sources distribution. Our model assumes they are just below the crust in the PKT region whereas another model assumes they are globally enriched on top of the core-mantle boundary. They both match some of the observations but can't be both correct. But their starting point are both linked to the fate of the predicted KREEP layer that arises from magma ocean crystallisation, and figuring out its evolution will set strong constraints on lunar formation. It is therefore crucial to conduct dynamical modeling of KREEP evolution just after magma ocean crystallisation to test if the right initial conditions can be found for both types of models. Another approach is to investigate an asymmetric magma ocean crystallisation as was already proposed 30 years ago, but never clearly modeled.

From the core thermodynamic study, we have shown that even if a chemical dynamo can explain the peak in paleomagnetism between 4 and 3 Ga ago, our models predict that the dynamo will be sustained up to the present day. It is possible that better fitting models can be found by exploring the parameter space more precisely, especially by changing the mantle initial conditions, but to make progress in this project it is necessary to test if our proposed solutions are viable. Thermodynamical modeling of the iron-snow regime in the lunar pressure range has to be conducted in order to constrain the conditions necessary for its onset and if, once started, the process can sustain magnetic field generation or not. Another line of work would be to model the core flow in a thin shell and test if it is consistent with magnetic field generation. This study is strongly linked to the detection of the potential inner core of the Moon. If an inner core is confirmed, chances are that current core models coherent with its size will predict a present day magnetic field and thus the question becomes "how to stop the lunar dynamo?" instead of "how to explain the long duration of the lunar magnetic era?".
<figure><img src="image_58.png" /></figure>
# Part IV

## Appendices and bibliography
<figure><img src="image_59.png" /></figure>
# Gravity field calculation

## A.1 Gravity field

The gravitational potential $U$ is derived from Newton's law of gravitation

$$U(\mathbf{r}) = \int_V \frac{G\rho(\mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|} dV', \qquad (A.1)$$

where $\mathbf{r}$ is the vector position, $G$ the gravitational constant, $\rho$ the density distribution and $V$ the volume. Exterior to a given mass distribution, the gravitational potential satisfies the Laplace equation

$$\nabla^2 U(\mathbf{r}) = 0. \qquad (A.2)$$

In spherical coordinates, the solution of this equation can be expressed in spherical harmonics as

$$U(\mathbf{r}) = \frac{GM}{r} \sum_{l=0}^{\infty} \sum_{m=-l}^{l} \left(\frac{R_0}{r}\right)^l C_{lm} Y_{lm}(\theta, \phi), \qquad (A.3)$$

where $M$ is the mass of the Moon, $R_0$ the reference radius, $Y_{lm}$ the spherical harmonic functions of degree $l$ and order $m$, $C_{lm}$ the corresponding coefficients, and $\theta$ and $\phi$ are the colatitude and longitude, respectively. The spherical harmonics are normalized as follows

$$\int_{\Omega} Y_{lm}(\Omega) Y_{l'm'}(\Omega) d\Omega = 4\pi\delta_{ll'}\delta_{mm'}, \qquad (A.4)$$

where $d\Omega = \sin\theta d\theta d\phi$. For $r > R_0$, the two following identities hold

$$\frac{1}{|\mathbf{r} - \mathbf{r}'|} = \frac{1}{r} \sum_{l=0}^{\infty} \left(\frac{r'}{r}\right)^l P_l(\cos\gamma), \qquad (A.5)$$

$$P_l(\cos\gamma) = \frac{1}{2l+1} \sum_{m=-l}^{l} Y_{lm}(\theta, \phi) Y_{lm}(\theta', \phi'), \qquad (A.6)$$

where $P_l$ is the Legendre polynomial of order $l$ and $\gamma$ the angle between $\mathbf{r}$ and $\mathbf{r}'$. Inserting Equation (A.5) in Equation (A.1) leads to the definition

$$C_{lm} = \frac{1}{M(2l+1)} \int_V \left(\frac{r'}{R_0}\right)^l \rho(\mathbf{r}') Y_{lm}(\Omega') dV'. \qquad (A.7)$$
In order to calculate the coefficients $C_{lm}$ numerically, we assume the Moon to be constituted of $N$ thin shells of constant thickness with prescribed lateral density variations. For a given shell, $C_{lm}(r)$ is given by

$$C_{lm}(r) = \frac{4\pi r^2}{M(2l + 1)} \left(\frac{r}{R_0}\right)^l \rho_{lm}(r) \Delta R, \qquad (A.8)$$

where $\Delta R$ is the shell thickness and $\rho_{lm}(r)$ the spherical harmonics expansion of $\rho$ on that shell which can be computed as

$$\rho_{lm}(r) = \frac{1}{4\pi} \int \rho(\theta, \phi, r) Y_{lm}(\theta, \phi) d\Omega. \qquad (A.9)$$

Finally,

$$C_{lm} = \sum_{n=1}^{N} C_{lm}(r_n). \qquad (A.10)$$

The gravitational field is then calculated by taking the first derivative of (A.3) with respect to $r$

$$g(r) = \frac{GM}{r^2} \sum_{l=0}^{\infty} \sum_{m=-l}^{l} \left(\frac{R_0}{r}\right)^l (l+1) C_{lm} Y_{lm}(\theta, \phi). \qquad (A.11)$$

where we use the convention that $g$ is positive when directed downward. This allows us to calculate the effect on gravity from changes in density within the mantle, either due to thermal expansion or compositional changes. However, induced surface topography plays a role as well that needs to be estimated. Two approaches can be considered, as described in Appendix B: either surface topography is maintained dynamically or statically. Regardless how we choose to compute this topography, its influence on the potential can be calculated according to Equation (A8):

$$C_{lm}^{surf} = \frac{4\pi}{(2l+1)M} R_0^2 (\rho h)_{lm}. \qquad (A.12)$$

where the topography $h_{lm}$ is the spherical harmonics expansion of the topography $h$, referenced to radius $R_0$.

The Laplacian operator being linear, the gravitational influence of these mass anomalies can be considered independently and directly added to the coefficients of Eq. (A10)

$$C_{lm}^{tot} = C_{lm} + C_{lm}^{surf}. \qquad (A.13)$$

## A.2 Calculation of static and dynamic topography

Thermal expansion leads to a volume increase of the material. Because our ther-mochemical models are incompressible and have fixed boundaries, this effect is only taken into account within the Boussinesq approximation: the density decreases locally, but the volume stays constant. However, for gravity calculations, volume
changes need to be considered. On the one hand, assuming a strengthless lithosphere and the direct transmission of stresses vertically, this increase in volume directly translates to a surface uplift. On the other hand, if one considers an infinite elastic lithosphere, the induced topography is zero. Our calculations should therefore be seen as an upper bound on the contribution. There are two ways to compute topography. The static approach assumes that once topography is emplaced, it stays in place whereas the dynamic topography is the topography that can be sustained by radial stresses at the surface.

## Static topography

Our numerical grid is regular, therefore the sum of the volume expansion of each cell $\delta V_N$ along one vertical profile is equal to the volume increase at the surface $V_{uplift}$

$$V_{uplift} = \sum_{N} \delta V_{N}, \qquad (A.14)$$

where $N$ is the number of shells of the model. Thermal expansion $\alpha$ dictates that

$$\delta V_N = \alpha V_N \delta T_N, \qquad (A.15)$$

where $\delta T_N$ is the local increase in temperature with respect to a constant reference. Writing $S_i$ the surface area of the cell at shell $i$, we can compute the surface uplift as

$$h = \frac{1}{S_0} \sum_{N} \alpha V_N \delta T_N, \qquad (A.16)$$

where $V_N = S_N \Delta R$, $\Delta R$ being the thickness of the shell.

## Dynamic topography

The other approach assumes that the current topography is sustained dynamically. Our models have fixed boundaries, but the radial stresses at these boundaries can be used a posteriori to compute the induced dynamic topography that would be present with a free surface using

$$h = \frac{\tau_{rr}}{\Delta \rho g_0}, \qquad (A.17)$$

where $\Delta \rho$ is the density jump across the interface and $g_0$ the gravitational acceleration at this same boundary (Peltier, 1989). The radial stress is defined by

$$\tau_{rr} = P - 2\eta \frac{dv_r}{dr}, \qquad (A.18)$$

with $P$ being the dynamic pressure, $\eta$ the viscosity and $v_r$ the radial viscosity at the interface (Landau and Lifshit\ddot{i}, s\ddot{i}, j, 1959). The radial stresses are the direct result of the mantle dynamics and therefore includes the effect of thermal expansion. We found that in our case, the assumption of either static or dynamic topography give similar results. Therefore the static approach is used here for simplicity.
<figure><img src="image_60.png" /></figure>
# Core budget calculations

## B.1 Entropy budget

Entropy is a measure of the available energy in a system. When only reversible processess exist, this value stays constant. However dissipation is an irreversible process and the available energy in a closed system decreases with time (i.e. entropy increases with time). The total derivative of the entropy can be written as

$$ \rho T \frac{ds}{dt} = \rho T \left(\frac{\partial s}{\partial t}\right)_{P,c} \frac{dT}{dt} + \rho T \left(\frac{\partial s}{\partial c}\right)_{P,T} \frac{dc}{dt} + \rho T \left(\frac{\partial s}{\partial P}\right)_{T,c} \frac{dP}{dt} \quad (B.1) $$

where the right-hand side corresponds to the contribution from core cooling, chemical reactions and core contraction, respectively. The second and third terms have been shown to be small (e.g., Nimmo, 2007) and we will retain only the core cooling term here. We then use Maxwell's relation for the partial derivative of the entropy and rewrite the total derivative of entropy as

$$ \rho T \frac{ds}{dt} = \rho c_p \frac{dT}{dt}. \quad (B.2) $$

Second, the local entropy budget can be written as (e.g., Gubbins et al., 2004)

$$ \rho \frac{ds}{dt} = -\frac{\nabla \cdot q}{T} + \frac{\mu \nabla \cdot i}{T} + \frac{J^2}{\sigma T}, \quad (B.3) $$

where q and i are the heat and solute flux vector, respectively, J is the electric current density, σ is the electrical conductivity and μ is the chemical potential. We can then use Eq (B.2) to obtain

$$ \frac{\rho c_p}{T} \frac{dT}{dt} = -\frac{\nabla \cdot q}{T} + \frac{\mu \nabla \cdot i}{T} + \frac{J^2}{\sigma T}. \quad (B.4) $$

Now we can rewrite the first term on the right-hand side of Eq (B.4) as

$$ \begin{aligned} \frac{\nabla \cdot q}{T} &= \nabla \cdot \left(\frac{q}{T}\right) - \frac{q \nabla T}{T^2} \\ &= \nabla \cdot \left(\frac{q}{T}\right) - k \left(\frac{\nabla T}{T}\right)^2. \end{aligned} \quad (B.5) $$

Using this result in Eq (B.4), we obtain

$$ \frac{\rho c_p}{T} \frac{dT}{dt} = -\nabla \cdot \left(\frac{q}{T}\right) + k \left(\frac{\nabla T}{T}\right)^2 + \frac{\mu \nabla \cdot i}{T} + \frac{J^2}{\sigma T}, \quad (B.6) $$
which can then be integrated over the core volume to get

$$ \int \frac{\rho c_p}{T} \frac{dT}{dt} dV = -\frac{Q_c}{T_c} + \int k \left(\frac{\nabla T}{T}\right)^2 dV + \frac{Q_L}{T_i} + \frac{\Phi}{T_\phi}, \quad (B.7) $$

where we used the divergence theorem on the first and last term on the right-hand side of Eq (B.6).

Replacing the energy budget $Q_c = Q_L + Q_g + Q_s$ in Eq (B.7) and regrouping similar terms, we obtain

$$ \int \rho c_p \left( \frac{1}{T_c} - \frac{1}{T} \right) \frac{dT}{dt} dV + Q_L \left( \frac{1}{T_c} - \frac{1}{T_i} \right) + \frac{Q_g}{T_c} = \int k \left( \frac{\nabla T}{T} \right)^2 dV + \frac{\phi}{T_i} \quad (B.8) $$

where we assumed that most of the dissipation occurs at the inner core boundary. This can finally be identified with the entropy budget presented in Chapter 6 to yield

$$ E_S = \int \rho c_p \left( \frac{1}{T_c} - \frac{1}{T} \right) \frac{dT_c}{dt} dV, \quad (B.9) $$

$$ E_L = Q_L \left( \frac{1}{T_c} - \frac{1}{T_i} \right), \quad (B.10) $$

$$ E_g = \frac{Q_g}{T_c}, \quad (B.11) $$

$$ E_k = \int k \left( \frac{\nabla T}{T} \right)^2 dV. \quad (B.12) $$

## B.2 Simplified equations

In this section, we derive a simplified version of Equations (6.2) to (6.4) to second order in (r/D). For definition of the variables, please refer to Chapter 6.

### Secular term

The starting equation is the following

$$ Q_s = \int \rho c_p \frac{dT_c}{dt} dV. \quad (B.13) $$

Assuming that the outer core follows an adiabatic gradient and that the inner core is isothermal, the entire core thermal state is defined by one temperature. The temperature profile in the outer core is defined by

$$ T_a(r, T_c) = T_c \exp \left( -\frac{r^2 - r_c^2}{D^2} \right), \quad (B.14) $$

as defined in Equation (6.6). A Taylor expansion of second order in (r/D) gives

$$ T_a(r, T_c) = T_c \left( 1 - \frac{r^2 - r_c^2}{D^2} \right). \quad (B.15) $$
The ratio (r/D) is of order 0.1, thus the error on temperature is less than 0.01 K.
The secular cooling term can then be developed as

$$
\begin{align*}
Q_s &= \int \rho c_p \frac{dT_c}{dt} \left(1 - \frac{r^2 - r_c^2}{D^2}\right) dV \\
&= M_c c_p \frac{dT_c}{dt} - 4\pi \rho c_p \frac{dT_c}{dt} \int r^2 \frac{r^2 - r_c^2}{D^2} dr \\
&= M_c c_p \frac{dT_c}{dt} - 4\pi \rho c_p \frac{dT_c}{dt} \left(\frac{r_c^5}{5D^2} - \frac{r_c^5}{3D^2}\right) \\
&= M_c c_p \frac{dT_c}{dt} \left(1 + \frac{2}{5} \frac{r^2}{D^2}\right), \tag{B.16}
\end{align*}
$$

where $M_c = 4\pi\rho r_c^3/3$.

Latent heat term

The starting equation is the following

$$
Q_L = 4\pi r_i^2 L_H \rho^{ic} \frac{dr_i}{dt}, \qquad (B.17)
$$

where

$$
\frac{dr_i}{dt} = \frac{1}{(\Delta - 1)dT_a/dP} \frac{1}{\rho^{ic}g} \frac{T_i}{T_c} \frac{dT_c}{dt}. \quad (B.18)
$$

From Equation (B.15), $dT_a/dT = 2rT/D^2$. In addition, assuming hydrostatic
equilibrium $dT/dP = 1/\rho g$. Thus

$$
\begin{align*}
Q_L &= 4\pi r_i^2 L_H \rho^{ic} \frac{dr_i}{dt} \\
&= \frac{4\pi r_i^2 L_H T_i}{\Delta - 1 T_c} \frac{1}{\rho D} \frac{dT_c}{dt} \\
&= \frac{4\pi L_H \rho D f r_c}{\Delta - 1 2 T_c} \frac{dT_c}{dt} \\
&= \frac{3}{2} M_c \frac{f L_H D^2}{T_c r_c^2} \frac{1}{\Delta - 1} \frac{dT_c}{dt}, \tag{B.19}
\end{align*}
$$

where $f = r_i/r_c$ and $T_i \simeq T_c$ has been assumed.

Gravity term

The starting equation is the following

$$
Q_g = \int \rho \phi \alpha_c \frac{Dc}{Dt} dV. \qquad (B.20)
$$

It can be shown (see Nimmo, 2007) that

$$
Q_g = \left[ \int_{oc} \rho \psi dV - M_{oc} \psi(r_i) \right] \alpha_c \frac{Dc}{Dt} \quad (B.21)
$$

$$
= (A - B) \cdot C. \tag{B.22}
$$
The several parts of this equation can be written as

$$ 
\begin{aligned}
A &= \frac{4\pi}{3}\rho \int_{oc} \frac{2}{3}\pi G \rho r^4 dr \\
&= \frac{(4\pi)^2}{6} \rho^2 G \left( \frac{r_c^5 - r_i^5}{5} \right) \\
&= \frac{(4\pi)^2}{6} \rho^2 G r_c^5 \left( \frac{1 - f^5}{5} \right)
\end{aligned} 
\quad (B.23) $$

In addition,

$$ 
\begin{aligned}
B &= \frac{4}{3}\pi\rho(r_c^3 - r_i^3) \cdot \frac{2}{3}\pi G \rho r_i^2 \\
&= \frac{(4\pi)^2}{6} \rho^2 G \left( \frac{r_c^3 - r_i^3}{3} \cdot r_i^2 \right) \\
&= \frac{(4\pi)^2}{6} \rho^2 G r_c^5 \left( \frac{1 - f^3}{3} \cdot f^2 \right)
\end{aligned} 
\quad (B.24) $$

and using Equation (B.18) again,

$$ 
\begin{aligned}
C &= \alpha_c \frac{4\pi r_i^2 \rho_i c}{M_{oc}} \frac{dr_i}{dt} \\
&= \alpha_c \frac{4\pi r_i^2 \rho_i c}{M_{oc}} \frac{D^2}{2T_c f r_c (\Delta - 1)} \frac{dT_c}{dt} \\
&= \frac{\Delta \rho_c}{\rho_i} \frac{c}{\Delta c} \frac{3}{2r_c^2} \frac{f}{1 - f^3} \frac{D^2}{T_c} \frac{1}{\Delta - 1} \frac{dT_c}{dt}
\end{aligned} 
\quad (B.25) $$

where we have used the fact that $\alpha_c = \Delta\rho_c/(\rho_i\Delta c)$. Now assuming $c/\Delta c = 1$, and merging A, B and C, one has

$$ 
\begin{aligned}
Q_g &= \frac{(4\pi)^2}{6} \rho^2 G r_c^5 \left( \frac{1 - f^5}{5} - f^2 \cdot \frac{1 - f^3}{3} \right) \cdot C \\
&= 3\pi\rho G M_c F \frac{\Delta\rho_c}{\rho_i} \frac{D^2}{T_c} \frac{1}{\Delta - 1} \frac{dT_c}{dt}
\end{aligned} 
\quad (B.26) $$

where

$$ F = \frac{f}{1 - f^3} \left( \frac{1}{5} + \frac{2f^5}{15} - \frac{f^3}{3} \right). 
\quad (B.27) $$
# List of notations

## Text abbreviations

ARM Anhysteretic-remanent magnetization

CMB Core - mantle boundary

ICB Inner core - outer core boundary

KREEP Potassium, Rare Earth Elements and Phosphorous

PKT Procellarum KREEP Terrane

SPA South Pole - Aitken basin

SRM Shock-remanent magnetization

TRM Termo-remanent magnetization

## Part I - Variables and parameters

<table><tr><td>α</td><td>Thermal expansivity</td><td>K<sup>-1</sup></td></tr><tr><td>α<sub>0</sub></td><td>Reference thermal expansivity</td><td>K<sup>-1</sup></td></tr><tr><td>Δρ</td><td>Peridotite to harzburgite density difference</td><td>kg m<sup>-3</sup></td></tr><tr><td>ΔR</td><td>Shell thickness</td><td>m</td></tr><tr><td>ΔT</td><td>Temperature drop across the mantle</td><td>K</td></tr><tr><td>η</td><td>Viscosity</td><td>Pa s</td></tr><tr><td>η<sub>0</sub></td><td>Reference viscosity</td><td>Pa s</td></tr><tr><td>η<sub>max</sub></td><td>Maximum viscosity</td><td>Pa s</td></tr><tr><td>κ<sub>0</sub></td><td>Reference thermal diffusivity</td><td>m<sup>2</sup> s<sup>-1</sup></td></tr><tr><td>μ<sub>0</sub></td><td>Permeability of free space</td><td>kg s<sup>-2</sup> A<sup>-2</sup></td></tr><tr><td>φ</td><td>Longitude</td><td>rad</td></tr><tr><td>ρ<sub>0</sub></td><td>Reference density</td><td>kg m<sup>-3</sup></td></tr><tr><td>θ</td><td>Latitude</td><td>rad</td></tr><tr><td>e&#773;<sub>r</sub></td><td>Unit vector in radial direction</td><td>-</td></tr><tr><td>u&#773;</td><td>Velocity vector</td><td>m s<sup>-1</sup></td></tr><tr><td>B</td><td>Surface magnetic field</td><td>T</td></tr><tr><td>C</td><td>Depletion field</td><td>-</td></tr><tr><td>C<sub>0</sub></td><td>Depletion required to obtain harzburgite</td><td>-</td></tr><tr><td>C<sub>lm</sub></td><td>Gravity coefficient</td><td>-</td></tr><tr><td>D</td><td>Mantle thickness</td><td>m</td></tr><tr><td>D<sub>c</sub></td><td>Crustal thickness</td><td>m</td></tr><tr><td>D<sub>K</sub></td><td>KREEP layer thickness</td><td>m</td></tr><tr><td>E</td><td>Activation energy</td><td>J mol<sup>-1</sup></td></tr><tr><td>F</td><td>Melt fraction</td><td>-</td></tr><tr><td>g</td><td>Surface gravity acceleration</td><td>m s<sup>-2</sup></td></tr><tr><td>k<sub>c</sub></td><td>Crust thermal conductivity</td><td>W m<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>k<sub>m</sub></td><td>Mantle thermal conductivity</td><td>W m<sup>-1</sup> K<sup>-1</sup></td></tr></table>
<table><tr><td>l</td><td>Spherical harmonics degree</td><td>-</td></tr><tr><td>L<sub>m</sub></td><td>Latent heat of melting</td><td>J kg<sup>-1</sup></td></tr><tr><td>m</td><td>Spherical harmonics order</td><td>m</td></tr><tr><td>P</td><td>Hydrostatic pressure</td><td>Pa s</td></tr><tr><td>p</td><td>Dynamic pressure</td><td>Pa</td></tr><tr><td>Q</td><td>Internal heat production rate</td><td>-</td></tr><tr><td>R<sub>0</sub></td><td>Reference lunar radius for gravity calculations</td><td>m</td></tr><tr><td>R<sub>c</sub></td><td>Lunar core radius</td><td>m</td></tr><tr><td>R<sub>p</sub></td><td>Lunar radius</td><td>m</td></tr><tr><td>Ra<sub>C</sub></td><td>Chemical Rayleigh number</td><td>-</td></tr><tr><td>Ra<sub>T</sub></td><td>Thermal Rayleigh number</td><td>-</td></tr><tr><td>T</td><td>Temperature</td><td>K</td></tr><tr><td>t</td><td>Time</td><td>s</td></tr><tr><td>T<sub>0</sub></td><td>Reference temperature</td><td>K</td></tr><tr><td>T<sub>liq</sub></td><td>Mantle liquidus temperature</td><td>K</td></tr><tr><td>T<sub>sol</sub></td><td>Mantle solidus temperature</td><td>K</td></tr><tr><td>T<sub>surf</sub></td><td>Surface temperature</td><td>K</td></tr><tr><td>Y<sub>lm</sub></td><td>Spherical harmonic function</td><td>-</td></tr></table>

Part II - Variables and parameters

<table><tr><td>α<sub>c</sub></td><td>Core density coefficient</td><td>-</td></tr><tr><td>χ</td><td>Light element mass fraction</td><td>wt.%</td></tr><tr><td>Δχ</td><td>Composition difference across the ICB</td><td>kg m<sup>-3</sup></td></tr><tr><td>Δρ<sub>c</sub></td><td>Density difference across the ICB</td><td>kg m<sup>-3</sup></td></tr><tr><td>Δ</td><td>Core liquidus to adiabat gradient ratio</td><td>-</td></tr><tr><td>η</td><td>Magnetic diffusivity</td><td>m<sup>2</sup> s<sup>-1</sup></td></tr><tr><td>Ω</td><td>Rotation rate</td><td>s<sup>-1</sup></td></tr><tr><td>ψ</td><td>Gravitational potential</td><td>J kg<sup>-1</sup></td></tr><tr><td>D</td><td>Core temperature scale height</td><td>m</td></tr><tr><td>E<sub>φ</sub></td><td>Dissipated entropy</td><td>W m<sup>-2</sup> K<sup>-1</sup></td></tr><tr><td>E<sub>g</sub></td><td>Entropy production due to chemical buoyancy</td><td>W m<sup>-2</sup> K<sup>-1</sup></td></tr><tr><td>E<sub>k</sub></td><td>Entropy sink due to conduction along the adiabat</td><td>W m<sup>-2</sup> K<sup>-1</sup></td></tr><tr><td>E<sub>l</sub></td><td>Entropy production due to latent heat release</td><td>W m<sup>-2</sup> K<sup>-1</sup></td></tr><tr><td>E<sub>s</sub></td><td>Entropy production due to secular cooling</td><td>W m<sup>-2</sup> K<sup>-1</sup></td></tr><tr><td>f</td><td>Inner core to core ratio</td><td>-</td></tr><tr><td>f<sub>eff</sub></td><td>Scaling law efficiency factor</td><td>s<sup>-1</sup></td></tr><tr><td>G</td><td>Gravitational constant</td><td>m<sup>3</sup> kg<sup>-1</sup> s<sup>-2</sup></td></tr><tr><td>L<sub>c</sub></td><td>Latent heat of crystallisation</td><td>J kg<sup>-1</sup></td></tr><tr><td>M<sub>c</sub></td><td>Core mass</td><td>kg</td></tr><tr><td>M<sub>oc</sub></td><td>Outer core mass</td><td>kg</td></tr><tr><td>Q<sub>CMB</sub></td><td>Core mantle boundary heat flow</td><td>W m<sup>-2</sup></td></tr><tr><td>Q<sub>g</sub></td><td>Chemical buoyancy heat flow</td><td>W m<sup>-2</sup></td></tr><tr><td>Q<sub>l</sub></td><td>Latent heat heat flow</td><td>W m<sup>-2</sup></td></tr></table>
<table><tr><td>Q<sub>s</sub></td><td>Secular cooling heat flow</td><td>W m<sup>-2</sup></td></tr><tr><td>r<sub>c</sub></td><td>Core radius</td><td>m</td></tr><tr><td>r<sub>i</sub></td><td>Inner core radius</td><td>m</td></tr><tr><td>Re<sub>m</sub></td><td>Magnetic Reynolds number</td><td>-</td></tr><tr><td>T<sub>a</sub></td><td>Core adiabat</td><td>K</td></tr><tr><td>T<sub>c</sub></td><td>Core-mantle boundary temperature</td><td>K</td></tr><tr><td>T<sub>m</sub></td><td>Core melting temperature</td><td>K</td></tr><tr><td>V<sub>oc</sub></td><td>Outer core volume</td><td>m<sup>-3</sup></td></tr></table>
<figure><img src="image_61.png" /></figure>
Bibliography

Andrews-Hanna, J. C., S. W. Asmar, J. W. Head, W. S. Kiefer, A. S. Konopliv, F. G. Lemoine, I. Matsuyama, E. Mazarico, P. J. McGovern, H. J. Melosh, G. A. Neumann, F. Nimmo, R. J. Phillips, D. E. Smith, S. C. Solomon, G. J. Taylor, M. A. Wieczorek, J. G. Williams, and M. T. Zuber (2013), Ancient Igneous Intrusions and Early Expansion of the Moon Revealed by GRAIL Gravity Gradiometry, *Science*, **339**(6120), 675–678. (Cited on page 39.)

Antonenko, I., J. W. Head, J. F. Mustard, and B. Ray Hawke (1995), Criteria for the Detection of Lunar Cryptomaria, *Earth, Moon and Planets*, **69**(2), 141–172. (Cited on page 23.)

Aubert, J., S. Labrosse, and C. Poitou (2009), Modelling the palaeo-evolution of the geodynamo, *Geophysical Journal International*, **179**(3), 1414–1428. (Cited on pages 66, 69 and 76.)

Bercovici, D. (2003), The generation of plate tectonics from mantle convection, *Earth and Planetary Science Letters*, **205**(3), 107–121. (Cited on page 12.)

Beuthe, M. (2008), Thin elastic shells with variable thickness for lithospheric flexure of one-plate planets, *Geophysical Journal International*, **172**(2), 817–841. (Cited on page 47.)

Breuer, D. (2003), Early plate tectonics versus single-plate tectonics on Mars: Evidence from magnetic field history and crust evolution, *Journal of Geophysical Research*, **108**(E7), 5072. (Cited on page 12.)

Buono, A. S., and D. Walker (2011), The Fe-rich liquidus in the Fe-FeS system from 1 bar to 10 GPa, *Geochimica et Cosmochimica Acta*, **75**(8), 2072–2087. (Cited on pages 54, 76 and 78.)

Byrne, C. J. (2008), A Large Basin on the Near Side of the Moon, *Earth, Moon and Planets*, **101**(3-4), 153–188. (Cited on page 25.)

Canup, R. M. (2012), Forming a Moon with an Earth-like Composition via a Giant Impact, *Science*, **338**(6110), 1052–1055. (Cited on page 15.)

Chabot, N. L., A. J. Campbell, W. F. McDonough, D. S. Draper, C. B. Agee, M. Humayun, H. C. Watson, E. Cottrell, and S. A. Saslow (2008), The Fe-C system at 5GPa and implications for Earth's core, *Geochimica et Cosmochimica Acta*, **72**(16), 4146–4158. (Cited on pages 76 and 77.)

Christensen, U. R. (1984), Convection with pressure- and temperature-dependent non-Newtonian rheology, *Geophysical Journal of the Royal Astronomical Society*, **77**, 343–384. (Cited on page 27.)
Christensen, U. R., and J. Aubert (2006), Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields, *Geophysical Journal International*, **166**(1), 97–114. (Cited on pages 69 and 75.)

Christensen, U. R., V. Holzwarth, and A. Reiners (2008), Energy flux determines magnetic field strength of planets and stars, *Nature*, **457**(7226), 167–169. (Cited on pages 52, 53 and 76.)

Cisowski, S. M., D. W. Collinson, S. K. Runcorn, A. Stephenson, and M. D. Fuller (1983), A review of lunar paleointensity data and implications for the origin of lunar magnetism, *Journal of Geophysical Research*, **88**(S02), A691–A704. (Cited on page 61.)

Colaprete, A., P. H. Schultz, J. Heldmann, D. Wooden, M. Shirley, K. Ennico, B. Hermalyn, W. S. Marshall, A. Ricco, R. C. Elphic, D. Goldstein, D. Summy, G. D. Bart, E. Asphaug, D. Korycansky, D. Landis, and L. Sollitt (2010), Detection of Water in the LCROSS Ejecta Plume, *Science*, **330**(6003), 463–468. (Cited on page 18.)

Collinson, D. W. (1993), Magnetism of the Moon-a lunar core dynamo or impact magnetization?, *Surveys in geophysics*, **14**(1), 89–118. (Cited on pages 60 and 62.)

Crosby, A., and D. McKenzie (2005), Measurements of the elastic thickness under ancient lunar terrain, *Icarus*, **173**(1), 100–107. (Cited on page 47.)

Cuk, M., and S. T. Stewart (2012), Making the Moon from a Fast-Spinning Earth: A Giant Impact Followed by Resonant Despinning, *Science*, **338**(6110), 1047–1052. (Cited on page 15.)

Darwin, G. H. (1880), On the Secular Changes in the Elements of the Orbit of a Satellite Revolving about a Tidally Distorted Planet, *Philosophical Transactions of the Royal Society of London*, **171**, 713–891. (Cited on page 15.)

de Koker, N., G. Steinle-Neumann, and V. Vlcek (2012), Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earth's core, *Proceedings of the National Academy of Sciences*. (Cited on pages 79 and 90.)

de Smet, J. (1999), The evolution of continental roots in numerical thermo-chemical mantle convection models including differentiation by partial melting, *Lithos*, **48**, 153–170. (Cited on page 29.)

Desai, P. D. (1986), Thermodynamic Properties of Iron and Silicon, *Journal of Physical and Chemical Reference Data*, **15**(3), 967–983. (Cited on page 90.)

Dunlop, D. J. (2011), Physical basis of the Thellier-Thellier and related paleointensity methods, *Physics of the Earth and Planetary Interiors*, **187**(3-4), 118–138. (Cited on page 60.)
Dwyer, C. A., D. J. Stevenson, and F. Nimmo (2012), A long-lived lunar dynamo driven by continuous mechanical stirring, *Nature*, **479**(7372), 212–214. (Cited on pages 53 and 62.)

Dyal, P., C. W. Parkin, and C. P. Sonett (1970), Apollo 12 Magnetometer: Measurement of a Steady Magnetic Field on the Surface of the Moon, *Science*, **169**(3), 762–764. (Cited on page 59.)

Elardo, S. M., D. S. Draper, and C. K. Shearer, Jr (2011), Lunar Magma Ocean crystallization revisited: Bulk composition, early cumulate mineralogy, and the source regionsof the highlands Mg-suite, *Geochimica et Cosmochimica Acta*, **75**(11), 3024–3045. (Cited on page 16.)

Elkins-Tanton, L. T., J. A. Van Orman, B. H. Hager, and T. L. Grove (2002), Re-examination of the lunar magma ocean cumulate overturn hypothesis: melting or mixing is required, *Earth and Planetary Science Letters*, **196**(3), 239–249. (Cited on page 25.)

Elkins-Tanton, L. T., S. Burgess, and Q.-Z. Yin (2011), Earth and Planetary Science Letters, *Earth and Planetary Science Letters*, **304**(3-4), 326–336. (Cited on pages 16, 33 and 55.)

Ferrari, A. J., W. S. Sinclair, W. L. Sjogren, J. G. Williams, and C. F. Yoder (1980), Geophysical parameters of the Earth-Moon System, *Journal of Geophysical Research*, **85**(B7), 3939. (Cited on page 64.)

Garcia, R. F., J. Gagnepain-Beyneix, S. Chevrot, and P. Lognonné (2011), Physics of the Earth and Planetary Interiors, *Physics of the Earth and Planetary Interiors*, **188**(1-2), 96–113. (Cited on pages 17, 54 and 65.)

Garrick-Bethell, I., B. P. Weiss, D. L. Shuster, and J. Buz (2009), Early Lunar Magnetism, *Science*, **323**(5), 356. (Cited on pages 53 and 61.)

Ghods, A., and J. Arkani-Hamed (2007), Impact-induced convection as the main mechanism for formation of lunar mare basalts, *Journal of Geophysical Research*, **112**(E3), E03,005. (Cited on page 25.)

Goldstein, B. E., and R. J. Phillips (1976), Magnetic evidence concerning a lunar core, *Lunar and Planetary*.... (Cited on page 64.)

Golle, O., C. Dumoulin, G. Choblet, and O. Čadek (2012), Topography and geoid induced by a convecting mantle beneath an elastic lithosphere, *Geophysical Journal International*, **189**(1), 55–72. (Cited on page 47.)

Grimm, R. E. (2013), Geophysical constraints on the lunar Procellarum KREEP Terrane, *Journal of Geophysical Research: Planets*, **118**(4), 768–778. (Cited on pages 26, 46, 47, 49, 50 and 56.)
Gubbins, D., D. Alfè, G. Masters, G. D. Price, and M. Gillan (2004), Gross thermodynamics of two-component core convection, *Geophysical Journal International*, **157**(3), 1407-1414. (Cited on page 107.)

Haruyama, J., M. Ohtake, T. Matsunaga, T. Morota, C. Honda, Y. Yokota, M. Abe, Y. Ogawa, H. Miyamoto, and A. Iwasaki (2009), Long-lived volcanism on the lunar farside revealed by SELENE terrain camera, *Science*, **323**(5916), 905-908. (Cited on pages 16 and 23.)

Haskin, L. A. (1998), The Imbrium impact event and the thorium distribution at the lunar highlands surface, *Journal of Geophysical Research*, **103**, 1679. (Cited on page 23.)

Hauck, S. A. I., J. M. Aurnou, and A. J. Dombard (2006), Sulfur's impact on core evolution and magnetic field generation on Ganymede, *Journal of Geophysical Research*, **111**(E9), E09,008. (Cited on pages 66 and 92.)

Head, J. W. (1976), Lunar volcanism in space and time, *Reviews of Geophysics*, **14**(2), 265-300. (Cited on page 16.)

Head, J. W., and L. S. Crumpler (1989), Divergent plate boundary characteristics and crustal spreading in Aphrodite Terra, Venus: A test of some predictions, *Earth, Moon and Planets*, **44**(3), 219-231. (Cited on page 12.)

Hernlund, J. W., and P. J. Tackley (2008), Modeling mantle convection in the spherical annulus, *Physics of the Earth and Planetary Interiors*, **171**(1), 48-54. (Cited on page 82.)

Hess, P. C., and E. M. Parmentier (1995), A model for the thermal and chemical evolution of the Moon's interior: Implications for the onset of mare volcanism, *Earth and Planetary Science Letters*, **134**(3), 501-514. (Cited on pages 33, 55 and 91.)

Hess, P. C., and E. M. Parmentier (2001), Thermal evolution of a thicker KREEP liquid layer, *Journal of Geophysical Research*, **106**(E11), 28,023-28-032. (Cited on pages 26 and 54.)

Hide, R. (1972), Comments on the Moon's Magnetism, *The Moon*, **4**(1), 39-39. (Cited on pages 63 and 93.)

Hiesinger, H., J. W. Head, U. Wolf, R. Jaumann, and G. Neukum (2003), Ages and stratigraphy of mare basalts in Oceanus Procellarum, Mare Nubium, Mare Cognitum, and Mare Insularum, *Journal of Geophysical Research*, **108**(E), 5065. (Cited on pages 3, 23 and 24.)

Hiesinger, H., J. W. Head, U. Wolf, R. Jaumann, and G. Neukum (2010), Ages and stratigraphy of lunar mare basalts in Mare Frigoris and other nearside maria based on crater size-frequency distribution measurements, *Journal of Geophysical Research*, **115**(E3), E03,003. (Cited on page 16.)
Hillgren, V. J., C. K. Gessmann, and J. Li (2000), An experimental perspective on the light element in Earth's core, *Origin of the earth and moon*, *1*, 245-263. (Cited on page 65.)

Hirschmann, M. M. (2000), Mantle solidus: Experimental constraints and the effects of peridotite composition, *Geochemistry, Geophysics, Geosystems*, *1*(10). (Cited on pages 29 and 34.)

Hood, L. L. (1986), Geophysical constraints on the lunar interior, *Origin of the Moon*, *-1*, 361-410. (Cited on page 64.)

Hood, L. L., and N. A. Artemieva (2008), Antipodal effects of lunar basin-forming impacts: Initial 3D simulations and comparisons with observations, *Icarus*, *193*(2), 485-502. (Cited on page 63.)

Hood, L. L., D. L. Mitchell, R. P. Lin, M. H. Acuña, and A. B. Binder (1999), Initial measurements of the lunar induced magnetic dipole moment using Lunar Prospector Magnetometer data, *Geophysical Research Letters*, *26*(15), 2327-2330. (Cited on page 64.)

Hussmann, H., and T. Spohn (2004), Thermal-orbital evolution of Io and Europa, *Icarus*, *171*(2), 391-410. (Cited on page 11.)

Hüttig, C., and K. Stemmer (2008), Finite volume discretization for dynamic viscosities on Voronoi grids, *Physics of the Earth and Planetary Interiors*, *171*(1-4), 137-146. (Cited on page 29.)

Ita, J., and S. D. King (1994), Sensitivity of convection with an endothermic phase change to the form of governing equations, initial conditions, boundary conditions, and equation of state, *Journal of Geophysical Research*, *99*, 15,919. (Cited on page 28.)

Jakosky, B. M., and R. J. Phillips (2001), Mars' volatile and climate history, *Nature*, *412*(6), 237-244. (Cited on page 12.)

Jolliff, B. L., J. J. Gillis-Davis, L. A. Haskin, R. L. Korotev, and M. A. Wieczorek (2000), Major lunar crustal terranes: Surface expressions and crust-mantle origins, *Journal of Geophysical Research*, *105*(E), 4197-4216. (Cited on pages 16, 23, 24, 30, 31 and 69.)

Jutzi, M., and E. Asphaug (2012), Forming the lunar farside highlands by accretion of a companion moon, *Nature*, *476*(7358), 69-72. (Cited on page 26.)

Kamata, S., S. Sugita, Y. Abe, Y. Ishihara, Y. Harada, T. Morota, N. Namiki, T. Iwata, H. Hanada, H. Araki, K. Matsumoto, and E. Tajika (2013), Viscoelastic deformation of lunar impact basins: Implications for heterogeneity in the deep crustal paleo-thermal state and radioactive element concentration, *Journal of Geophysical Research*, *118*(3), 398-415. (Cited on pages 25 and 31.)
Karato, S.-i. I., and P. Wu (1993), Rheology of the upper mantle - A synthesis, *Science*, **260**, 771-778. (Cited on page 28.)

Keken, P. E., S. D. King, H. Schmeling, U. R. Christensen, D. Neumeister, and M. P. Doin (1997), A comparison of methods for the modeling of thermochemical convection, *Journal of Geophysical Research*, **102**(B), 22,477-22,495. (Cited on page 29.)

Khan, A., and K. Mosegaard (2002), An inquiry into the lunar interior: A nonlinear inversion of the Apollo lunar seismic data, *Journal of Geophysical Research*, **107**(E6), 3-1-3-23. (Cited on page 29.)

Khan, A., K. Mosegaard, and K. L. Rasmussen (2000), A new seismic velocity model for the Moon from a Monte Carlo inversion of the Apollo lunar seismic data, *Geophysical Research Letters*, **27**(1), 1591-1594. (Cited on page 17.)

Khan, A., J. A. D. Connolly, J. Maclennan, and K. Mosegaard (2007), Joint inversion of seismic and gravity data for lunar composition and thermal state, *Geophysical Journal International*, **168**(1), 243-258. (Cited on page 65.)

Kirk, R. L., and D. J. Stevenson (1989), The competition between thermal contraction and differentiation in the stress history of the moon, *Journal of Geophysical Research*, **94**, 12,133-12,144. (Cited on pages 16 and 55.)

Klima, R. L., J. Cahill, J. Hagerty, and D. Lawrence (2013), Remote detection of magmatic water in BullialdusCrater on the Moon, *Nature Geoscience*, **6**(9), 737-741. (Cited on page 18.)

Komabayashi, T., and Y. Fei (2010), Internally consistent thermodynamic database for iron to the Earth's core conditions, *Journal of Geophysical Research*, **115**(B3), B03,202. (Cited on page 77.)

Konrad, W., and T. Spohn (1997), Thermal history of the moon - Implications for an early core dynamo and post-accretional magmatism, *Advances in Space Research*, **19**, 1511. (Cited on pages 27, 29, 33, 50, 62 and 70.)

Korenaga, J. (2010), On the likelihood of plate tectonics on super-Earths: does size matter?, *The Astrophysical Journal*, **725**(1), L43-L46. (Cited on page 12.)

Korotev, R. L. (2000), The great lunar hot spot and the composition and origin of the Apollo mafic ("LKFM") impact-melt breccias, *Journal of Geophysical Research*, **105**(E), 4317-4346. (Cited on page 31.)

Labrosse, S. (2003), Thermal and magnetic evolution of the Earth's core, *Physics of the Earth and Planetary Interiors*, **140**(1), 127-143. (Cited on page 71.)

Landau, L. D., and E. M. Lifshitï, sï,ï (1959), *Fluid mechanics*, Pergamon. (Cited on page 105.)
Laneuville, M., M. A. Wieczorek, D. Breuer, and N. Tosi (2013), Asymmetric thermal evolution of the Moon, *Journal of Geophysical Research*, 118, 1435–1452. (Cited on pages 17, 62, 66, 69, 70 and 93.)

Langseth, M. G., S. J. Keihm, and K. Peters (1976), Revised lunar heat-flow values, in *7th Lunar and Planetary Science Conference*, pp. 3143–3171, Lamont-Doherty Geological Observatory, Palisades, N.Y. (Cited on pages 36 and 39.)

Lawrence, D. J. (2011), Water on the Moon, *Nature Geoscience*, 4(9), 586–588. (Cited on page 18.)

Lawrence, D. J., W. C. Feldman, B. L. Barraclough, A. B. Binder, R. C. Elphic, S. Maurice, and D. R. Thomsen (1998), Global Elemental Maps of the Moon: The Lunar Prospector Gamma-Ray Spectrometer, *Science*, 281, 1484. (Cited on page 23.)

Lawrence, D. J., R. C. Elphic, W. C. Feldman, T. H. Prettyman, O. Gasnault, and S. Maurice (2003), Small-area thorium features on the lunar surface, *Journal of Geophysical Research*, 108(E), 5102. (Cited on pages 3 and 24.)

Lawrence, K., C. Johnson, L. Tauxe, and J. Gee (2008), Lunar paleointensity measurements: Implications for lunar magnetic evolution, *Physics of the Earth and Planetary Interiors*, 168(1-2), 71–87. (Cited on page 61.)

Le Bars, M., L. Lacaze, S. Le Dizès, P. Le Gal, and M. Rieutord (2010), Tidal instability in stellar and planetary binary systems, *Physics of the Earth and Planetary Interiors*, 178(1-2), 48–55. (Cited on page 63.)

Le Bars, M., M. A. Wieczorek, Ö. Karatekin, D. Cébron, and M. Laneuville (2012), An impact-driven dynamo for the early Moon, *Nature*, 479(7372), 215–218. (Cited on pages 53 and 62.)

Lin, D. N. C., P. Bodenheimer, and D. C. Richardson (1996), Orbital migration of the planetary companion of 51 Pegasi to its present location, *Nature*, 380(6575), 606–607. (Cited on page 11.)

Lognonné, P., J. Gagnepain-Beyneix, and H. Chenet (2003), A new seismic model of the Moon: implications for structure, thermal evolution and formation of the Moon, *Earth and Planetary Science Letters*, 211(1-2), 27–44. (Cited on page 29.)

Loper, D. E. (2002), On lunar asymmetries 1. Tilted convection and crustal asymmetry, *Journal of Geophysical Research*, 107(E6), 5046. (Cited on page 25.)

Metzger, A. E., E. L. Haines, R. E. Parker, and R. G. Radocinski (1977), Thorium concentrations in the lunar surface. I - Regional values and crustal content, in *8th Lunar and Planetary Science Conference*, pp. 949–999, California Institute of Technology, Jet Propulsion Laboratory, Pasadena, Calif. (Cited on page 23.)
Meyer, J., L. T. Elkins-Tanton, and J. Wisdom (2010), Coupled thermal-orbital evolution of the early Moon, *Icarus*, 208(1), 1–10. (Cited on page 12.)

Mimoun, D., M. A. Wieczorek, L. Alkalai, W. B. Banerdt, D. Baratoux, J.-L. Bougeret, S. Bouley, B. Cecconi, H. Falcke, J. Flohrer, R. F. Garcia, R. E. Grimm, M. Grott, L. Gurvits, R. Jaumann, C. L. Johnson, M. Knapmeyer, N. Kobayashi, A. Konovalenko, D. J. Lawrence, M. L. Feuvre, P. Lognonné, C. R. Neal, J. Oberst, N. Olsen, H. Röttgering, T. Spohn, S. Vennerstrom, G. Woan, and P. Zarka (2011), Farside explorer: unique science from a mission to the farside of the moon, *Experimental Astronomy*, 33(2-3), 529–585. (Cited on pages 3 and 24.)

Mizutani, H., T. Matsui, and H. Takeuchi (1972), Accretion process of the moon, *The Moon*, 4(3-4), 476–489. (Cited on page 15.)

Morbidelli, A., J. E. Chambers, and J. I. Lunine (2000), Source regions and timescales for the delivery of water to the Earth, ... *Planetary Science*. (Cited on page 11.)

Morota, T., J. Haruyama, C. Honda, M. Ohtake, Y. Yokota, J. Kimura, T. Mat-
sunaga, Y. Ogawa, N. Hirata, H. Demura, A. Iwasaki, H. Miyamoto, R. Nakamura,
H. Takeda, Y. Ishihara, and S. Sasaki (2009), Mare volcanism in the lunar farside
Moscovience region: Implication for lateral variation in magma production of the
Moon, *Geophysical Research Letters*, 36(21), L21,202. (Cited on page 45.)

Nakamura, Y., D. Lammlein, G. Latham, and M. Ewing (1973), New seismic data on the state of the deep lunar interior, *Science*. (Cited on page 17.)

Nakamura, Y., G. V. Latham, and H. J. Dorman (1982), Apollo Lunar Seismic Experiment—Final summary, *Journal of Geophysical Research*, 87(S01), A117. (Cited on page 17.)

Namur, O., B. Charlier, C. Pirard, J. Hermann, J.-P. Liégeois, and J. Vander Auwera (2011), Anorthosite formation by plagioclase flotation in ferrobasalt and implications for the lunar crust, *Geochimica et Cosmochimica Acta*, 75(17), 4998–5018. (Cited on page 15.)

Neumann, G. A., M. T. Zuber, D. E. Smith, and F. G. Lemoine (1996), The lunar crust: Global structure and signature of major basins, *Journal of Geophysical Research*, 101(E), 16,841–16,864. (Cited on page 25.)

Nimmo, F. (2007), Thermal and compositional evolution of the core, *Treatise on geophysics*. (Cited on pages 71, 107 and 109.)

Nimmo, F. (2009), Energetics of asteroid dynamos and the role of compositional convection, *Geophysical Research Letters*, 36(10), L10,201. (Cited on pages 66, 72, 75, 79 and 89.)

Nimmo, F., and D. McKenzie (1998), Volcanism and tectonics on Venus, *Annual Review of Earth and Planetary Sciences*, 26(1), 23–51. (Cited on page 12.)
Nimmo, F., and D. J. Stevenson (2000), Influence of early plate tectonics on the thermal evolution and magnetic field of Mars, *Journal of Geophysical Research*, 105(E), 11,969–11,980. (Cited on page 12.)

Nishida, K., H. Terasaki, E. Ohtani, and A. Suzuki (2008), The effect of sulfur content on density of the liquid Fe–S at high pressure, *Physics and chemistry of minerals*, 35(7), 417–423. (Cited on page 77.)

Nozette, S., C. L. Lichtenberg, P. D. Spudis, R. Bonner, W. Ort, E. Malaret, M. S. Robinson, and E. M. Shoemaker (1996), The Clementine Bistatic Radar Experiment, *Science*, 274(5), 1495–1498. (Cited on page 18.)

Ohtake, M., H. Takeda, T. Matsunaga, Y. Yokota, J. Haruyama, T. Morota, S. Yamamoto, Y. Ogawa, T. Hiroi, Y. Karouji, K. Saiki, and P. G. Lucey (2012), Asymmetric crustal growth on the Moon indicated by primitive farside highland materials, *Nature Geoscience*, 5(6), 384–388. (Cited on page 17.)

Parmentier, E. M., S. Zhong, and M. T. Zuber (2002), Gravitational differentiation due to initial chemical stratification: origin of lunar asymmetry by the creep of dense KREEP?, *Earth and Planetary Science Letters*, 201(3), 473–480. (Cited on page 25.)

Peltier, W. R. (1989), Mantle convection, plate tectonics and global dynamics. The fluid mechanics of astrophysics and geophysics, *Gordon and Breach Science Publishers, 4*. (Cited on page 105.)

Phillips, R. J., M. A. Bullock, and S. A. I. Hauck (2001), Climate and interior coupled evolution on Venus, *Geophysical Research Letters*, 28(9), 1779–1782. (Cited on page 12.)

Plesa, A. C., N. Tosi, and C. Hüttig (2013), Thermo-chemical convection in planetary mantles: advection methods and magma ocean overturn simulations, in *Integrated information and computing systems for natural, spatial, and social sciences*, edited by C. P. Rückemann, pp. 302–323, IGI-Global. (Cited on page 29.)

Purucker, M. E. (2008), A global model of the internal magnetic field of the Moon based on Lunar Prospector magnetometer observations, *Icarus*, 197(1), 19–23. (Cited on page 59.)

Purucker, M. E., and J. B. Nicholas (2010), Global spherical harmonic models of the internal magnetic field of the Moon based on sequential and coestimation approaches, *Journal of Geophysical Research*, 115(E12), E12,007. (Cited on page 60.)

Qin, C., A. C. Muirhead, and S. Zhong (2012), Correlation of deep moonquakes and mare basalts: Implications for lunar mantle structure and evolution, *Icarus*, 220(1), 100–105. (Cited on page 25.)
Richards, M. A., and B. H. Hager (1984), Geoid anomalies in a dynamic earth, *Journal of Geophysical Research (ISSN 0148-0227)*, 89, 5987-6002. (Cited on page 47.)

Righter, K. (2002), Does the Moon Have a Metallic Core? Constraints from Giant Impact Modeling and Siderophile Elements, *Icarus*, **158**(1), 1–13. (Cited on page 65.)

Roberts, J. H., and S. Zhong (2006), Degree-1 convection in the Martian mantle and the origin of the hemispheric dichotomy, *Journal of Geophysical Research*, **111**(E6), E06,013. (Cited on page 28.)

Russell, C. T., P. J. J. Coleman, and B. E. Goldstein (1982), Measurements of the lunar induced magnetic moment in the geomagnetic tail - Evidence for a lunar core, *In: Lunar and Planetary Science Conference*, *12*, 831–836. (Cited on page 64.)

Saal, A. E., E. H. Hauri, M. L. Cascio, J. A. Van Orman, M. C. Rutherford, and R. F. Cooper (2008), Volatile content of lunar volcanic glasses and the presence of water in the Moon's interior, *Nature*, **454**(7201), 192–195. (Cited on page 18.)

Schubert, G., D. L. Turcotte, and E. R. Oxburgh (1969), Stability of planetary interiors, *Geophysical Journal of the Royal Astronomical Society*, **18**, 441–460. (Cited on page 36.)

Scott, D. R., and D. J. Stevenson (1989), A self-consistent model of melting, magma migration and buoyancy-driven circulation beneath mid-ocean ridges, *Journal of Geophysical Research*, **94**, 2973–2988. (Cited on page 28.)

Shea, E. K., B. P. Weiss, W. S. Cassata, D. L. Shuster, S. M. Tikoo, J. Gattacceca, T. L. Grove, and M. D. Fuller (2012), A Long-Lived Lunar Core Dynamo, *Science*, **335**(6067), 453–456. (Cited on pages 53 and 61.)

Shearer, C. K., P. C. Hess, and M. A. Wieczorek (2006), Thermal and magmatic evolution of the Moon, in *New views of the Moon*, Mineralogical Society of America. (Cited on pages 35, 40, 55 and 65.)

Solomon, S. C. (1979), Formation, history and energetics of cores in the terrestrial planets, *Physics of the Earth and Planetary Interiors*, 19(2), 168–182. (Cited on page 70.)

Solomon, S. C., and J. Longhi (1977), Magma oceanography. I - Thermal evolution, in *8th Lunar and Planetary Science Conference*, pp. 583–599, MIT, Cambridge, Mass. (Cited on page 16.)

Spohn, T., W. Konrad, D. Breuer, and R. Ziethe (2001), The Longevity of Lunar Volcanism: Implications of Thermal Evolution Calculations with 2D and 3D Mantle Convection Models, *Icarus*, **149**(1), 54–65. (Cited on pages 27, 29, 36 and 54.)
Stegman, D. R., A. M. Jellinek, S. A. Zatman, J. R. Baumgardner, and M. A. Richards (2003), An early lunar core dynamo driven by thermochemical mantle convection, *Nature*, **421**(6919), 143–146. (Cited on pages 27, 50, 54 and 62.)

Stevenson, D. J. (1987), *Origin of the Moon – the collision hypothesis*, *Annual Review of Earth and Planetary Sciences*, **15**, 271–315. (Cited on page 15.)

Stevenson, D. J. (2003), *Planetary magnetic fields*, *Earth and Planetary Science Letters*, **208**(1-2), 1–11. (Cited on page 13.)

Stevenson, D. J., T. Spohn, and G. Schubert (1983), Magnetism and thermal evolution of the terrestrial planets, *Icarus*, **54**, 466–489. (Cited on pages 12, 62, 79 and 88.)

Suavet, C., B. P. Weiss, W. S. Cassata, D. L. Shuster, J. Gattacceca, L. Chan, I. Garrick-Bethell, J. W. Head, T. L. Grove, and M. D. Fuller (2013), Persistence and origin of the lunar core dynamo, *Proceedings of the National Academy of Sciences*, **110**, 8453–8458. (Cited on pages 53, 56 and 61.)

Tackley, P. J. (2000), *Mantle Convection and Plate Tectonics: Toward an Integrated Physical and Chemical Theory*, *Science*, **288**(5473), 2002–2007. (Cited on page 12.)

Takahashi, F., and H. Tsunakawa (2009), Thermal core-mantle coupling in an early lunar dynamo: Implications for a global magnetic field and magnetosphere of the early Moon, *Geophysical Research Letters*, **36**(24), L24,202. (Cited on page 52.)

Taylor, S. R. (1982), *Planetary science: A lunar perspective*, Lunar and Planetary Institute. (Cited on pages 29, 30, 32 and 45.)

Taylor, S. R., G. J. Taylor, and L. A. Taylor (2006), *The Moon: A Taylor perspective*, *Geochimica et Cosmochimica Acta*, **70**(24), 5904–5918. (Cited on page 30.)

Terasaki, H., K. Nishida, Y. Shibazaki, T. Sakamaki, A. Suzuki, E. Ohtani, and T. Kikegawa (2010), Density measurement of Fe 3C liquid using X-ray absorption image up to 10 GPa and effect of light elements on compressibility of liquid iron, *Journal of Geophysical Research*, **115**(B6), B06,207. (Cited on page 77.)

Tikoo, S. M., B. P. Weiss, J. Buz, E. A. Lima, E. K. Shea, G. Melo, and T. L. Grove (2012), Magnetic fidelity of lunar samples and implications for an ancient core dynamo, *Earth and Planetary Science Letters*, **337-338**, 93–103. (Cited on pages 61 and 62.)

Tobie, G., J. I. Lunine, and C. Sotin (2006), Episodic outgassing as the origin of atmospheric methane on Titan, *Nature*, **440**(7080), 61–64. (Cited on page 12.)

Tronche, E. J., and W. van Westrenen (2011), The lunar magma ocean: an experimental solidification study, in *42nd Lunar and Planetary Science Conference*, p. 1415. (Cited on page 16.)
Turcotte, D. L., R. J. Willemann, W. F. Haxby, and J. Norberry (1981), Role of membrane stresses in the support of planetary topography, *Journal of Geophysical Research*, **86**, 3951–3959. (Cited on page 47.)

van der Meer, D. G., W. Spakman, D. J. J. van Hinsbergen, M. L. Amaru, and T. H. Torsvik (2009), Towards absolute plate motions constrained by lower-mantle slab remnants, *Nature Geoscience*, **3**(1), 36–40. (Cited on page 38.)

van Westrenen, W., and R. J. de Meijer (2012), Forming the Moon from Terrestrial Silicate-Rich Material—2012 Edition, *43rd Lunar and Planetary Science Conference*. (Cited on page 15.)

Warren, P. H. (1985), The magma ocean concept and lunar evolution, *Annual Review of Earth and Planetary Sciences*, **13**(1), 201–240. (Cited on page 15.)

Warren, P. H. (2001), Compositional structure within the lunar crust as constrained by Lunar Prospector thorium data, *Geophysical Research Letters*, **28**(1), 2565–2568. (Cited on pages 25 and 30.)

Warren, P. H., and K. L. Rasmussen (1987), Megaregolith insulation, internal temperatures, and bulk uranium content of the moon, *Journal of Geophysical Research*, **92**, 3453–3465. (Cited on pages 36, 39 and 45.)

Warren, P. H., and J. T. Wasson (1979), The origin of KREEP, *Reviews of Geophysics and Space Physics*, **17**, 73–88. (Cited on pages 25 and 30.)

Wasson, J. T., and P. H. Warren (1980), Contribution of the mantle to the lunar asymmetry, *Icarus*, **44**, 752–771. (Cited on page 25.)

Watson, K., B. C. Murray, and H. Brown (1961), On the Possible Presence of Ice on the Moon, *Journal of Geophysical Research*, **66**, 1598–1600. (Cited on page 18.)

Watters, T. R., M. S. Robinson, R. A. Beyer, M. E. Banks, J. F. Bell, M. E. Pritchard, H. Hiesinger, C. H. van der Bogert, P. C. Thomas, E. P. Turtle, and N. R. Williams (2010), Evidence of Recent Thrust Faulting on the Moon Revealed by the Lunar Reconnaissance Orbiter Camera, *Science*, **329**(5994), 936–940. (Cited on page 39.)

Watts, A. B., and S. Zhong (2000), Observations of flexure and the rheology of oceanic lithosphere, *Geophysical Journal International*, **142**(3), 855–875. (Cited on page 47.)

Weber, R. C., P. Y. Lin, E. J. Garnero, Q. Williams, and P. Lognonné (2011), Seismic Detection of the Lunar Core, *Science*, **331**(6015), 309–312. (Cited on pages 17, 54 and 65.)

Wetherill, G. W. (1975), Late heavy bombardment of the moon and terrestrial planets, *Lunar and Planetary Science Conference* .... (Cited on page 11.)
White, S. M., J. A. Crisp, and F. J. Spera (2006), Long-term volumetric eruption rates and magma budgets, *Geochemistry, Geophysics, Geosystems*, 7(3), Q03,010. (Cited on pages 35 and 40.)

Wieczorek, M. A. (2007), Gravity and topography of the terrestrial planets, *Treatise on geophysics*. (Cited on pages 46 and 47.)

Wieczorek, M. A., and R. J. Phillips (2000), The “Procellarum KREEP Terrane”: Implications for mare volcanism and lunar evolution, *Journal of Geophysical Research*, 105(E8), 20,417–20,430. (Cited on pages 16, 23, 26, 31, 33 and 36.)

Wieczorek, M. A., M. T. Zuber, and R. J. Phillips (2001), The role of magma buoyancy on the eruption of lunar basalts, *Earth and Planetary Science Letters*, 185(1), 71–83. (Cited on page 45.)

Wieczorek, M. A., B. L. Jolliff, A. Khan, M. E. Pritchard, B. P. Weiss, L. L. Williams, L. L. Hood, K. Righter, C. R. Neal, C. K. Shearer, Jr, I. S. McCallum, S. Tompkins, B. R. Hawke, C. A. Peterson, J. J. Gillis-Davis, and D. B. J. Bussey (2006), The constitution and structure of the lunar interior, in *New views of the Moon*, Mineralogical Society of America. (Cited on pages 17, 35, 65 and 66.)

Wieczorek, M. A., B. P. Weiss, and S. T. Stewart (2012), An Impactor Origin for Lunar Magnetic Anomalies, *Science*, 335(6073), 1212–1215. (Cited on pages 53, 60 and 63.)

Wieczorek, M. A., G. A. Neumann, F. Nimmo, W. S. Kiefer, G. J. Taylor, H. J. Melosh, R. J. Phillips, S. C. Solomon, J. C. Andrews-Hanna, S. W. Asmar, A. S. Konopliv, F. G. Lemoine, D. E. Smith, M. M. Watkins, J. G. Williams, and M. T. Zuber (2013), The Crust of the Moon as Seen by GRAIL, *Science*, 339(6120), 671–675. (Cited on pages 17, 29, 32, 45 and 50.)

Williams, J. G., D. H. Boggs, C. F. Yoder, J. T. Ratcliff, and J. O. Dickey (2001), Lunar rotational dissipation in solid body and molten core, *Journal of Geophysical Research*, 106(E), 27,933–27,968. (Cited on page 64.)

Williams, K. K., and M. T. Zuber (1998), Measurement and Analysis of Lunar Basin Depths from Clementine Altimetry, *Icarus*, 131(1), 107–122. (Cited on page 45.)

Williams, Q. (2009), Bottom-up versus top-down solidification of the cores of small solar system bodies: Constraints on paradoxical cores, *Earth and Planetary Science Letters*, 284(3-4), 564–569. (Cited on pages 66, 79, 87, 88, 90 and 92.)

Wood, J. A., and H. E. Mitler (1974), Origin of the Moon by a Modified Capture Mechanism, or Half a Loaf is Better Than a Whole One, *Abstracts of the Lunar and Planetary Science Conference*, 5, 851. (Cited on page 15.)

Yang, H., and R. A. Secco (1999), Melting boundary of Fe-17%Si up to 5.5 GPa and the timing of core formation, *Geophysical Research Letters*, 26(2), 263–266. (Cited on pages 76 and 77.)
Zhang, J., and F. Guyot (1999), Thermal equation of state of iron and Fe0. 91Si0. 09, *Physics and chemistry of minerals*, 26(3), 206–211. (Cited on page 77.)

Zhang, N., E. M. Parmentier, and Y. Liang (2013), A 3D numerical study of the thermal evolution of the Moon after cumulate mantle overturn: The importance of rheology and coresolidification, *Journal of Geophysical Research, in press*, 1–57. (Cited on pages 17, 91, 92 and 93.)

Zhong, S. (2002), Effects of lithosphere on the long-wavelength gravity anomalies and their implications for the formation of the Tharsis rise on Mars, *Journal of Geophysical Research*, 107(E7), 5054. (Cited on page 47.)

Zhong, S., E. M. Parmentier, and M. T. Zuber (2000), A dynamic origin for the global asymmetry of lunar mare basalts, *Earth and Planetary Science Letters*, 177(3), 131–140. (Cited on pages 16, 25 and 54.)

Zhong, S., C. Qin, G. A., and J. Wahr (2012), Can tidal tomography be used to unravel the long-wavelength structure of the lunar interior?, *Geophysical Research Letters*, 39(15), n/a–n/a. (Cited on page 56.)

Ziethe, R., K. Seiferlin, and H. Hiesinger (2009), Duration and extent of lunar volcanism: Comparison of 3D convection models to mare basalt ages, *Planetary and Space Science*, 57(7), 784–796. (Cited on pages 27, 29, 36 and 54.)

Zuber, M. T., D. E. Smith, M. M. Watkins, S. W. Asmar, A. S. Konopliv, F. G. Lemoine, H. J. Melosh, G. A. Neumann, R. J. Phillips, S. C. Solomon, M. A. Wieczorek, J. G. Williams, S. J. Goossens, G. Kruizinga, E. Mazarico, R. S. Park, and D. N. Yuan (2013), Gravity Field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) Mission, *Science*, 339(6120), 668–671. (Cited on pages 17, 49, 50 and 51.)