Impact plasma amplification of the ancient lunar dynamo

Abstract

Spacecraft magnetometry and paleomagnetic measurements of lunar samples provide evidence that the Moon had a magnetic field billions of years ago. Because this field was likely stronger than that predicted by scaling laws for core convection dynamos, a longstanding hypothesis is that an ancient dynamo was amplified by plasma from basin-forming impacts. However, there have been no self-consistent models that quantify whether this process can generate the required field intensities. Our impact and magnetohydrodynamic simulations show that for an initial maximum surface field of only 2 microtesla, plasmas created from basin-forming impacts can amplify a planetary dipole field at the basin antipode to ~43 microtesla. This process, coupled with impact-induced body pressure waves focusing at the antipode, could produce magnetization that can account for the crustal fields observed today.

Large impacts in the presence of a weak dynamo field can explain strong lunar crustal magnetic anomalies.

INTRODUCTION

The Moon lacks a present-day global magnetic field, yet spacecraft and in situ observations of the crust and laboratory analyses of Apollo samples have identified natural remanent magnetization (NRM) that formed in an ancient magnetic field (1–4). In particular, analyses of lunar samples provide records of past magnetic fields between 4.25 and ~1.5 billion years (Ga) ago (1–4). These analyses show that before 3.56 Ga ago, the field intensity likely reached >10 to 100 μT, similar to that of the present-day Earth (1, 2). Most of the lunar sample NRMs are thought to have been acquired as thermoremanent magnetizations (TRMs) during cooling over periods of days to millions of years (1, 2, 5). However, the NRM of a few Apollo samples may be in the form of shock remanent magnetization (SRM) acquired through near-instantaneous exposure to high pressures (>0.1 GPa) (6–8). Moreover, large regions (spanning >10 to 100 km) of the lunar crust produce anomalies >10 nT at spacecraft orbit altitudes (~30 km), which are inferred to have been magnetized by paleofields >1 μT depending on the mechanism of magnetization (9–12). Some of the strongest such crustal anomalies are located antipodally to ~3.7- to 3.9-Ga-old large impact basins (Serenitatis, Crisium, Orientale, and Imbrium) (13–15).

The source of the high inferred paleointensities and crustal fields is a longstanding and central unknown in lunar science. Because of the long cooling timescales required by TRM acquisition, a temporally steady, core dynamo magnetic field is a widely preferred field source [e.g., (16, 17)]. However, given the Moon’s small core [~14% of the lunar radius, $R_M$ (18)], convective dynamo scaling laws can only account for surface magnetic fields of ~3 μT (1), at least 10 times lower than the strongest inferred paleointensities. This conundrum has elicited a range of alternative proposed external, internal, and amplified magnetic field sources to explain the ancient lunar records.

Proposed external magnetic fields include the solar nebula field, Earth’s dynamo field, and the interplanetary magnetic field (IMF) (1). Yet, by 3.56 Ga ago, these magnetic fields are either thought to have already dissipated [solar nebula field (19)] and/or be too weak [assuming a dipolar geometry, Earth’s tens of microteslas surface field was ≤1 nT at the expected location of the lunar orbit (20), while the IMF was ~10 nT at 1 AU (21)]. Internal magnetic fields generated from noncore convection dynamo mechanisms, such as differential precession of the mantle and core (22, 23) and a silicate magma ocean (24, 25), might have had sufficient energy to account for paleointensities up to ~100 μT. However, it is unclear if a magma ocean was sufficiently electrically conductive and whether mantle precession can generate flows with geometries suitable for dynamo action [see (1, 2)].

Alternatively, it has been suggested that an external energy source could generate or amplify a preexisting field near the lunar surface. One such process may be the generation of transient magnetic fields by impact plasmas due to the differential motion of ionized ejecta and impact-generated plasma within a few basin radii of the impact (26–28). Although simulations suggest this mechanism may be capable of producing magnetic fields >10 μT [without accounting for magnetic energy losses due to the high resistivity of the lunar crust (21, 29, 30)], the duration of these transient fields is on the order of minutes or less (1, 26) and therefore cannot explain the long TRM acquisition timescales in most Apollo samples. A set of related hypotheses envision that a local internally or externally generated magnetic field could have been amplified by plasmas generated from basin-forming impacts (12–15, 31). Because of its ionization and near-perfect conductivity (31), plasma expanding around the Moon will transport and compress any ambient magnetic field into the antipodal region. This process will amplify the preexisting field, possibly explaining the strong crustal fields observed today at the antipodes of the Serenitatis, Crisium, Orientale, and Imbrium impact basins (13, 14). One such proposed preexisting field source is the IMF and the field it induces inside the conducting layers of the Moon (14). However, impact hydrocode and three-dimensional (3D) magnetohydrodynamic (MHD) simulations of this process showed that an Imbrium-sized impact could only produce surface fields of <0.1 μT under the most favorable conditions (21), which is two to three orders of magnitude below the paleointensities inferred from the Apollo samples and those required to produce the strongest crustal anomalies (see the Supplementary Text and fig. S12).

Another preexisting field source that might be amplified is that of a weak (i.e., compatible with convective dynamo scaling laws) core dynamo (13–15, 31). By assuming conservation of magnetic flux and pressure balance at the antipode where the plasma converges, Hood and Artemieva (14) estimated that an initial ~10-μT field at the antipode would be amplified to ~1500 μT (i.e., amplification factor of ~150) lasting hours to 1 day after impact. The estimated magnetic field strength and duration can account for quickly cooled, thin magnetized layers containing TRM, as well as material that might experience substantial pressures and contain SRM.

Although pioneering, this first-principles estimation in (14) lacks some important considerations relating to the impact-plasma process that could affect the evolution of the magnetic field. The spatial and temporal evolution of the plasma and magnetic field are governed by coupled, nonlinear equations of mass, momentum, energy, and magnetic induction, such that numerical techniques are required to solve for this 3D process. In particular, there are several approximations in (14) that make the estimated field amplification and its duration uncertain. First, the dipole magnetic field is convected with the plasma in all directions (including away from the Moon), which limits the magnitude of magnetic flux delivered to the antipodal region. Second, as detailed in (21), the radially varying electric resistivity profile of the Moon [e.g., highly conducting core, moderately conducting mantle, and poorly conducting crust (29, 30); fig. S1] dictates that changes in the magnetic field occur on different timescales (for the crust less than 0.1 s, while for the deep mantle, greater than hours to days). Thus, along with affecting the temporal evolution of the magnetic field internal and external to the Moon, the resistive lunar crust will destroy amplified magnetic field energy through ohmic dissipation (21), thereby hindering the intensity and duration of the amplified surface field. Third, the magnetic flux conservation-amplification approximated in (14) took the maximum field strength of the unperturbed dipole field and uniformly applied a singular field value to a ~30,000 km² antipodal convergence zone without taking into account the initial 3D geometry of the magnetospheric (32) magnetic field. Fourth, (14) did not quantify the dependence of antipodal magnetic field amplification on impact location relative to the orientation of the magnetospheric dipole field (see the Results section). In addition, if a core-convection dynamo was present between 4.25 and 3.56 Ga ago, the initial magnetic field surface intensity was most likely not to have exceeded ~3 μT (1) (rather than 10 μT). Therefore, to assess the impact-generated plasma amplification of a lunar dynamo magnetic field, this process should be self-consistently modeled.

In this study, we captured the above mechanisms and their coupled, nonlinear and time-variable interaction, and evaluated the possibility of impact plasma amplification of a lunar dynamo magnetic field using an impact hydrocode and self-consistent 3D-MHD simulations. Then, given the location and timing of the magnetic field and rock magnetic properties of the lunar crust, we inferred the possible NRM that the crust could acquire. We used previously published results from the hydrodynamic, shock physics multimaterial, multirheology, Lagrangian-Eulerian code iSALE-2D (33, 34) that modeled the formation of an Imbrium-sized basin and the subsequent plasma (21). We chose the Imbrium basin formation event because it is the largest basin formed around ~3.7 to 3.9 Ga and has the strongest crustal field anomalies at its antipode (10, 14). To form such a basin, we modeled a 60-km-radius impactor hitting the lunar crust vertically at 17 km s⁻¹ (21). We then extracted the plasma properties of the basin-formation simulation and incorporated the ionized (31) vapor population as a plasma source in our 3D-MHD simulations [following (21)]. The MHD simulations were performed with the Block Adaptive Tree Solar-Wind Roe Upwind Scheme (BATS-R-US) code (35, 36), further developed from (21) to include the impact plasma interaction with the lunar magnetosphere.

We applied the lunar impact model of BATS-R-US in two stages. First, we simulated the steady-state lunar magnetosphere interaction with the ancient solar wind. Second, we released the impact-generated plasma inside the magnetosphere from a spherical surface area representing the basin region on the lunar surface. These simulations also incorporate the effects of the varying resistivity profile of the lunar body (21, 35, 37). For simplicity and also because of the prevalence of a dipole geometry for dynamo-generated magnetic fields in the present-day solar system (32), we assumed a body-centered dipole field geometry [although we note that the lunar dynamo may have had substantial multipolar power (38)]. Unless otherwise noted, we set the dipole moment to 5.24 × 10¹⁹ Am², which corresponds to a surface field at the magnetic equator and pole of 1 and 2 μT, respectively. During the simulations, the rotation and orbital motion of the Moon were ignored as the magnetic field amplification only lasted ~1 hour.

To test various impact scenarios and their effect on the resulting amplification, we varied the impact location from the magnetic pole (polar impact) to the magnetic equator (equatorial impact) (see the Supplementary Text). The simulations for the polar and equatorial impacts were achieved using equally spaced grids with ~30-km cells at the lunar surface; these were deemed sufficient because higher-resolution runs (~16-km cells) did not significantly change (<2% difference) the maximum amplified surface field strength (see the Supplementary Text). To apply this process to other proposed lunar dynamo mechanisms, we also varied the surface dipole field strength to establish the relationship between the initial magnetic field and the final amplified field (see the Supplementary Text). The estimated properties of the solar wind of the young Sun during the time of the Imbrium impact were derived in (21) as detailed in the Supplementary Text. Note that while (21) considered a range of wind conditions, in this case, the Moon is not directly exposed to the IMF and the thermal pressure of the impact plasma is ~15 orders of magnitude stronger than the solar wind ram pressure, such that the solar wind does not directly affect the dynamics of the impact plasma. We, therefore, adopt the same wind conditions for all simulations (table S1). More details of the model setup, computational tools, and relevant parameters used in performing the simulations are found in the the Materials and Methods, as well as the Supplementary Text.

RESULTS

For the polar (Fig. 1 and fig. S3) and equatorial (Fig. 2 and fig. S4) impacts, the evolution of the system broadly follows the analytical magnetic field confinement prediction presented in (14). The impact plasma expands out of the impact basin, stretching out the volume of space containing the magnetospheric field and forming a magnetic cavity (i.e., a volume of greatly diminished field magnitude) (39). The conducting impact plasma carries the frozen-in magnetic field and compresses it at the antipodal region outside the Moon. The reconfiguration of frozen-in flux therefore amplifies the magnetic field at the compression area because the surface area of the antipodal convergence zone is smaller than the initial lunar hemisphere over which the field was originally distributed (see fig. S2). Inside the Moon, the magnetic field responds to the changing field outside and diffuses toward the antipode while also dissipating magnetic energy [see equation S4 in (21)].

Fig. 1. Amplification of the lunar dynamo field by an Imbrium-sized impact at the magnetic pole.

2D slices of the 3D-MHD simulation of impact plasma expanding from the surface magnetic pole within an ancient lunar magnetosphere of 1-μT equatorial surface field strength. (A to C) show the initial condition steady-state lunar magnetosphere, while panels (D to I) show the impact plasma expansion at 30 and 56 min after impact, respectively, which are the times of plasma antipodal convergence and maximum antipodal surface magnetic field of ~43 μT (blue curve in Fig. 3), respectively. (A), (D), and (G) show the evolution of the (log-scale) plasma mass density, $\mathrm{\rho }$, with velocity flow lines (white arrows scaled to relative speed). (A) shows the initial magnetospheric velocity field, where the polar outflow speeds are higher than the impact plasma expansion, though the momentum flux they deliver is negligible, as the density inside the magnetosphere is low. (B), (E), and (H) show the evolution of the total magnetic field magnitude normalized to the 2-μT surface polar field, $B$/$B$_pole,0, with magnetic field direction (black arrows). (C), (F), and (I) show a cartoon depiction of the impact plasma (orange “cloud”) expanding and compressing the lunar dipole field (black arrowed streamlines) into the antipodal region. (I) illustrates the magnetic geometry, by which the impact plasma compresses parallel polar field lines together into a small region, increasing the magnitude of the magnetic field. The white circular outline depicts the lunar surface while the shaded white region depicts the 0.5 R_M surface. The central black arrow shows the direction (not intensity) of the dynamo dipole moment. The solar wind is flowing in the +X direction with characteristics described in table S1. The impact is launched from X = 0 and Z = 1 R_M.

Fig. 2. Amplification of the lunar dynamo field by an Imbrium-sized impact at the magnetic equator.

2D slices of the 3D-MHD simulation of impact plasma expanding from the surface magnetic equator within an ancient lunar magnetosphere of 1 μT equatorial surface field strength. (A to C) show the initial condition steady-state lunar magnetosphere, while (D to I) show the impact plasma expansion at 30 and 40 min after impact, which are the times of plasma antipodal convergence and maximum antipodal surface magnetic field of ~6 μT (red curve Fig. 3), respectively. (A), (D), and (G) show the evolution of the (log-scale) plasma mass density, $\mathrm{\rho }$, with velocity flow lines (white arrows scaled to relative speed). (A) shows the initial magnetospheric velocity field, where the polar outflow speeds are higher than the impact plasma expansion, though the momentum flux they deliver is negligible, as the density inside the magnetosphere is low. (B), (E), and (H) show the evolution of the total magnetic field magnitude normalized to the 1-μT surface equatorial field, $B$/$B$_equator,0, with magnetic field direction (black arrows). (C), (F), and (I) show a cartoon depiction of the impact plasma (orange “cloud”) expanding and compressing the lunar dipole field (black arrowed streamlines) into the antipodal region. (I) illustrates the magnetic geometry, by which the impact plasma compresses anti-parallel equatorial field lines together into a small region, allowing for some amplification while creating a central region of weakened magnetic field. The white circular outline depicts the lunar surface. The central black arrow shows the direction of the dynamo dipole moment. The solar wind is flowing in the +X direction with characteristics described in table S1. The impact is launched from X = 1 R_M and Z = 0.

For the polar impact (movies S1 and S2), the magnetic field converging at the antipode is composed of parallel field lines that are compressed together (Fig. 1). In this configuration, starting at ~44 min after impact, we find a maximum magnetic field of ~180 μT at ~700 km above the lunar surface and a field of ~43 μT in the antipodal surface, staying above the initial polar surface field strength for ~40 min (Fig. 3). As seen in Fig. 1, the surface amplified magnetic field spatially varies from ~43 μT at the antipode to 10 μT at >500 km away from the antipode. The maximum ~180-μT field at ~700-km altitude corresponds to an amplification factor of ~120 (from the average initial hemispherical surface field), which is of order the amplification predicted by (14). In addition, we find similar amplification for impacts at ≥60° latitude from the magnetic equator (see the Supplementary Text). We further tested the polar impact scenario to find that the maximum amplification was approximately proportional to the initial surface dipole field strength (0.1, 1, and 10 μT), as expected because of magnetic flux being proportional to field strength (see the Supplementary Text).

Fig. 3. Antipodal surface magnetic field and pressure wave evolution during the expansion of impact plasma.

Shown are the time evolution of the lunar antipodal surface magnetic field magnitude for the equatorial impact (red curve) and polar impact (blue curve). As seen by the red curve, the equatorial impact maximum magnetic field in the antipodal surface region reaches about ~6 μT, representing a ~6 times amplification from the initial equatorial surface field (lower black dotted line). The maximum magnetic field from the equatorial impact is limited by the geometry of the antipodal compressed field (see Results), where antiparallel field lines are brought together, resulting in a lesser maximum field strength relative to the polar impact. The blue curve depicts the maximum antipodal surface magnetic field due to polar impact, reaching around ~43 μT, equivalent to a ~21 times amplification factor relative to the initial polar surface field strength (dashed black line). The polar impact represents the ideal geometry for maximum antipodal magnetic field amplification, as the impact plasma compresses parallel field lines together (see Results). The black and orange triangles represent times when the iSALE-2D impact simulation produces body wave pressures >0.5 and >0.8 GPa in the antipodal crust (see the Supplementary Text and fig. S11), respectively. The latter pressure wave convergence times correspond with the time of maximum amplified antipode magnetic field, which suggests that this strong, amplified lunar dipole field could be recorded in crustal material via SRM acquisition.

For the equatorial impact (Fig. 2), the magnetic field converging at the antipode is composed of fields of opposite polarity arriving from the two polar regions. This leads to a significantly smaller amplification at the surface, up to a maximum value ~6 μT and lasting above the initial 1 μT value for ~20 min (Fig. 3). This reduction in amplification is due to the compression of antiparallel field lines, causing the antipodal compression area to include a central region of low-magnitude magnetic field. This antiparallel field geometry creates a magnetic reconnection region, where magnetic energy is converted into thermal and kinetic energy. Fluid descriptions of plasmas underlying the MHD approximation cannot capture the microkinetic processes responsible for magnetic reconnection. However, its effects on the magnetic field can be mimicked through numerical diffusion and our simulations represent a reasonable approximation of physical reconnection with respect to global dynamics (40). The polar impact does not exhibit opposite polarity field geometry in the antipodal region and achieves the highest amplification factors in this study.

Another factor limiting field amplification is the Moon’s internal electric resistivity. Because of the extremely low conductivity [~10⁻⁷ S m⁻¹ (29, 30)] of the lunar crust, spatial gradients in the magnetic field are diffused and destroyed via ohmic dissipation. As derived in the section S3.2 of (21), the dissipative power of the lunar crust is proportional to the square of the current density, which can be approximated by the square of the gradient in the magnetic field. In (21), typical gradients of 30 nT in the lunar crust translate to dissipation of 10% of the initial crustal IMF-induced magnetic energy every second. Given that the simulated maximum antipodal magnetic field is ~43 μT (and varies by ~10 μT over ~300 km depth), this amplified crustal field is subjected to the dissipative power of ~10¹⁶ W, effectively capable of dissipating energy of order the initial lunar dipole crustal magnetic field energy in milliseconds (21). The influence of ohmic dissipation is especially evident in the polar impact, where the surface maximum antipodal magnetic field is over a factor of 4.5 times weaker than the maximum field just ~700 km above the lunar surface (Fig. 1), which is not subject to magnetic dissipation. As a result, only the field ~700 km above surface is amplified to the level predicted by (14). To further test the role of ohmic dissipation in removal of the field, we examined the case of an exaggerated initial IMF-induced field of 1000 nT, without an internal dipole field (Supplementary Text and fig. S13). We have shown (see the Discussion section) that such a field cannot be as efficiently amplified, as the lack of an internal field source allows for larger magnetic field gradients to form. The findings from these simulations demonstrate that a self-consistent, 3D-resistive MHD model is crucial for appropriately solving for the spatial and temporal evolution of the impact plasma amplification of the lunar magnetic field.

DISCUSSION

Our simulations of impact-generated plasma amplification of a 1-μT equatorial surface dynamo field produced surface fields up to ~43 μT, with the amplified antipodal magnetic field exceeding the initial dipole field from ~40 to ~80 min after impact (Fig. 3). Although this amplified value is in the range of the Apollo sample paleointensities (1, 5), it cannot explain the magnetization of most TRM-bearing lunar samples, which acquired their NRM over far longer timescales (see above). However, the amplified field is also potentially strong enough to have produced lunar crustal magnetization at the antipodes of the Imbrium, Serenitatis, Orientale, and Crisium basins (9, 41). To evaluate the latter possibility, we must assess the capability of crustal rocks in these regions to record these strong, short-lived amplified magnetic fields.

Simulations of Imbrium-basin forming impacts show that the ejecta first ballistically reach the antipode at >4 hours after impact (14, 42). Thus, the short time duration of the amplified magnetic field excludes the possibility that this field could magnetize impact ejecta landing in the antipode (13, 14). An alternative mechanism that could enable the amplified magnetic field to magnetize antipodal material is body pressure waves (43, 44). Observations (45), analytical calculations (43), and numerical simulations [see the Supplementary Text and (44)] suggest that basin-forming impacts can induce pressure waves that focus at the antipode, imparting pressures of 0.1 to 2 GPa in the near surface crust up to ~60 min after impact (Fig. 3 and fig. S11). The impact simulation (see the Materials and Methods) performed for this study yielded antipodal (within a circular area of radius ~100 and 30 km depth) pressures up to 1 GPa when the amplified field was >30 μT. To estimate whether sufficient pressure existed concurrently with the amplified field, we first calculated the maximum pressure experienced at each location inside the antipodal region during times when the amplified field was >30 μT. Then, we averaged this spatial map of maxima over the entire region, which we find to be ~0.45 GPa. These pressures were not exceeded at later times when the amplified field decayed (Fig. 3 and fig. S11), implying that this SRM could survive the impact event. Given that these pressures occur in the antipode crust [farside temperatures <300 K during the period of field amplification given ancient and modern selenotherms (46, 47)] (Fig. 3), this enables antipodal material to acquire an SRM at the time and location of maximum field amplification.

To establish whether such SRM could generate the intensity of the observed antipodal anomalies (11, 12), we modeled their magnetic fields at spacecraft altitudes (Fig. 4). Our goal was to establish whether the thickness, magnetic recording efficiency (referred to as susceptibility), and paleofield intensity required to generate a 10-nT field at 30-km altitude are compatible with what is expected for magnetization sources at the basin antipodes (Fig. 4). We represented the magnetized volume of crustal material with a cylindrical disk. The disk radius of 30 km was chosen to maximize the magnetic field, although increasing the disk radius to 100 km only decreases the produced magnetic field by a factor of ~2 (9, 48). We estimated a range of SRM susceptibilities (${\mathrm{\chi }}_{\text{SRM}}$) for shock pressures <2 GPa for various lunar and meteoritic materials. These were estimated by dividing the TRM susceptibilities (${\mathrm{\chi }}_{\text{TRM}}$), reported in (9), by values of ${\mathrm{\chi }}_{\text{TRM}}/{\mathrm{\chi }}_{\text{SRM}}$ measured by (7, 49).

Fig. 4. Shock remanent susceptibility, paleointensity, and layer thickness of magnetized materials that can produce the strongest lunar crustal anomalies.

Thicknesses (color bar) required to magnetize crustal material and generate a 10-nT field observed at 30-km altitude for varying ambient, ancient magnetic fields (paleointensities), and SRM susceptibilities (${\mathrm{\chi }}_{\text{SRM}}$). The magnetized material is derived to represent a cylindrical disk volume with a 30 km radius and ranging thicknesses (heights) (9, 48). The ${\mathrm{\chi }}_{\text{SRM}}$ values for the SPA metal-rich ejecta (gray shaded region) are calculated from the mean published ${\mathrm{\chi }}_{\text{TRM}}$ values in (9), with the upper bound representing an upper limit of ${\mathrm{\chi }}_{\text{SRM}}/{\mathrm{\chi }}_{\text{TRM}}$= 0.1 and the lower bound representing a lower limit ${\mathrm{\chi }}_{\text{SRM}}/{\mathrm{\chi }}_{\text{TRM}}$ = 0.01, from the SRM experiments of (7, 49). The ${\mathrm{\chi }}_{\text{SRM}}$ values for the mafic impact-melt breccias and mare basalts are modified by ${\mathrm{\chi }}_{\text{SRM}}/{\mathrm{\chi }}_{\text{TRM}}=0.1$, to represent an upper limit of their magnetic properties. The left-most red vertical line shows the maximum antipodal magnetic field (~43 μT) in the polar impact simulation observed during the time of antipodal pressure wave convergence. As seen from the two horizontal dashed lines, the most magnetic known native lunar materials (mafic impact-melt breccias) are likely not able to explain the large crustal magnetic anomalies. Given the presence of metal-rich material from the SPA impact (>4-km-thick layers, black squiggly line), it is conceivable that the predicted maximum amplified antipodal magnetic fields could be recorded during SRM acquisition by this impactor material with ${\mathrm{\chi }}_{\text{SRM}}$ of ≳8 × 10⁻³ SI and potentially explain large crustal anomalies. The right-most red vertical line shows the amplification factor of ~21 applied to the silicate magma ocean dynamo-generated field (initially ~20 μT), which can explain the strongest crustal fields through SRM of mafic impact melt sheets of thickness 5 to 10 km (see the Supplementary Text).

Figure 4 shows the range of permissible magnetic properties for a cylindrical volume carrying an SRM generating a 10-nT field at 30-km altitude. We begin by considering source rocks with magnetizations like that of mafic impact melt breccias, which are some of the most magnetic (TRM susceptibility) known lunar materials. We estimate that such materials are not likely to produce the strong crustal fields, as they would require layer thicknesses (>50 km) larger than the average lunar crust (50–53). However, the Imbrium and Serenitatis antipodes lie within the ~4.2-Ga-old South Pole-Aitken (SPA) basin (9). Simulations of the SPA formation event predict the deposition of a >4-km-thick ejecta layer of the impactor core (9), composed of metal-rich material approaching the northern edge of the basin. Reprocessing of gravity data from the Gravity Recovery and Interior Laboratory (GRAIL) mission suggests that the northern rim region of the SPA basin might have a higher density of impact basin ejecta (iron-rich material) based on correlations between free air-gravity, topography, and crustal magnetic field location (54). These ejecta could be one to two orders of magnitude more magnetic than most native lunar materials (7, 49). Even assuming it has ${\mathrm{\chi }}_{\text{SRM}}$ = 8 × 10⁻³ SI (~10 times that of mafic impact melt breccias), a layer thickness <4 km can readily account for the magnetic anomalies. Therefore, it is plausible that impact plasma amplification of a lunar dynamo with a nominal surface equatorial field of just 1 μT, which is compatible with scaling laws for core convection dynamos, could explain some of the strongest crustal magnetic anomalies.

The strongest anomalies could be further explained by thinner or less magnetic layers if the initial dynamo field were stronger than the initial 1-μT equatorial field considered above. For example, a basal silicate magma ocean dynamo is predicted to generate a surface polar paleofield of ~20 μT (24, 25). The proportional dependence of amplification factor on initial field strength (see the Supplementary Text) predicts that the dipolar surface field of this stronger dynamo would be amplified to ~420 μT. For such a field, the antipodal anomalies could be produced by just a 5- to 10-km-thick layer of mafic impact melt breccias containing SRM (Fig. 4), well within the expected layer thicknesses for such materials.

There are multiple strong crustal anomalies that lie at intermediate positions (~47° to 110° angular distance from the Imbrium basin center) between Imbrium and its antipode (e.g., Reiner Gamma, Airy, Hartwig, Descartes, and Abel). In one specific explanation, these anomalies have been attributed to magnetized Imbrium ejecta, possibly containing impactor metal-rich material (55). For these intermediate anomaly locations, the maximum amplified paleofield, which arises from the surface currents that form between the compressed dipole field and the impact plasma cloud, is at most ~3× the local dipole field (see the Supplementary Text). However, the initial pressure wave reaches these anomaly locations within a few minutes, whereas the potential metal-rich ejecta material would arrive hours after. We also do not find any wavefront pressures that exceed ~0.2 GPa (after the initial body waves) in these intermediate path anomalies, so this likely would not allow for the subsequent ejecta arrival to experience SRM. Even if there were higher pressures (>0.5 GPa) coinciding in time with the weak, ~3- to 5-μT amplified field, this would require a 10- to 20-km-thick layer with ${\mathrm{\chi }}_{\text{SRM}}\ge$ 0.1 to account for the strong measured crustal fields. Thus, if these intermediate path crustal magnetic fields are products of Imbrium ejecta, they are more likely generated from a TRM recording of the nominal dynamo field.

Although basin ejecta that is deposited in the antipode are not able to record the greatly amplified dipole field due to its short lifetime, once settled, the ejecta might record the local dynamo field via TRM (14, 42). This deposition and cooling of this ejecta would occur after the SRM recording of the amplified dipole field. For the SPA region (antipodal to Imbrium and Serenitatis), the SRM recorded by the exogenic material could be superimposed with the Imbrium ejecta TRM and potential magnetized magmatic dike swarms (56), adding to the overall crustal field signature. Given that the Imbrium ejecta material cooling time is longer than the duration of the amplified dipole field, this TRM would be a record of the relaxed, initial surface dipole field and potential surrounding magnetized materials.

The short-lived impact-generated plasma amplification of a lunar dipole field provides a mechanism to explain some of the strongest and most spatially extensive crustal anomalies on the Moon. Current and future lunar sample return and magnetometer missions, like the Endurance rover (57) and the Chang’e-6 lander (58), can explore and sample the Imbrium and Serenitatis basin antipodes (SPA region) and search for evidence of SRM from ancient lunar dipole antipodal amplification. These samples might include rocks that show petrographic evidence for shock (59) and paleomagnetic evidence for SRM (7, 49). Furthermore, the impact antipodal magnetic field amplification process may explain components of the crustal magnetic field records of other terrestrial planetary bodies with (past) internal dynamo-generated magnetic fields, like Mercury (60), Mars (61), and meteorite parent bodies (62, 63).

MATERIALS AND METHODS

Impact simulations of an Imbrium-sized basin

The Imbrium-scale impact simulation was performed using the iSALE-2D shock physics code, a 2D, multimaterial, multirheology, simplified arbitrary Lagrangian-Eulerian (SALE) hydrocode (33, 34). We used the same impact simulation as that in (21). For details, see the Materials and Methods of that study.

3D MHD modeling overview

Each MHD simulation starts by modeling the interaction between the ancient solar wind and the lunar core dynamo field before an impact. Once this solution reaches a steady state (i.e., the solution becomes approximately constant in time), we then launch the impact-generated plasma (21) into the computational domain, simulating a basin-scale lunar impact.

Single-fluid ideal MHD justification

For the approximation of MHD, we discuss the subsequent evolution of the highly ionized, impact plasma. Multiple ionized species (e.g., Na, K, Si, O₂, and Al) would be generated from the impactor and lunar surface material. The nominal impact generated plasma characteristics are given by number density (10²⁶ m⁻³), ambient lunar dipole field (1 to 2 μT), temperature range (10³ to 10⁴ K), and singly charged species of average mass 21 amu (based on the chemical composition of gabbroic anorthosite). For the solar wind interaction with the pre-impact lunar magnetosphere, the ion and electron gyroradii and Debye length are <10% of the lunar radius (table S1). For the impact plasma, we find that the ion and electron inertial lengths (∼3 × 10⁻⁵ m and ~5 × 10⁻⁷ m, respectively), ion and electron gyroradii (<10 and <0.02 m, respectively), and Debye length (~10⁻¹⁰ m) are orders of magnitude smaller than the global length scale (lunar radius, ~1.7 × 10⁶ m) and the antipodal amplification region (~10⁵ m). Thus, the use of a fluid approximation to model the large-scale evolution of this plasma system is justified.

To justify the treatment of the impact plasma as perfectly conducting (i.e., neglecting plasma resistivity), we start with the creation of the ionized, impact plasma. The modeled impactor creating an Imbrium-sized basin is composed of gabbroic anorthosite and has a radius of 60 km and a velocity of 17 km s⁻¹. On the basis of scaling laws (31, 64) and our impact simulations (21), this impactor type and delivered kinetic energy (~10²⁸ J) results in large-scale vaporization of the impactor and target surface material. For this delivered impactor kinetic energy, initial temperatures at the impact site reach ≳10⁴ K, leading to nearly complete ionization of the vapor and corresponding electrical conductivities of 10⁴ to 10⁷ S m⁻¹ (31, 65, 66). We then estimate the magnitudes of the magnetic convection and diffusion terms of the induction equation (Eq. 3) over the relevant temporal and spatial scales as well as calculate the magnetic Reynolds number, R_mag, (ratio of magnetic convection to diffusion terms), to justify the treatment of the impact plasma as perfectly conducting. We find that for the smallest cell size (~17 km for plasma-containing cells in our MHD simulations), together with the lower end of the conductivity range (10⁴ S m⁻¹), the diffusion timescale is >10³ hours, much longer than the ~1 hour of simulated time. The minimum cell size is applicable for this calculation as the impact plasma thermal expansion velocity (~3 km s⁻¹) shows that the impact plasma cloud grows to >10 km in radius within seconds. In addition, the frozen-in approximation (the consequence of using a perfectly conducting plasma when R_mag > > 1) is valid as the conductivity range yields an R_mag > 10⁵ at the length scales of the smallest lunar surface cell resolution (~17 km). Thus, it is valid to treat the impact plasma as perfectly conducting in this modeling scenario.

For approximating the plasma with single-fluid MHD (despite it being comprised of several ions), we first note that the main result of this study, the maximum antipodal surface field amplification, is controlled by the compression of the dipole field by the impact plasma. This process is accounted for in the MHD approximation in the convection term of the magnetic induction equation (Eq. 3). If multifluid MHD were used, the primary effect (on our main science result) of simulating separate species would be seen in the modification of the magnetic induction equation in the multi-fluid regime [see equation 47 in (35)], which includes the convection of the magnetic field from separate charged species, the Hall term (ion-electron drifts), and electron pressure gradient terms (Biermann battery). We first note that given the large base number density (10²⁶ m⁻³) of the impact plasma, both the Hall term and Biermann battery terms are negligible for this environment, as they are estimated to be, respectively, ~10 and ~50 orders of magnitude smaller than the convection term in the smallest cell resolution length scales (~10⁴ m). The magnitude of the Hall and Biermann terms relative to the convection term would be the same, or even smaller, for larger cells (occurring away from the body), so these terms are negligible everywhere. For the convection term, it is important to see if ion drifts can change the bulk nature of the impact plasma, thus altering the utilization of a single, average velocity. Some of the possible relevant ion drifts are the gravitational, diamagnetic, and thermal ion drifts. For the given plasma characteristics, the gravitational and diamagnetic drift velocities are >3 orders of magnitude slower than the bulk expansion speed (~3 km/s). One way to quantify the effect of generated ion (thermal) drift velocities is with the Knudsen number (67, 68), which for our impact plasma is ~10⁻¹⁷. Multispecies plasmas with small Knudsen numbers (much less than unity) have efficient exchange of momentum and energy between particles, meaning that any ion (thermal) drifts and temperature gradients will be equilibrated around the collisional timescale (~10⁻¹⁵ s, approximately instantaneously), which is many orders of magnitude faster than the relevant timescales of the impact plasma expansion around the Moon (10² to 10³ s). This allows for the plasma to be approximated with a single-fluid MHD (single bulk velocity and mass density and magnetic induction-diffusion equation with bulk velocity convection), not necessitating separate continuity, momentum, and pressure (or energy) equations for each species (68).

Governing equations, grid structure, boundary conditions, and numerical parameters

There is a robust history of using MHD to model the global-scale interaction between the solar wind and planetary bodies (32). For our MHD simulations, we use the BATS-R-US code (35, 37, 69). Unless otherwise noted, for both the magnetosphere and impact plasma evolution simulations, we solve the ideal and resistive MHD formulations (Eqs. 1 to 4 below) explicitly to second-order accuracy (for which the error scales with the square of the cell size) in space and time (70)

$$\frac{\mathrm{\partial \rho }}{\mathrm{\partial }t}+\nabla ·\left(\mathrm{\rho }\mathit{u}\right)=0$$ (1)

$$\begin{array}{c}\frac{\mathrm{\partial }\left(\mathrm{\rho }\mathit{u}\right)}{\mathrm{\partial }t}+\nabla ·(\mathrm{\rho }\mathit{u}\mathit{u}+p\mathrm{I}+\frac{B^2}{2{\mathrm{\mu }}_0}-\frac{\text{BB}}{{\mathrm{\mu }}_0})=\mathrm{\rho }\mathit{g}\hfill \end{array}$$ (2)

$$\frac{\mathrm{\partial }\mathit{B}}{\mathrm{\partial }t}+\nabla \mathtt{\times }\mathbf{E}=0$$ (3)

$$\begin{array}{c}\frac{\mathrm{\partial }}{\mathrm{\partial }t}(\frac{1}{2}\mathrm{\rho }{u}^2+\frac{p}{\mathrm{\gamma }-1}+\frac{B^2}{2{\mathrm{\mu }}_0})+\nabla ·[\frac{1}{2}\mathrm{\rho }{u}^2\mathit{u}+\frac{\mathrm{\gamma }p}{\mathrm{\gamma }-1}\mathit{u}+\frac{\mathit{E}\times \mathit{B}}{{\mathrm{\mu }}_0}]=\mathrm{\rho }(\mathit{g}·\mathit{u})\hfill \end{array}$$ (4)

In Eqs. 1 to 4, $\mathit{B}$ is the magnetic field vector, $\mathit{E}\mathit{=}\mathit{-}\mathit{u}\mathit{\times }\mathit{B}\mathit{+}\nabla \times \mathit{B}/\left({\mathrm{\mu }}_0\mathrm{\sigma }\right)$ is the electric field including the finite conductivity, $\mathrm{\sigma }$, inside the Moon, t is time, $\mathrm{\gamma }$ = 5/3 is the ideal gas polytropic index, $p$ is the thermal pressure, $\mathit{g}$ is the lunar gravitational acceleration vector, $\mathrm{\rho }$ is the plasma mass density, $\mathit{u}$ is the plasma bulk velocity vector, $I$ is the identity matrix, and ${\mathrm{\mu }}_0$ is the magnetic permeability of free space [applicable for the lunar interior (29)]. Note that, if applicable, the nonbolded variables are the scalar magnitudes of the corresponding bolded (vector) quantities. Outside the lunar body, where the solar wind plasma is a perfect conductor, the ideal MHD equations are solved with $\mathrm{\sigma }\to \infty$. Inside the lunar body, $\mathrm{\rho }$ and $\mathit{u}$ are set to zero, leaving the evolution of $\mathit{B}$ to be governed by the finite-conductivity approximation of the induction-diffusion equation (Eq. 3 with $\mathit{u}\mathit{=}\mathbf{0}$). The conductivity of the Moon varies from ~7 × 10⁻⁷ S m⁻¹ in the crust to ~10 S m⁻¹ at the core boundary (fig. S1) (21, 29, 30).

We use a spherical grid for which the radial extent of a cell increases logarithmically outward (fig. S1). This structure allows for smaller cell sizes inside the body and its environs, which is needed to capture sharp changes in the magnetic field solution. The global size of the computational grid is chosen to encompass the size of the magnetosphere, which is dependent on the strength of the lunar dipole moment and the solar wind dynamic pressure (70). In addition, to solve for the full evolution of the impact plasma around the system, it is important for the domain to be large enough so that the impact plasma does not reach the edges of the domain during the chosen simulation times, which would otherwise lead to the simulation becoming numerically unstable (once the impact plasma reaches the solar wind outer boundary, the inflow boundary condition for the solar wind is violated). Therefore, the computational domain is chosen to span from 0.2 to 30 lunar radii ($R_M$ = 1737 km). With BATS-R-US’s computational mesh refinement utilities, additional cell size resolution is applied to the computational grid within 3 $R_M$ to further resolve the magnetic field amplification. The inner boundary is set at the surface of the highly conducting lunar core at radius of ~0.2 $R_M$. At the core-mantle boundary (0.2 $R_M$), lunar surface (1 $R_M$), and outer computational boundary (30 $R_M$), the radial extents of the cells are 0.015, 0.017, and 2 $R_M$, respectively, while the angular extents of the cells are approximately 4°, 0.92°, and 3.6°, equivalent to 0.014, 0.016, and 1.9 $R_M$ spacings in each of those distances, respectively.

The polar and azimuthal (angular) boundary conditions are periodic along the polar axis and zero meridian. At the core-mantle boundary (0.2 $R_M$), the inner boundary condition for the magnetic field is set to the constant value of the dipole field, which is unaffected over the timescales of the simulation as the diffusion timescale of the core is >10 days. Because the lunar surface is not a boundary for the magnetic field, as the resistivity term becomes nonnegligible inside the lunar surface, the magnetic field is evolved in accordance with the induction-diffusion equation (37). At the lunar surface, the flow boundary conditions vary adaptively according to the flow density and direction. The inflow solar wind is absorbed, and any outflow is inwardly reflected, as the lunar surface is not a significant source of plasma. Conversely, the dense impact plasma is emitted from the impact basin and is only permitted to have tangential velocity (via a surface boundary condition) with respect to the surface just outside the basin. At the outer boundary (30 $R_M$), far from the body, the boundary conditions for the plasma flow are set to inflow or outflow based on the direction of the solar wind velocity relative to the boundary normal vector.

To mitigate the violation of the divergence free condition of the magnetic field from numerical discretization errors in the solution of the induction equation (Eq. 3), we use both the eight-wave (36) and the hyperbolic cleaning methods (35). A semi-implicit scheme (35) is used to solve the magnetic diffusion equation inside the lunar body, as the explicit timestep is limited by the diffusion timescale, which can be very small (<10⁻⁵ s) in the lunar crust [see equations 15 and 16 in (71)]. The steady-state lunar magnetosphere simulations are performed to second-order accuracy with a Courant number of 0.8.

Several adjustments to the above are required to solve the time-accurate (35, 72) evolution postimpact, due to the constraints of computational power along with the accuracy and simulation time needed. The postimpact time-accurate coupled evolution of the plasma and fields are solved to second-order accuracy with a Courant number of 0.4. Furthermore, given that the explicit timestep derived for the desired spatial resolution would require months of real-world computer time to complete an impact simulation, the so-called “Boris correction” factor (35, 73) of 0.02 is applied to artificially reduce the speed of light, which is a limiting factor of the MHD fast wave speed. Although reducing the speed of light via the Boris correction can make the simulation less stable if the speed of light is reduced to a value comparable to plasma flow speeds, our simulations provided physical solutions as the impact plasma flow velocity remained two to three orders of magnitude lower than the artificially reduced speed of light. This Boris correction allows for a >10 times larger explicit timestep and is used extensively in magnetospheric simulations (35, 74, 75) where the magnetic field is strong (e.g., near planetary magnetic poles) and when the MHD fast wave speed is large, compared to the bulk flow speed, due to high particle number densities (e.g., in the impact plasma cloud, where it is 10²⁰ cm⁻³). Both the changes to the Courant number and the inclusion of the Boris correction were verified to not significantly affect the resultant magnetic field amplification process (separate tests holding all other parameters the same showed that these changes did not alter the maximum magnetic field amplification by more than ~6%). Last, to allow for the solution to propagate across the computational poles, the order of accuracy of the numerical scheme is reduced to first order in space (error scales with cell size) in the cells immediately surrounding the computational pole.

Magnetosphere simulations: Lunar planetary magnetic field and solar wind conditions

A sufficiently strong internal magnetic field can create a magnetospheric cavity around a planetary body, shielding it from the incident solar wind (32). The main parameters controlling the shape and dynamics of the interaction between the solar wind and a magnetosphere are the density, speed, and magnetic field of the solar wind plasma and the strength and topology of the body’s intrinsic magnetic field (70). Uncertainties on the solar wind parameters may affect the size of the magnetosphere, but we have confirmed that they have a negligible effect on the eventual field amplification postimpact, as the impact plasma thermal energy density is >15 orders of magnitude larger than the dynamic ram pressure of the solar wind (table S1). It has been proposed that perhaps ~40% of the lunar dynamo surface field was nondipolar due to the Moon’s slow rotation rate (38). However, given the overall unknown geometry of the lunar field and the dominance of dipolar fields for the terrestrial and giant outer planets at present, we chose to perform this study with a core-centered dipole field geometry. On the basis of scaling laws for thermal-convection dynamo generated magnetic fields in a lunar-sized core, we take the equatorial surface dipole field strength to be 1 μT (1).

Testing the capability of impact plasma to amplify the underlying dipole magnetic field requires an estimation of the ancient solar wind conditions at the Moon at the time of magnetization acquisition. To constrain the ancient solar wind characteristics, stellar evolution models (76, 77) have been used to predict the temporal evolution of the rotation rate, magnetic field intensity, chromospheric temperatures, and total mass for young (500 Myr to 1 Ga old: the age of the Sun ~4 Ga ago) Sun-like stars (1) and have been compared to available observations (63). This, in turn, enables the estimation of the mass loss rate and wind characteristics of these young solar analogs (78–80). In this study, we adopt the ancient solar wind bulk velocity (400 km s⁻¹) and mass density (26 amu cm⁻³) as estimated in (21). For an estimation of the IMF at 1 AU between 3.56 and 4.25 Ga ago, we assume a Parker spiral geometry (81). This yields an IMF strength of 30 nT, the same as used in (21), which is likely an upper limit due to the fact that it assumes the total solar surface contributes to the interplanetary magnetic flux (ignoring closed field line regions) and an r⁻¹ radial decrease in the field strength with heliocentric distance (ignoring the r⁻² decrease of the radial component of the IMF, where r is the radial distance from the center of the Sun). For the solar wind temperature, which determines the thermal pressure, we follow the modeling of (63) and choose a typical temperature of 200,000 K (21, 63). The maximum magnetic field amplification is more dependent on the lunar dipole field geometry and orientation with respect to the impact basin location, rather than the plausible range of solar wind characteristics derived from models and observations.

Impact plasma simulations: Emitting boundary and stopping criterion

To use the impact simulations to drive the MHD simulations, the iSALE-2D simulation results (21) of the time evolution of impact plasma density, temperature, and velocity are converted into a time-dependent emitting boundary in the MHD simulation grid, with the impact-generated plasma treated as an ionized, perfectly conducting, MHD fluid (31). At the emitting boundary, the impact plasma mass density is set to an exponentially decaying source with an initial amplitude of 10⁻² g cm⁻³. The temperature of the emitted impact plasma is fixed at 2000 K, given by the temperature of the vertically emitted vapor after expansion from the basin in the iSALE-2D simulations (21). The vaporized gas velocity in the iSALE-2D simulations is complex in its direction, as the speed is different in the center of the basin or close to the basin wall. However, those speeds are small compared to the speed the vapor gains once it expands due to the large pressure gradient between the vapor and the magnetosphere. Therefore, to simplify the boundary conditions, the speed of the emitted plasma in the MHD simulation is set to 0 km s⁻¹. We confirmed that the speeds achieved by this plasma as it expands away from the emitting boundary in the MHD simulation are similar to the speeds the vapor gains in the corresponding iSALE-2D simulation. Like elsewhere on the body, the magnetic field in the emitting boundary is continuous across the lunar surface boundary, meaning that it is initially equivalent to the ambient magnetospheric field. The duration of vapor emission from the boundary is set to be 250 s, which is the time it takes for the calculated iSALE-2D impact vapor mass flux to decay to a minimum [see figure S5 in (21)]. The location of the emitting boundary is centered around the specified magnetic latitude (e.g., magnetic pole and equator) depending on the simulation. The emitting boundary itself encompasses a 0.2 $R_M$ radius spherical cap, representing the size of the simulated basin around ~200 s after impact (21). Once the 250 s have passed, the emission stops and the boundary conditions for the basin spherical cap reverts to the original flow conditions previously stated.

Supplementary Materials

The PDF file includes:

Supplementary Text

Figs. S1 to S13

Table S1

Legends for movies S1 and S2

References

Other Supplementary Material for this manuscript includes the following:

Movies S1 and S2