The History of the Core Dynamos of Mars and the Moon Inferred … · 2019. 8. 23. · Draft 2 24...

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The History of the Core Dynamos of Mars and the Moon Inferred From Their Crustal Magnetization: A Brief Review

Journal: Canadian Journal of Earth Sciences

Manuscript ID cjes-2018-0068.R1

Manuscript Type: Article

Date Submitted by the Author: 06-Jun-2018

Complete List of Authors: Arkani-Hamed, Jafar; University of Toronto, Physics

Keyword:true polar wander of Mars and Moon, dynamo reversals of Mars and Moon, isolated magnetic anomalies of Mars and Moon, core dynamo of Mars and Moon

Is the invited manuscript for consideration in a Special

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Understanding magnetism and electromagnetism and their implications: A tribute to David W. Strangway

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Canadian Journal of Earth Sciences

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The History of the Core Dynamos of Mars and the Moon Inferred From Their Crustal 3

Magnetization: A Brief Review 4

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Jafar Arkani-Hamed1,2 6

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1Department of Physics, University of Toronto, Toronto, Canada, M5S-1A7, Tel: 905-822-0232, 8

Fax: 416-978-7606, E-Mail: [email protected] 9

2Department of Earth and Planetary Sciences, McGill University, Montreal, Canada, H3A-0E8. 10

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Abstract. 24

The core dynamos of Mars and the Moon have distinctly different histories. Mars had no core 25

dynamo at the end of accretion. It took ~100 Myr for the core to create a strong dynamo that 26

magnetized the martian crust. Giant impacts during 4.2-4.0 Ga crippled the core dynamo 27

intermittently, until a thick stagnant lithosphere developed on the surface and reduced the heat 28

flux at the core-mantle boundary, killing the dynamo at ~3.8 Ga. On the other hand, the Moon 29

had a strong core dynamo at the end of accretion that lasted ~100 Myr and magnetized its 30

primordial crust. Either precession of the core, or thermo-chemical convection in the mantle, or 31

chemical convection in the core created a strong core dynamo that magnetized the sources of the 32

isolated magnetic anomalies in later times. Mars and the Moon indicate dynamo reversals and 33

true polar wander. The polar wander of the Moon is easier to explain compared to that of Mars. 34

It was initiated by the mass deficiency at South Pole Aitken basin which moved the basin 35

southward by ~68o relative to the dipole axis of the core field. The formation of mascon maria at 36

later times introduced positive mass anomalies at the surface, forcing the Moon to make an 37

additional ~52o degree polar wander. Interaction of multiple impact shock waves with the 38

dynamo, the abrupt angular momentum transfer to the mantle by the impactors, and the global 39

overturn of the core after each impact were probably the factors causing the dynamo reversal. 40

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Key Words: 43

True polar wander of Mars and Moon, Dynamo reversals of Mars and Moon 44

Isolated magnetic anomalies of Mars and Moon, Core dynamo of Mars and Moon 45

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1. Introduction: 47

Mars and the Moon are two terrestrial bodies with similar magnetic field characteristics, both 48

have highly magnetized crusts but no core dynamos at present. They had strong core dynamos in 49

the past. The histories of their core dynamos are distinctly different, mainly because of their 50

different accretion processes and different core sizes. Terrestrial planets accrete from the 51

planetary nebula of dust and gas through four distinct stages (Wetherill and Stewart, 1989; 52

Weidenschilling, 1997; Chambers and Wetherill, 1998; Agnor et al., 1999; Kokubo and Ida, 53

1996; Chambers, 2004; Kokubo and Genda, 2010). First, dust particles collide and stick 54

together, forming some centimeter size grains that settle in the mid-plane of the nebula, orbiting 55

the Sun. Second, localized gravitational instabilities collapse the cloud of the centimeter size 56

grains and create planetesimals with a few kilometer radii. Third, through their mutual 57

gravitational attraction, planetesimals collide and merge to produce planetary embryos that can 58

grow to the Moon- to Mars-sized bodies. Dynamic friction caused by the planetesimals and 59

remaining nebula dust and gas maintains the growing embryos in almost circular orbits about the 60

Sun. By the end of this stage majority of planetesimals and small grains are used up in making 61

the embryos, and almost the entire nebula gas is dissipated. Fourth, the mutual gravitational 62

attraction of the well-grown embryos in the absence of appreciable dynamic friction increases 63

their orbital eccentricities, leading to orbit crossings and high-velocity collisions in the process of 64

forming a large planet like Earth. Based on its small mass and rapid formation timescale 65

obtained from 182Hf–182W chronometry, Kobayashi and Dauphas (2013) proposed that Mars 66

likely formed in a massive disk from planetesimals smaller than 10 km in radius. The 67

Thorium/Tungsten and Thorium/Hafnium ratios in the martian mantle, confirm that the growth 68

time of Mars was on the order of 2 Myr (Dauphas and Pourmand, 2011), well within the upper 69

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limit of 10 Myr suggested by Hansen (2009). It is not clear whether Mars is a runaway grown 70

embryo without experiencing the embryo–embryo scale high velocity collisions, or it has 71

actually experienced a few such collisions in its last stage of accretion. On the other hand, the 72

Moon is formed through the impact of a high-velocity Mars size body with the Earth (e.g., 73

Canup, 2012; Canup, and Asphaug, 2001; Canup, et al., 2013), or by collision of two half-Earth 74

size bodies (Nakajima and Stevenson, 2014, 2015). 75

The most important factor that probably resulted in two different histories of the martian and 76

lunar core dynamos is the size of the two bodies, with radii of ~1700 km and 390 km, 77

respectively. The core volume of the Moon is only 1% of the Moon’s volume and that of Mars is 78

about 12% of martian volume. The lunar core is small enough to lose the initially excited 79

thermally driven core dynamo within ~100 Myr after its accretion (Arkani-Hamed and Boutin, 80

2017). Because no thermally driven core dynamo could last longer, the magnetic source bodies 81

in the lunar crust that formed at later times must have been magnetized by a mechanically driven 82

core dynamo (Dwyer et al., 2011, Le Bars et al., 2011), or a vigorous thermo-chemical mantle 83

convection (Stegman et al., 2003), or chemical convection due to possible core solidification 84

(Laneuville, et al. 2014). On the other hand, the superheated large martian core at the end of 85

accretion could generate an appreciable core dynamo once it recovered from the crippling effect 86

of the formation of northern Lowland. 87

When a core dynamo initiated and when it ceased, was there only a single initiation and 88

cessation episode or there were multiple episodes, what was the mechanism powering the core 89

dynamo, and what was the cause of the dynamo cessation? These are the main outstanding 90

issues we investigate on the basis of the major characteristics of the magnetic anomalies of Mars 91

and the Moon. Section 2 is concerned with the core dynamo of Mars, while that of the Moon is 92

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addressed in Section 3. Section 4 presents major conclusions of this investigation. Appendix A 93

is devoted to the analysis of a small and isolated magnetic anomaly, which is the common 94

feature of Mars and the Moon used in this study. Because of the small core sizes of both Mars 95

and the Moon compared to their surface radii, it is assumed in this study that the crustal 96

magnetization is due to the dipolar component of the core field. The higher degree components 97

of the core field decrease much faster than the dipole component as they propagate from the 98

core-mantle boundary to the surface. 99

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2. Magnetic Anomalies of Mars: 101

Acuna et al. (1999) derived, for the first time, a global magnetic anomaly map of Mars using 102

Mars Global Surveyor (MGS) magnetic data acquired at 85–200 km altitudes. Several magnetic 103

anomaly maps of Mars were published within 5 years after the first publication (e.g., Acuna et 104

al., 2001; Purucker et al., 2000; Connerney et al., 2001; Arkani-Hamed, 2002a; Cain et al., 2003; 105

Langlais et al., 2004). A highly coherent model of martian magnetic field was derived using the 106

night time mapping-phase MGS magnetic data measured at 360-420 km altitudes (Arkani-107

Hamed, 2004a). The entire data were divided into two almost equal sets, and each set was 108

expressed in terms of the spherical harmonics of degree up to 90. The power spectra of these two 109

models were almost identical over harmonics of degree up to 62. Figure 1 shows the radial 110

component of the martian magnetic field at 370 km altitude, derived using the co-varying 111

harmonics of degrees up to 62 of the two models, which have degree correlation coefficients 112

higher than 0.85 over the entire harmonics retained, and higher than 0.95 over the harmonics of 113

degrees lower than 50. By removing the higher degree harmonics and presenting the magnetic 114

field at a constant altitude, the spherical harmonic model significantly reduces the low-115

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correlating non-crustal noise and removes the effects of the spacecraft altitude variations. In the 116

absence of a core field at present, the anomalies are of crustal origin. The magnetic anomalies of 117

Mars’ crust are about an order of magnitude stronger than those of Earth’s crust at comparable 118

altitudes. This emphasizes that the magnetic source bodies of Mars’ crust are highly magnetic 119

compared to the terrestrial ones. This is because the estimates of the paleointensity of Mars’ core 120

field based on the ~4.1 Ga meteorite ALH 84001 (e.g., Weiss et al., 2008) and magnetostrophic 121

balance calculations (Arkani-Hamed, et al., 2008) are comparable to, if not weaker than, Earth’s 122

magnetic field. 123

Figure 1 is dominated by strong and closely spaced complex magnetic anomalies over terrae 124

Cimmeria and Sirenum, likely arising from large and closely located magnetic bodies. The 125

proximity of these strong anomalies precludes the determination of the paleomagnetic pole 126

position of Mars on the basis of these anomalies. However, there are 10 small and well-isolated 127

anomalies that can be successfully modeled by simple prisms of uniform magnetization (Arkani-128

Hamed, 2001). Using isolated magnetic anomalies has an advantage that a given magnetic 129

anomaly is simple enough to provide a reliable direction of the magnetizing field, hence the 130

paleomagnetic pole position. The resulting paleomagnetic poles are clustered, 7 of the poles are 131

clustered within a circle of 30o radius centered at about 50oE and 25oS (Arkani-Hamed, 2002b). 132

The cluster partly overlaps the paleomagnetic pole locations suggested by Sprenke and Baker 133

(2000). Also, the paleomagnetic poles obtained by modeling two isolated anomalies (Hood and 134

Zakharian, 2001; Hood and Richmond, 2002) fall inside the 30o radius circle. The lack of core 135

dynamo at present and the clustering of the paleomagnetic poles, while their magnetic source 136

bodies are widely distributed over the globe, indicate that the martian crust has been magnetized 137

by a long lasting global magnetic field in the past, likely produced by a core dynamo. 138

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2.1 History of Martian Core Dynamo: 142

The thermal evolution models of a growing proto-Mars (e.g., Senshu et al., 2002) show that 143

partial melting occurred in the upper parts of the mantle when the radius of the proto-Mars 144

exceeded ~80% of the present radius of Mars. The geochemical analyses of martian meteorites 145

imply a magma ocean of 700–800 km deep in the upper parts of the mantle by the end of 146

accretion (Righter et al., 1998). Once the temperature exceeds the solidus temperatures of 147

silicates, iron melts completely due to its lower melting temperature compared to those of the 148

silicates. The high-density iron blobs descend through the underlying mantle, initiating the core 149

formation. The gravitational energy released by the descending iron blobs results in a 150

superheated molten core with temperatures over 700K above the temperature at the base of the 151

lower mantle (e.g., Spohn et al., 2001). The descent time of an iron blob strongly depends on the 152

size of the blob and the viscosity of the mantle (Samuel and Tackley, 2008), it is usually shorter 153

than 1 Myr (Monteux and Arkani-Hamed, 2013). Concurrent with the core formation, the 154

differentiation of magma ocean in the upper mantle produces a primordial crust which floats on 155

the surface and cools rapidly. The cooling of the superheated core to the mantle in the early 156

stages after the accretion is expected to power a thermally driven core dynamo that is capable of 157

magnetizing the newly forming primordial crust as the crust cools below the magnetic blocking 158

temperatures of its minerals (e.g., Spohn et al., 2001; Arkani-Hamed, 2005). However, no core 159

dynamo probably existed in the early history of Mars. 160

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Figure 1 shows some major geologic structures such as the northern Lowland, the Tharsis bulge, 161

and the Tharsis volcanic mountains that have almost no magnetic signatures, which provide 162

constraints on the active period of the core dynamo. The lack of strong magnetic anomalies 163

inside the Lowland, and the similarity of the magnetic dichotomy to the topographic dichotomy 164

surrounding the Lowland imply that the Lowland formation process has likely demagnetized the 165

underlying crust, and no appreciable magnetic field existed to re-magnetize the newly formed 166

volcanic crust inside the Lowland. The Lowland is probably created in the later stages of 167

accretion of Mars by either a giant impact (Wilhelms and Squyres, 1984; Cameron, A.G.W., 168

1997), or several large but not giant impacts (Frey et al., 2002), or a giant hemispheric mantle 169

plume beneath the Lowland (Roberts and Zhong, 2006; Citron et al. 2018), or a giant impact 170

probably occurred at the antipodal location of the Lowland (Reese et. al., 2010). The single 171

giant impact at the Lowland site has been supported by many investigators (Andrews-Hanna et 172

al., 2008; Marinova et al., 2008; Nimmo et al., 2008; Arkani-Hamed, 2010) and it is adopted in 173

this study. Accordingly, the shock wave generated by the giant impact propagates in the mantle 174

and the core, resulting in differential heating with strong heating directly beneath the impact site. 175

The fast spinning and differentially heated low viscosity core stably stratifies, resulting in 176

spherically symmetric temperature that increases with radius and prevents the thermal 177

convection in the core and the initiation of a thermally driven core dynamo (Arkani-Hamed and 178

Olson, 2010). The stagnant lid thermal evolution models of Mars (Arkani-Hamed, 2010, 2012) 179

suggest that it takes about 50–120 Myr for the core to overcome the crippling effects of the giant 180

impact and establish a vigorous convection, powering a dynamo. During this long period, the 181

newly created volcanic crust inside the Lowland cools below the magnetic blocking temperature 182

range of its minerals, and cannot acquire thermoremanent magnetization in the absence of a core 183

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field (Arkani-Hamed and Boutin, 2012a). The lack of a magnetic anomaly associated with 184

Utopia basin, a ~3400 km diameter basin centered at 45oN and 115oE inside the Lowland, 185

supports this scenario. This is because a large impact that created the basin at about 350 Myr 186

after the formation of the Lowland could demagnetize the entire volcanic crust beneath the 187

impact site if the crust had been magnetized prior to the impact. The sharp change of the crustal 188

magnetization across the basin boundary is expected to create an appreciable magnetic anomaly, 189

called the magnetic edge effect, at satellite altitudes of about 400 km. Such a magnetic anomaly 190

is not observed (see Figure 1). 191

There are other evidence indicating the non-magnetic primordial crust. Figure 2 shows no 192

appreciable magnetic anomalies over a vast area south of 30oS and in the longitude range from 193

west of Hellas basin to Argyre basin, referred to as the South Province (Arkani-Hamed and 194

Boutin, 2012a), which is comparable in area to Tharsis bulge. The figure also shows no magnetic 195

anomalies over Tempe Terra in the northernmost part of highlands on Mars, extending from 196

30oN to 55oN and from 270oE to 300oE. Both areas have high densities of impact craters and 197

impact-related Quasi Circular Depressions (QCD, Frey et al., 2002) indicating that the 198

underlying crust is very ancient, likely primordial. Using MOLA topography data together with 199

the JPL gravity model (jgmro-110B2), Arkani-Hamed and Boutin (2012a and 2012b) determined 200

the crustal structure underlying impact craters and impact-related QCDs larger than 200 km in 201

diameter in both premordial areas and concluded that the impacts that have created these features 202

were capable of significantly disturbing and demagnetizing the entire underlying crust. The 203

craters and QCDs are expected to have well-defined magnetic edge effects if the surrounding 204

crust is magnetic. The lack of distinct magnetic anomalies associated with these features 205

indicates that the surrounding primordial crust is not magnetic. 206

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Investigations of the heating of Mars by giant impactors capable of producing craters larger than 207

500 km in diameter (e.g., Roberts et al., 2009; Arkani-Hamed, 2010, 2012, Roberts and Arkani-208

Hamed, 2012, 2014, 2017; Kuang et al., 2014) have concluded that the impactors could have 209

crippled the core dynamo, but only for a short period. The stagnant lid thermal evolution model 210

of martian mantle after the Borealis impact that created the martian Lowland (Arkani-Hamed, 211

2010) suggests that the impact-induced stratified core cools to the mantle while creating a thin 212

convecting shell at the top, which increases in thickness in due time. The shell becomes thick 213

enough capable of generating a core dynamo after about 50-120 Myr. The strong magnetic 214

anomalies over Cimmeria and Sinerum terrae indicate that the core dynamo remained active to 215

magnetize the underlying crust once it overcame the crippling effects of Borealis impactor. 216

When the core dynamo actually ceased is a matter of debate. Rock magnetic measurements of 217

the oldest martian meteorite ALH84001 (e.g., Collinson, 1997; Kirschvink et al., 1997; Weiss et 218

al., 2002; Antretter et al., 2003) indicate that it was magnetized on the martian surface during 219

Noachian period, between 4.1 and 3.8 Ga (Carr and Head, 2010). The lack of magnetic 220

anomalies inside giant impact basins Hellas, Argyre and Isidis suggests that the impacts have 221

demagnetized the crust, and there has been no active core dynamo to re-magnetize it (Acuna et 222

al., 1999; Mohit and Arkani-Hamed, 2004; Hood et al., 2003). The shock wave generated by a 223

giant impact propagates in the crust and demagnetizes the crust within less than 1 hour, but it 224

may take several million years for the demagnetized crust to acquire magnetization in the 225

presence of a dynamo field. This is largely because the remagnetization is controlled by the 226

cooling of the crust below the magnetic blocking temperatures of its minerals by thermal 227

conduction, which is a very slow process. Lillis et al. (2008, 2013) investigated the magnetic 228

field over 20 impact basins formed between 4.22 and 3.81 Ga (Frey, 2008) and concluded that 229

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the core field decayed rapidly within less than 100 Myr at around 4.1 Ga. The impact heating of 230

the martian core by the 8 largest of the 20 impacts, chronologically Daedalia, Ares, Amazonis, 231

Chryse, Scopolus, Acidalia, Utopia, and Hellas shows that each of the impacts is capable of 232

crippling the core dynamo for a limited time (Arkani-Hamed, 2012). The thermal evolution 233

models of Mars, based on coupling a spherically symmetric 1D core model with a 3D mantle 234

convection model while using a temperature- and pressure-dependent mantle viscosity, show that 235

the collective battering the core dynamo by the impacts and the gradual thickening of the 236

stagnant lid at the surface eventually killed the dynamo (Roberts and Arkani-Hamed, 2017). 237

Figure 3 shows the crippling effects of each impact on the core, the larger the impact the stronger 238

is the crippling. The core dynamo was strong until Ares impact (we name the impacts after the 239

giant basins). Being the second largest impact, Ares introduced substantial perturbations to the 240

core temperature and together with the following Amazonis impact constrained the core 241

convection to the upper about 200 km for about 30 Myr. During this long period, the downward 242

heat conduction from the high temperature stratified region near the core-mantle boundary and 243

the upward heat conduction from the deeper parts of the core along the adiabatic gradient 244

reduced the super-adiabatic deeper parts of the core to sub-adiabatic. The strong dynamo that 245

existed deep in the core prior to Ares impact might have retained its strength while it was 246

gradually decreasing from super-critical to sub-critical until Acidalia impact, the third largest 247

impact, which likely killed the subcritical dynamo. The core convection has never become 248

vigorous enough to regenerate a strong dynamo capable of magnetizing the crust since ~3.8 Ga. 249

Figure 1 shows no appreciable magnetic anomalies associated with Syria planum, implying no 250

core dynamo was active during the long-lived volcanism that lasted from late Noachian to early 251

Amazonian, 3.8 to 3.0 Ga (Carr and Head, 2010). The entire volcanic layer could have acquired 252

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appreciable magnetization if the core dynamo were active. Likewise, no significant magnetic 253

anomalies are associated with Tharsis bulge, formed through major volcanic activities in 254

Noachian to early Hesperian, 4.1 to 3.7 Ga (Carr and Head, 2010), although minor volcanism 255

likely continued to the recent past (Hartmann and Neukum, 2001). Many places of Tharsis 256

buldge have been affected by tectonic activities, such as Valles Marineris and shield volcanoes, 257

which could have created detectable magnetic anomalies if the Tharsis plains were appreciably 258

magnetized. The Valles has a mean depth of ~5 km, a width of 100–400 km, and a length of 259

~3500 km. If the Tharsis plains were magnetized prior to the formation of the canyon, an 260

appreciable magnetic edge effect is expected at satellite altitudes. Moreover, the large shield 261

volcanoes, Olympus, Arsia, Pavonis, and Ascreaus have poured out a huge amount of volcanic 262

lava during their formation from early Hesperian to late Amazonian 3.7 to 1.5 Ga (Carr and 263

Head, 2010). The magnetization of the thick lava by an existing core field can easily be detected 264

at the satellite altitude of ~400 km even if the magnetizing core field was an order of magnitude 265

weaker than the present Earth’s core field (Hood and Hartdegen, 1997). The lack of magnetic 266

signatures associated with the shield volcanos indicate that no core dynamo was active during the 267

formation of the volcanoes. The pre-existing Tharsis plains that are overlain by the shield 268

volcanoes are not appreciably magnetized either. If they were, the formation of the volcanoes 269

could have thermally demagnetized the underlying plains and created low-magnetic patches 270

giving rise to detectable magnetic anomalies. The lack of appreciable magnetic anomalies over 271

Tharsis bulge is related to the absence of a strong core dynamo when the major parts of the bulge 272

were forming (Arkani-Hamed, 2004b; Johnson and Phillips, 2004). 273

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2.2 Driving Mechanism of Martian Core Dynamo: 275

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Planetary scientists have not yet reached consensus about the driving mechanism of the martian 276

core dynamo that operated probably between 4.4 and 3.8 Ga. The same is also true about the 277

processes that killed the dynamo. One possible scenario is that the core dynamo was maintained 278

by a vigorous thermal convection in a superheated liquid core (e.g., Stevenson et al., 1983; 279

Nimmo and Stevenson, 2000; Stevenson, 2001; Breuer and Spohn, 2003). Accordingly, once a 280

stagnant lithosphere developed on the convecting mantle, and Mars became a one-plate planet, it 281

hampered heat loss from the mantle and subsequently from the core. The core dynamo ceased 282

because of the reduction of heat flux from the core that decreased the vigor of core convection. 283

The formation of Mars through accreting small planetesimals and the core formation in the later 284

stages of accretion result in a superheated core that supports this driving mechanism (Spohn et 285

al., 2001). This scenario is viable ~50-120 Myr after the accretion of Mars, bearing in mind the 286

crippling effect of the Borealis impact that occurred almost at the end of accretion. Another 287

scenario relates the generation of the core dynamo to chemical convection due to solidification of 288

an inner core that could release light elements causing core convection (Schubert et al., 2000), 289

and argues that the core dynamo actually started later than 4 Ga when the martian core cooled 290

enough to start solidifying the inner core. However, the oldest martian meteorite (ALH84001) 291

was probably magnetized on the martian surface before 4 Ga, as mentioned above. Moreover, 292

the upper part of the core is probably liquid at present (Yoder et al., 2003). It is likely that the 293

lower mantle of Mars was heated up by the radioactive elements in the early history causing 294

decrease in the core cooling rate, hence hampering the core solidification (Spohn, et al., 2001; 295

Arkani-Hamed, 2005). 296

Mechanical excitation of the planetary core dynamos has been proposed in the last two decades 297

(e.g., Lacaze et al., 2006; Tilgner, 2005, 2007; Wu and Roberts, 2009, 2012; Lin et al., 2015; 298

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Reddy, et al., 2018). The proximity in time of the impacts that created the giant basins on Mars 299

and the cessation of the martian core dynamo (Lillis et al., 2008, 2013) suggests a causative 300

relationship between them (Kuang et al., 2014; Roberts and Arkani-Hamed, 2017). On the basis 301

of experimental, numerical and theoretical studies (e.g., Moffatt, 1970; Olson, 1981; Singer and 302

Olson, 1984; Kerswell, 1994; Tilgner, 2005; Lacaze et al., 2004, 2005, 2006), Arkani-Hamed et 303

al. (2008) proposed that tidally induced elliptical instability in the martian core by a large 304

retrograde satellite could have excited the core dynamo of Mars for hundreds of millions of 305

years. 306

Figure 4 shows an example for the orbital evolution of an asteroid assumed to be captured by 307

Mars as a retrograde satellite. It is determined using the two-body orbital dynamic equation 308

(Bertotti and Farinella, 1990), 309

dR/dt = -3κ sin(2δ)(m/M)(a5/R

11/2)[G(M +m)]1/2, 310

where κ (= 1.53) is the Love number of Mars (Yoder et al., 2003), a (= 3390 km) is the radius of 311

Mars, R is the orbital radius of the satellite, G is the gravitational constant, and M and m are the 312

masses of Mars (6.39x1023 kg) and asteroid (1.95x1020 kg), respectively. δ is the phase angle of 313

the maximum tidal deformation of Mars relative to the Mars–satellite line, produced because of 314

the time delay between the maximum tidal force exerted on Mars and the maximum deformation 315

of Mars due to its an-elastic response. Based on the scaling relationship between the mass and 316

velocity of an impactor and the resulting size of a crater [Holsapple and Schmidt, 1982; Schmidt 317

and Housen, 1987] the satellite could be capable of creating a Utopia size basin upon impacting 318

on Mars. Included in Figure 4 is the rate of tidal energy dissipation in Mars determined by 319

dE/dt = d/dt [(Im Ω2 – GMm/r)/2] (5) 320

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where Im and Ω are the moment of inertia and the angular velocity of Mars, respectively. The 321

rate of tidal energy dissipation is over two orders of magnitude greater than the rate of Ohmic 322

dissipation, ~108 W, expected in the martian core [Arkani-Hamed et al., 2008]. 323

Arkani-Hamed (2009) identified 4 subsets of basins from the 20 giant impact basins reported by 324

Frey (2008) that trace great circles on Mars. The probability that out of 20 randomly distributed 325

points on a sphere a given subset traces a great circle within +/- 3 degrees latitude was calculated 326

to be less than 6%. The author suggested that a given great circle was not due to a random 327

chance, rather it was the prevailing equator of Mars when the parent asteroid of a corresponding 328

subset of impactors was orbiting Mars as a satellite. The tidal energy dissipated in Mars due to 329

any of the 4 parent asteroids, ranging in mass from 1021 to 3x1021 kg, would be well over 2 330

orders of magnitude larger than the energy needed to maintain a strong core dynamo. Even if 331

only one of the satellites were retrograde, it could have lasted for over 800 million years (see 332

Figure 4). The tidal forces exerted on Mars could have created an ellipsoidal core-mantle 333

boundary that could have enhanced the mechanical energy transfer from the mantle to the core 334

(e.g., Wu and Roberts, 2009). If only 1% of the tidal energy was partitioned to the core, it was 335

sufficient to power a strong core dynamo. The spin-orbit coupling of Mars and the parent 336

retrograde satellite gradually reduced the orbital radius of the parent body. Shortly after the 337

parent body entered the Roche limit of Mars and disintegrated, the fragments likely followed the 338

same great circle and impacted on Mars producing the corresponding impact basins. Based on 339

the ages and age limits of the basins provided by Frey (2008), the basins of a given subset were 340

probably formed in a short period. Upon fragmentation the tidal force of the parent body, that 341

was deforming the streamlines in the martian core and exciting the elliptical instability, 342

diminished and the dynamo ceased. 343

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The tidally driven scenario of the martian core dynamo seems viable, but requires a detailed 344

dynamic verification. The capture of a large asteroid as a retrograde satellite can be complicated 345

largely due to the small mass of Mars. Agnor and Hamilton (2006) investigated the capture of 346

Triton by Neptune. The authors suggested that Triton was one of a two-body system, like Pluto 347

and Sharon, that approached Neptune. The larger of the two bodies was captured by Neptune but 348

the smaller one escaped. The capture process is not considered in the present study. Our starting 349

point in the above example is after the capture when the asteroid becomes a retrograde satellite. 350

A large asteroid can also be captured by Mars as a prograde satellite. If it is captured at a 351

distance farther that the co-orbiting radius ~20600 km, where the orbital period of the satellite 352

equals to the rotational period of Mars, the satellite recedes from Mars. On the other hand, if it is 353

captured at a distance shorter than the co-orbiting radius, it spirals down and impacts Mars. An 354

above-mentioned Utopia type asteroid captured as a prograde satellite at a distance slightly 355

shorter than the co-orbiting radius impacts Mars within about 70,000 years (See Figure 4 of 356

Arkani-Hamed, 2009). Although the tidal deformation of Mars would be appreciable and the 357

elliptical instability of the core would be strong, the entire period is too short to relate the long 358

lasting core dynamo of Mars to the tidal excitation by a prograde satellite. However, a 359

retrograde satellite captured at distances much longer than the co-orbiting radius remains orbiting 360

Mars for a long period as seen in Figure 4. 361

362

3. Magnetic Anomalies of the Moon: 363

The rock magnetic measurements of lunar rock samples during the Apollo era (e.g., Nagata et al., 364

1970; Runcorn et al., 1970; Strangway et al., 1970) and the surface magnetometer surveys by 365

Apollo 12 and Apollo 14 (Dyal et al., 1970, 1971) revealed for the first time that the lunar rocks 366

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are appreciably magnetized. The Apollo 15 and 16 sub satellites measurements in the equatorial 367

region and at about 100 km altitudes showed that the lunar crust is coherently magnetized over 368

tens to hundreds of km (Coleman et al., 1972; Dyal et al., 1974; Hood et al., 1981). The global 369

measurements of the magnetic field of the Moon by the Lunar Prospector’s magnetometer and 370

electron reflectometer (Lin et al., 1998; Purucker, 2008), and by Selene (Kaguya) mission 371

(Tsunakawa et al., 2010, 2014, 2015) established that the lunar crust is appreciably magnetized 372

on a global scale, emphasizing that the magnetizing field was likely generated by a core dynamo. 373

Figure 5 shows three versions of the radial component of the lunar magnetic field: the 150 degree 374

spherical harmonic model at 30 km altitude of the Lunar Prospector data (Purucker, 2008), the 375

Kaguya model at 100 km altitude (Tsunakawa, H. et al., 2010), and the Lunar Prospector Level-2 376

(LP-2) data at variable spacecraft altitudes ranging from 10 km to 100 km. The strong 377

correlation among the models emphasizes the validity of the anomalies. 378

379

3.1 History of the Lunar Core Dynamo: 380

The nature of the magnetizing field was debated during the Apollo era. Nine different 381

mechanisms were proposed: 1. A magnetic field associated with the solar wind, 2. The terrestrial 382

magnetic field when the Moon was very close to Earth, 3. An ancient magnetized solid core, 4. 383

Lunar core dynamo generated in a liquid core, 5. Small pockets of Fe-FeS eutectic close to the 384

surface that generated magnetic dynamo, 6. A local unipolar dynamo where current is induced in 385

a highly conducting lava basin by the electric field near the surface, 7. A thermoelectric dynamo 386

generated in the cooling lunar crust, 8. Electric current systems in ionized volcanic ash flows, 387

and 9. Crustal piezo-remanent magnetization induced by impact related shock waves propagating 388

in the iron grains of the crust. Daily and Dyal (1979) examined the viability of these 9 389

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mechanisms in a review article and only three were selected plausible: the impact-related shock 390

magnetization, the magnetization by an early solar wind field, and the magnetization by a liquid 391

core dynamo. On the basis of limited rock magnetic measurements during the Apollo missions, 392

Strangway et al. (1971) and Runcorn et al. (1971) suggested that the magnetizing field was 393

global in nature and was created by the core dynamo that was powered by thermal convection in 394

a liquid iron core of the Moon. The lunar rock samples were from loose rocks on the surface, 395

hence the directions of the core field at the Apollo landing sites were not constrained. 396

The paleomagnetic investigations have revealed a long lasting core dynamo with magnetic field 397

intensity of about 10-100 µT on the lunar surface at around 4.2-3.5 Ga (e.g., Cisowski et al., 398

1983; Fuller and Cisowski, 1987; Garrick-Bethell et al., 2009; Cournède et al., 2012; Shea et al., 399

2012; Suaveta et al., 2013; Weiss and Tikoo, 2014). Analysis of the crustal magnetic anomalies 400

of the Moon has also led to the conclusion that the lunar dynamo existed for a long period. The 401

electron reflectometer data over some Nectarian age basins (Crisium, Mendel–Rydberg, Bailly, 402

Humboldtianum and Moscoviense) show magnetic anomalies near their centers (e.g., Halekas et 403

al., 2003). The anomalies are related to the thermoremanent magnetization of the impact melt 404

rocks acquired during the Nectarian period, between the formation of Nectaris basin and 405

Imbrium basin, 3.92–3.85 Ga (Stoffler and Ryder, 2001). Moreover, majority of early Nectarian 406

basins have central magnetic anomalies with high intensities, implying a strong core field in the 407

early Nectarian period. Hood (2011) derived magnetic anomalies over Moscoviense, Mendel–408

Rydberg, Humboldtianum, and Crisium basins, using the low-altitude Lunar Prospector 409

magnetometer data and suggested thermoremanent magnetization of impact melt rocks in a long 410

lasting magnetizing field, hence supporting the existence of a core dynamo at the formation 411

times of the basins. The two magnetic anomalies located inside the South Pole-Aitken basin 412

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(SPAB) at the antipodal regions of young impact basins Imbrium and Serenitatis, are related to 413

the shock remanent magnetization created by converging impact induced ionized plasma and 414

shock waves (e.g., Hood and Artemieva, 2008). The antipodal magnetic anomalies can be used 415

to argue for the existence of a core dynamo with appreciable intensity at the impact time, 416

because the magnetic field of the solar wind alone may not be strong enough to magnetize a 417

thick crustal layer capable of creating a magnetic anomaly detectable at the satellite altitudes. 418

It is worth mentioning that there is no appreciable magnetic anomaly over the antipodal zone of 419

South Pole-Aitken basin. With a diameter of about 2500 km, it is the largest impact basin on the 420

Moon formed at about 200 Myr prior to the formation of Imbrium and Serenitatis basins (Merle 421

et al., 2014). Although the shock heating of the lunar core was strong enough to cripple a likely 422

pre-existing core dynamo, the magnetic field of the core could not vanish abruptly. In the 423

absence of the dynamo, the core field freely decays within about (Rc/π)2 / µ = 500 years, where 424

Rc is the lunar core radius (~390 km) and µ is the magnetic diffusivity of the core, (~ 1 m2/s, 425

Arkani-Hamed and Olson, 2010). The core field actually did not decay appreciably in a very 426

short time of a few hours during the convergence of the impact-induced ionized plasma at the 427

antipodal zone (e.g., Hood and Artemieva, 2008), hence it could have been strong to magnetize 428

the crust by the shock magnetization. The lack of magnetic anomalies in the antipodal region of 429

the SPAB may imply the lack of core dynamo at the impact time that created the SPAB, or a less 430

important contribution of the shock magnetization to the total magnetization of the crust. More 431

probably, however, the antipodal zone of SPAB coincides with Procellarum Terrane, which is 432

underlain by a thick KREEP (Potassium, Rare-Earth Elements, and Phosphorus) layer that kept 433

the temperature of the upper mantle and the lower parts of the crust well above the magnetic 434

blocking temperatures for a long time (Laneuville et al., 2013). Moreover, the upper parts of the 435

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crust possibly bearing shock remanent magnetization was probably thermally demagnetized by 436

the extensive volcanism that covered almost all of the Terrane. 437

Arkani-Hamed and Boutin (2014) studied the demagnetization of the ancient lunar highland crust 438

by impacts that have created craters with diameters larger than 100 km, to investigate the 439

probability that a strong core dynamo existed when the newly forming lunar crust was cooling 440

below the magnetic blocking temperatures of its minerals in the early history. The impacts that 441

are capable of creating the craters are also capable of significantly disturbing the crust directly 442

beneath and demagnetizing the entire crust of ~60 km thickness (e.g., Reindler and Arkani-443

Hamed, 2001; Arkani-Hamed and Boutin, 2012a). Such a pervasive demagnetization can 444

produce a distinct magnetic anomaly, the edge effect, at satellite altitudes if the surrounding 445

primordial crust is magnetic. Using the vertical component of the LP-2 data, the least 446

contaminated data set, the authors modeled the magnetic anomalies associated with 20 craters 447

with distinct edge effects, all located on the ancient crust of the lunar far side (see Appendix A). 448

The resulting paleomagnetic pole positions are clustered while craters are widely distributed, 449

implying a stable magnetizing field of a core dynamo in the very early history of the Moon. 450

Also investigated by Arkani-Hamed and Boutin (2014) were the isolated magnetic anomalies on 451

the highlands with no obvious topographic signatures, indicating that the magnetic source bodies 452

are deep seated. The authors modeled 10 isolated magnetic anomalies having sufficient data to 453

obtain reliable magnetic maps. Note that the formation times of the source bodies of the isolated 454

anomalies are not well constrained, hence the models can only show the basic characteristics of 455

the source bodies, but cannot provide reliable information about the time they were magnetized. 456

There is evidence for possible dynamo reversals and true polar wander in the early history of the 457

Moon. Allowing for dynamo reversals, the paleomagnetic poles obtained from the magnetic 458

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signatures associated with the craters trace a consistent path suggestive of a true polar wander of 459

the Moon and a stable core dynamo. However, the polar wander is less evident from the 460

magnetic poles determined using isolated magnetic anomalies. The poles cluster in three 461

locations, implying that the core dynamo was less stable during the magnetization of the source 462

bodies. 463

The complex group of strong magnetic anomalies concentrated on the northern rim of SPAB are 464

interpreted by the magnetization of highly magnetic ejecta from an iron-rich impactor that 465

created the basin (Wieczorek et al., 2012). According to this hypothesis, the magnetic source 466

bodies were created within a very short time after the impact. However, detailed modeling of the 467

magnetic anomalies (Arkani-Hamed and Boutin, 2017) concluded that the magnetic source 468

bodies are large intrusive, created during a very long period. It takes a long time for an intrusive 469

source body to cool below its magnetic blocking temperatures and acquire magnetization (e.g., 470

Arkani-Hamed and Celetti, 1989; Purucker et al., 2012). The associated magnetic anomaly 471

arises from the lateral variations of the vertically integrated magnetization of the source body. 472

Figure 6a shows the vertical component of the magnetic field over SPAB derived using the radial 473

component of the LP-2 data. The magnetic anomalies, identified by circles that contain major 474

part of the anomalies, show two distinctly different polarities. In the absence of radioactive age 475

data the anomalies are numbered chronologically based on the polar wander path of the Moon 476

traced by the paleomagnetic poles (see below). Anomalies 1 to 5 have positive lobes in the north 477

of their negative lobes, whereas anomalies 7 to 14 have negative lobes in the north of their 478

positive lobes. The well-isolated strong but small anomaly near the center of Leibnitz crater 479

(anomaly 3) belongs to the first set of anomalies and anomaly 9 that is located close but outside 480

of the basin has the same polarity of the second category. Judging from the impact 481

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demagnetization of martian crust by a large impacting body that created Hellas basin on Mars 482

(Mohit and Arkani-Hamed, 2004; Lillis et al., 2010), which is comparable in size to SPAB, the 483

impact that has created SPAB has most likely demagnetized the entire crust within a radius of 484

~1.4 times the basin radius. Halekas et al. (2003) investigated the magnetic field over 34 multi-485

ring impact basins of the Moon using the LP electron reflectometer data, and concluded that all 486

of the impacts have significantly reduced the magnetization of the crust to distances of about 487

1.5–2 basins’ radii. Hence, anomaly 9 is likely created after the formation of the SPAB. We 488

note the overlap of two anomalies with distinctly different polarities. The small anomaly 14 is 489

embedded in the large anomaly 5, implying that the source body of the small anomaly is formed 490

well after the magnetization of the source body of the large anomaly. Otherwise, the formation 491

of the large body would have obliterated the pre-existing source of the small anomaly. The very 492

existence of the magnetic anomalies inside SPAB, and anomaly 9 outside but within ~1.4 basin 493

radius, indicate that the source bodies were magnetized after the formation of the basin that 494

occurred at around 4.1 Ga. It is, therefore, feasible that the source bodies of the first category 495

anomalies are magnetized after the formation of SPAB, but earlier than the magnetization time 496

of the source bodies of the second category, and that there was a dynamo reversal between these 497

two periods. 498

The two categories of the magnetic anomalies inside SPAB indicate two distinctly different polar 499

wander paths (Figure 6b). In the absence of the large mascon maria such as Smythii, Crisium, 500

Serenitatis, Imbrium, and Orientale, the huge mass deficiency associated with the formation of 501

SPAB was likely the main driving force which moved the basin southward. The north pole of 502

the dipole component of the core field, i.e., the paleomagnetic pole, was moving northward 503

relative to the basin as the source bodies were getting younger. Figure 6b emphasizes that the 504

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magnetic source bodies of the first category magnetic anomalies were forming and being 505

magnetized by the core dynamo as the true polar wander driven by the SPAB was taking place. 506

Therefore, anomaly 1 is the oldest and anomaly 6 is the youngest among the first category 507

anomalies. The source body of the paleomagnetic pole #6 is actually the north Crisium anomaly 508

(Hood, 2011) which is outside the SPAB (Arkani-Hamed and Boutin, 2017), hence is not 509

included in Figure 6a. Based on the well-defined linear polar wander path expected from the 510

true polar wander theory (e.g., Matsuyama, et al, 2006), the paleomagnetic poles trace the true 511

polar wander path of the Moon for about 68o. Moreover, the almost linear trace of 512

paleomagnetic poles and their locations relative to the SPAB indicate that the true polar wander 513

was mainly driven by a single source, the mass deficiency associated with SPAB. 514

Figure 6b shows core dynamo reversal after the formation of the north Crisium anomaly. 515

Athough the reversal may have occurred spontaneously, the interaction of the shock waves 516

produced by the Serenitatis and Imbrium impacts with the core dynamo, the sudden transfer of 517

angular momentum to the mantle by the impactors, and the dynamic overturn of the core through 518

stratification following the impacts probably triggered the dynamo reversal. The shock wave 519

produced by either Imbrium or Serenitatis impacts propagates in the lunar mantle as an almost 520

spherical shock front. The shape of the shock front, however, changes to a drastically complex 521

pattern upon impinging the spherical core-mantle boundary and entering the core (e.g., Ivanov et 522

al., 2010; Arkani-Hamed and Ivanov, 2014). Moreover, the shock front propagating in the core 523

partly reflects and partly refracts at the antipodal core-mantle boundary. The core is shocked 524

twice, first by the direct shockwave propagating away from the impact site and next by the 525

reflected shock wave. It seems quite feasible that the core dynamo gets perturb drastically. The 526

interaction of the double shock waves with the core dynamo remains to be investigated. 527

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The formation of major surface mass concentrations (mascons) with different masses and 528

locations on the front side of the Moon, associated with large impact basins Smythii, Crisium, 529

Serenitatis, Imbrium, and Orientale, initiated a new polar wander at about 200 Myr after the 530

formation of SPAB, and moved the major mascons basins toward the equator. Moreover, a 531

pervasive volcanism due to concentration of KREEP in a thick layer beneath the present 532

Procellarum Terrane (Wieczorek and Phillips, 2000; Laneuville, et al., 2018), which likely 533

moved a huge amount of mass upward in the lunar interior (Laneuville et al., 2013), contributed 534

to the excess mass near the surface and resulted in further polar wander. The magnetic source 535

bodies that were forming inside SPAB after the dynamo reversal were being magnetized when 536

the north pole of the core field had already flipped. Therefore, their north paleomagnetic poles 537

were moving southward as the source bodies were getting younger. Accordingly, the source 538

body of anomaly 7 is the oldest and that of anomaly 14 is the youngest among the source bodies 539

formed after the core dynamo reversal. Due to the different formation times and locations of the 540

mascons, the polar wander path described by the second category magnetic anomalies is 541

somewhat scattered compared to that of the first category anomalies, as seen in Figure 6b. 542

The lunar interior was hot during the first 1 Gyr of its history. The majority of mare flooding 543

occurred between 3.6 and 3.8 Ga (Head, 1976; Geiss et al, 1977; Schultz and Spudis, 1983). 544

Bearing in mind that the time it took for the polar wander strongly depended on the poorly 545

estimated viscosity of the lunar mantle at about 4 Ga, it is not feasible to estimate the total time 546

required for the entire polar wander of about 120o. 547

548

3.2 Driving Mechanism of the Lunar Core Dynamo: 549

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The paleomagnetic poles obtained from the isolated features on the primordial crust of the Moon, 550

whether the isolated intrusive bodies or the impact craters, are clustered while the source bodies 551

are widely distributed, indicating that the source bodies were magnetized by a dipole field with 552

consistent direction which could have been a core dynamo field. 553

The Moon-forming models, either by collision of a Mars size body with the Earth (e.g., Benz et 554

al., 1986; Canup and Asphaug, 2001; Canup, 2004, 2012; Canup et al., 2013) or by the collision 555

of two half-Earth size bodies (Nakajima and Stevenson, 2014, 2015), suggest that a partially 556

molten silicate disk is formed in Earth orbit, and the Moon is formed as a hot body by accretion 557

of the high-temperature disk during 100 to 1000 years (Thompson and Stevenson, 1988). The 558

core formation in the partially molten Moon took place during its accretion and resulted in a 559

superheated core. The Moon cooled from the surface down and a cold stagnant lid formed on the 560

surface with increasing thickness and viscosity as time passed. The thermal evolution models of 561

the Moon calculated on the basis of the stagnant lid thermal convection simulations in the mantle 562

(Arkani-Hamed and Boutin, 2017) show high heat flux from the superheated core to the mantle. 563

The fast cooling of the core was capable of generating a thermally driven core dynamo in the 564

first about 100 Myr, i.e., during the differentiation of the silicate mantle and formation of the 565

lunar primordial crust. There is no evidence that the Moon was impacted by a large planetary 566

embryo in the later stages of its accretion to hamper the initiation of a thermally driven dynamo, 567

which was likely the case for Mars. The primordial lunar crust acquired thermoremanent 568

magnetization as it cooled through its magnetic blocking temperatures in the presence of the core 569

field. The magnetized primordial crust is consistent with the magnetic anomalies associated 570

with the large craters of more than 100 km in diameters resulted from the impact 571

demagnetization of the primordial crust (Arkani-Hamed and Boutin, 2014). 572

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Stegman et al. (2003) suggested that a high-density ilmenite layer probably produced in the 573

upper mantle at the later stages of solidification of the magma ocean sank and covered the core. 574

It subsequently heated up by its highly concentrated radioactive elements and became buoyant, 575

resulting in vigorous mantle convection which enhanced the heat loss from the core and 576

generated a strong thermally driven core dynamo for a few hundred million years. This 577

mechanism took about 400 Myr to generate a strong core dynamo. During this long period the 578

entire primordial crust could cool well below the magnetic blocking temperatures of its minerals 579

in the absence of a strong core field, hence could not acquire thermoremanent magnetization. 580

The cold crust could acquire weak induced magnetization in the presence of a core dynamo in a 581

later time, but the induced magnetization would decay rapidly once the core dynamo diminishes. 582

Dwyer et al. (2011) proposed that the rotation axes of the liquid core and the solid mantle of the 583

Moon did not initially coincide, and the Earth-driven precession resulted in differential motion of 584

the core and mantle of the Moon, which stirred the core and powered a core dynamo. The 585

precession driven dynamo was capable of creating a magnetic field of 1-10µT at the lunar 586

surface at around 4 Ga. The field decreased gradually below 0.01µT at around 2.7 Ga, when the 587

Earth–Moon distance exceeded ~48 times Earth’s radius and the dissipated power in the core 588

was insufficient to drive a dynamo. However, the precession driven dynamo was not probably 589

active in the first ~70 Myr of the lunar history when the Earth-Moon distance was less than ~26 590

times Earth radius, because the core closely followed the mantle (Meyer and Wisdom, 2011). 591

Hence, it cannot account for the magnetization of the lunar primordial crust. 592

Large oblique impacts may transfer a considerable amount of angular moment to the lunar 593

mantle, causing reorientation of its rotation axis relative to that of the liquid core and resulting in 594

differential rotation of the core and mantle that may power a core dynamo (e.g., Melosh, 1975; 595

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Wieczorek, M. A. and Le Feuvre, M., 2009). A precession driven dynamo initiated by a large 596

impactor that is capable of creating a crater ~700 km in diameter, may not last longer than 597

10,000 years (Le Bars et al., 2011). Because of the random locations and random impact angles 598

of the impactors during the very early history of the Moon, the pole positions of the possible 599

impact-driven core fields must have been random. This is in direct contradiction with the well-600

clustered paleomagnetic poles determined from the magnetic anomalies associated with the 601

impact craters, implying that the primordial crust of the Moon was not magnetized by a core 602

dynamo driven by random impacts. 603

The seismic detection of the lunar core revealed a solid inner core of about 240 km radius 604

overlain by a liquid outer core of about 390 km radius (Weber et al., 2011). The existence of an 605

inner core led Laneuville et al. (2014) to propose a chemically driven lunar core dynamo. 606

However, the core was very hot and core solidification may not have started when the primordial 607

crust was forming in the very early history. Hence, a chemically driven core dynamo might not 608

have existed to magnetize the primordial crust of the Moon. 609

The above mention mechanically and chemically driven core dynamo models are not consistent 610

with the magnetization of the primordial lunar crust, emphasizing that the thermally driven core 611

dynamo in the very early history of the Moon, due to the fast cooling of the initially superheated 612

core, was probably the responsible mechanism. However, such a thermally driven core dynamo 613

could not have lasted long enough to magnetize the lunar rock during 3.5-4.2 Ga. On the other 614

hand, the buoyant ilmenite layer model of Stegman et al. (2003), the precession driven dynamo 615

model of Dwyer et al. (2011), and a late activation of the chemically driven dynamo model of 616

Laneuville et al. (2014) could have created a strong core field on the lunar surface at around 3.5–617

4.2 Ga. 618

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619

4. Conclusions: 620

Mars and the Moon had superheated cores at the end of their accretion, due to the release of the 621

gravitational energy by the descent of iron inside the silicate mantle in the making of the cores. 622

Overlain by relatively colder mantles, both cores were capable of cooling fast and generating 623

core dynamos. However, the giant Borealis impact at the end of accretion of Mars prevented 624

core convention and initiation of a core dynamo. It took about 50-120 Myrs for the martian core 625

to generate a core dynamo, hence the primordial crust that was formed during the first ~100 626

Myrs was not magnetized. Each of the 8 large impacts that occurred during 4.2 to 4.0 Ga 627

crippled the existing core dynamo of Mars. However, having a large volume the martian core 628

was zealous, it regenerated a dynamo a new after each impact. In the mean time, the stagnant 629

lithosphere at the surface thickened and reduced the heat loss from the mantle. The temperature 630

difference between the core and the lower mantle decreased in time and the core convection 631

gradually weakened to a point that it could no longer support a core dynamo. After 9 episodes of 632

crippling and reactivation, by Borealis and the large 8 impactors, the core dynamo of Mars 633

ceased for good at ~3.8 Ga. 634

With no giant impact occurring at the end of accretion, the superheated lunar core generated a 635

strong thermally driven core dynamo that lasted about 100 Myr and magnetized the newly 636

forming primordial lunar crust. The magnetic source bodies of the Moon created at later times 637

were magnetized by either a precession driven dynamo, or a thermally driven dynamo due to 638

possibly vigorous thermo-chemical mantle convection, or a chemically driven dynamo resulting 639

from the core solidification. The lunar dynamo had two episodes of initiation and cessation. The 640

first initiation was at the later stages of accretion, which lasted ~100 Myr. The second initiation 641

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was some times before the heavy bombardment, ~4.1 Ga. There is no viable estimate as when 642

the second core dynamo of the Moon ceased to exist. Suffice to say that, similar to the case of 643

Mars, the gradual thickening of the stagnant lid at the surface and the relatively small size of the 644

lunar core were probably the major factors that gradually diminished the core dynamo. 645

646

Analysis of the isolated magnetic anomalies of both intrusive and impact craters provided a 647

means to determine the direction of the magnetizing field and reveal polar wander and core 648

dynamo reversals of both Mars and the Moon. The polar wander path of the Moon is simple to 649

interpret. The formation of SPAB at around 4.1 Ga created a huge surface mass deficiency that 650

derived ~68o true polar wander. The formation of large mascon basins at around 3.9 Ga initiated 651

a new true polar wander of about ~52o in later times. There was also a core dynamo reversal 652

between these two polar wander periods. 653

654

Acknowledgement. This research was supported by Natural Sciences and Engineering Research 655

Council (NSERC) of Canada, special Grant at McGill University, NSERC-GRF 241305, I would 656

like to thank two anonymous reviewers for their constructive comments. 657

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Figure Captions:

Figure 1. Radial component of the 62-degree spherical harmonic model of Mars magnetic field

at 370 km altitude (Arkani-Hamed, 2004a).

Figure 2. The vertical component of the magnetic field of Mars derived using MGS high altitude

nighttime magnetic data acquired during (A) 1999–2002 and (B) 2003–2006. (C) Shows the

locations of the craters (in green), the impact-related QCDs (in red), and the none-impact-related

QCDs (in blue), only in the non-magnetic South Province, which has a pink background in

panels A and B (Arkani-Hamed and Boutin, 2012a).

Figure 3. Evolution of the martian core properties for two viscosity models of the martian

mantle (Roberts and Arkani-Hamed, 2017). Black curves are for the Newtonian viscosity and

red curves are for the stress-dependent viscosity. The heat flux panel distinctly shows that shortly

after an impact the heat flux jumps due to the juxtaposition of the stratified high temperature

uppermost core to the colder mantle. The spikes from right to left specify the heat flux

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immediately after Daedalia, Ares, Amazonis, Chryse, Scopolus, Acidalia, Utopia, and Hellas

impacts, respectively. Note that the two viscosity models have overall similar behaviors.

Figure 4. The orbital radius of a retrograde asteroids (top) and the rate of tidal energy dissipated

inside Mars (bottom). The numbers on the curves denote the tidal delay time in minutes (see

text for details).

Figure 5. The global distributions of the radial component of the lunar magnetic field (Arkani-

Hamed and Boutin, 2014). (A) the 150-degree spherical harmonic model at 30 km altitude, (B)

the Kaguya data at 100 km altitude, and (C) the LP-2 data at the variable spacecraft altitudes.

The black stripes are the regions with no LP-2 data. The map projection is centered at 180E.

Figure 6. Magnetic anomalies of SPAB (A) and their paleomagnetic north pole positions (B)

(Arkani-Hamed and Boutin, 2017). The horizontal axis of panel A shows the east longitude and

the vertical axis is the latitude, both in degrees. Note that the north Crisium magnetic anomaly is

not included in panel A, because it is outside the frame of the panel, but its paleomagnetic pole

(#6) is included in panel B. The background gray color shows the regions with LP-2 magnetic

data, while the white strips denote places with no LP-2 magnetic data.

Figure A1. The vertical, upward component of the magnetic field (first two rows) and the

magnetic intensity (second two rows) at 50 and 100 km altitudes of a uniformly magnetized

vertical circular disk of 100 km diameter (Arkani-Hamed and Boutin, 2014). The numbers on

the top of the panels show the dip angle of the magnetization vector, 0 for horizontal and 90 for

vertical, upward. The vertically integrated bulk magnetization of the disk is 3x104 A. The

numbers on the horizontal and vertical axes of the lowest right panel show the rectangular

coordinate distances in km relative to the center of the prism.

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647

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648

649

650

651

Figure 1 652

653

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Figure 2 655

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658

Figure 3 659

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Figure 4 663

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Figure 5 667

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Figure 6 669

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Figure A1 673

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677

Appendix A: Modeling an Isolated Magnetic Anomaly: 678

A spherical crust of constant thickness with uniformly distributed magnetic minerals is a 679

magnetic annihilator that creates no magnetic field outside when it is magnetized by an internal 680

magnetic field regardless of the complexity of the field and magnetization intensity of the crust 681

(Runcorn, 1975). This is actually the simplest magnetic annihilator among very many complex 682

annihilators (e.g., Arkani-Hamed and Dyment, 1996). Such a crust cannot be distinguished 683

from a non-magnetic crust on the basis of magnetic anomaly analysis. On a local scale, a thin 684

flat and uniformly magnetized extended layer of constant thickness does not create magnetic 685

anomalies except near its edges. The layer is regarded a magnetic annihilator far from its edges. 686

We consider well-isolated magnetic anomalies because they are usually associated with simple 687

source bodies and allow modeling by simple elliptical prisms, hence determining the 688

paleomagnetic pole positions when the bodies acquired magnetization. Modeling a magnetic 689

anomaly is based on an implicit assumption that the surrounding crust creates no magnetic field. 690

We model an intrusive magnetic source body with no topographic signature by a uniformly 691

magnetized cylindrical prism of 10 km thickness with an elliptical horizontal cross section. The 692

prism is located on the surface vertically and extends to a 10 km depth. An elliptical prism 693

allows more degrees of freedom than a circular prism, thus provides a better fit between the data 694

and the model. The three components of the magnetization vector of the prism are determined 695

by fitting the vertical component of the model field to the vertical component of the Lunar 696

Prospector Level-2 (LP-2) data at the observation points, hence taking into account the actual 697

spacecraft altitudes (Arkani-Hamed and Boutin, 2014). The magnetic intensity anomaly of a 698

circular prism overlies the prism, with its major part inside a circle with a radius about twice the 699

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radius of the prism (Figure A1). It is worth mentioning that such a simplistic model is highly 700

idealized, it provides a first order estimate of the magnetic anomaly of an almost 701

equidimensional magnetic body. 702

The lack of a topographic signature obscures the exact location of a deep-seated source body. As 703

a first step, we estimate the horizontal projection of the center of the body using the magnetic 704

intensity anomaly. We then calculate the minimum misfit elliptical prism model by moving its 705

center at 20 km intervals inside a square that extends the major areal coverage of a magnetic 706

anomaly. We change its semi-major axis from 60 to 200 km with 20 km increments and its 707

semi-minor axis from 60 km to the semi-major axis again with 20 km increments. We also 708

change the orientation of the major axis of the prism with respect to north from 0 to 180o at 20o 709

intervals. We adopt the same procedure for modeling a magnetic anomaly associated with the 710

impact demagnetization of the crust beneath an impact crater, except that the cross-section of the 711

prism is circular, its center is at the center of the crater, and the magnetic data are over a circular 712

area with a radius twice the radius of the crater. The magnetization of the surrounding crust is in 713

the opposite direction of the magnetization of the model prism. 714

The paleomagnetic pole position associated with the magnetization vector of a source body is 715

determined adopting the procedure by Arkani-Hamed (2001) and assuming that the magnetizing 716

field near the surface is the dipole component of the core field. Because of the very small core 717

radii of the Moon and Mars compared to their actual radii the quadrupole component of the core 718

field decreases by about 4-5 times faster than the dipole component as it propagates from the 719

core-mantle boundary to the surface, and higher degree components decrease even further. 720

721

References: 722

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Arkani-Hamed, J. 2001. Paleomagnetic pole positions and pole reversals of Mars, Geophys. Res. 723

Lett., 28(17), 3409–3412. 724

Arkani-Hamed, J., and Boutin, D. 2014. Analysis of isolated magnetic anomalies and magnetic 725

signatures of impact craters: Evidence for a core dynamo in the early history of the Moon, Icarus, 726

237, 262–277. 727

Arkani-Hamed, J., and Dyment, J. 1996. The magnetic potential and magnetization contrasts of 728

the Earth's lithosphere, J. Geophys. Res., 101, 11,401-11,425. 729

Runcorn, S.K. 1975. On the interpretations of lunar magnetism. Phys. Earth Planet. Inter. 10, 730

327. 731

732

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