Possible crippling of the core dynamo of Mars by Borealis impactrcoe/eart290C/Arkani... ·...

Possible crippling of the core dynamo of Mars by Borealis impact

Jafar Arkani‐Hamed1,2

Received 19 March 2010; revised 4 October 2010; accepted 13 October 2010; published 31 December 2010.

[1] Assuming that the northern lowland of Mars is created by a giant Borealis impact,I investigate its consequences on the thermal state of the mantle and the core dynamofor four different impact models using the scaling laws of crater formation, the shockpressure model of Pierazzo et al. (1997), and the “foundering” shock heating modelof Watters et al. (2009). The impact heating enhances the temperature of the mantle by1000–3000 K down to ∼1000 km depth. The superheated upper mantle ascends rapidly asa giant plume and develops a strong convection in the entire mantle of the subimpacthemisphere, while the antipodal hemisphere remains almost undisturbed for the period of100 Myr considered in this study. The upwelling of the plume rapidly sweeps up theimpact‐heated base of the mantle and replaces it with the cold surroundings, reducing theeffects of the impact‐heated mantle on the heat loss of the core. However, direct shockheating stratifies the core and effectively suppresses a preexisting thermal convectionin the core. This cripples a preexisting thermally driven core dynamo. It takes 35–85 Myrfor the stratified core model to exhaust impact heat and resume global convection andpossibly regenerate a strong dynamo. Adding the superheated iron content of an impactoron the core does not create an appreciable dynamo but elongates the heat exhaustiontime and delays the regeneration of a strong dynamo by an additional ∼40 Myr. It isconcluded that Borealis impact, if it occurred, could have crippled the core dynamo ofMars for up to ∼70–120 Myr.

Citation: Arkani‐Hamed, J. (2010), Possible crippling of the core dynamo of Mars by Borealis impact, J. Geophys. Res., 115,E12021, doi:10.1029/2010JE003602.

1. Introduction

[2] The northern lowland is the most prominent feature ofMars, covering an area of ∼3 × 107 km2. On the basis ofcrater density analysis, Frey et al. [2002] suggested that thelowland was formed in the later stages of accretion or shortlyafter. Despite determined efforts by many investigators sincethe north‐south dichotomy was identified by the Mariner 9spacecraft [Hartmann, 1973], the origin of the lowlandremains an outstanding problem in the geological history ofMars. Two fundamentally different hypotheses have beenproposed for the origin of the lowland: Endogenic andexogenic. The endogenic hypothesis interprets the lowlanddue to thinning of the crust by a giant mantle plume [e.g.,Wise et al., 1979; McGill and Dimitriou, 1990; Zuber et al.,2000; Zhong and Zuber, 2001; Roberts and Zhong, 2006; Keand Solomatov, 2006]. The exogenic hypothesis relates theformation of the lowland to a single giant impact [Wilhelmsand Squyres, 1984] or to multiples of large but not giantimpacts [e.g., Frey and Schultz, 1988]. The single giantimpact hypothesis has recently gained some ground on the

basis of three articles published in Nature in 2008 [Andrews‐Hanna et al., 2008; Nimmo et al., 2008; Marinova et al.,2008]. Using Mars Global Surveyor gravity and topogra-phy data, Andrews‐Hanna et al. [2008] fitted an ellipse to thelowland with a major axis of 10,600 km and a minor axis of8500 km, centered at 67°N and 209°E, thus proposing a giantoblique impact for the origin of the lowland. Nimmo et al.[2008] showed that a vertical impact with energy in therange of 0.3 × 1028 to 1 × 1029 J could have produced thelowland.Marinova et al. [2008] examined numerous obliqueimpacts to create the lowland, using the impact angle andimpact velocity as major parameters. The authors identified a“sweet spot” in the parameter space they explored, corre-sponding to impact energies of 3–6 × 1029 J, impact angles of30°–60°, and impact velocities of 6–10 km/s, which yields abasin comparable to the lowland. Also, most recently Reeseet al. [2010] related the formation of the lowland to anantipodal giant impact.[3] In the present study I assume that the lowland is

formed by a giant Borealis impact and investigate its con-sequences on the mantle dynamics and the core dynamo ofMars. A large impact heats the interior through the shockwaves. Section 2 presents models for the impact‐inducedtemperature increases in Mars. The impact‐heated uppermantle ascends at high velocity and triggers upwelling of theentire column of the mantle down to the core‐mantleboundary directly beneath the impact site, which is presented

1Department of Physics, University of Toronto, Toronto, Ontario,Canada.

2Also at Department of Earth and Planetary Sciences, McGillUniversity, Montreal, Quebec, Canada.

Copyright 2010 by the American Geophysical Union.0148‐0227/10/2010JE003602

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, E12021, doi:10.1029/2010JE003602, 2010

E12021 1 of 20

http://dx.doi.org/10.1029/2010JE003602

in section 3. The direct shock heating of the core causesthermal stratification and suppresses a thermally driven coredynamo [Arkani‐Hamed and Olson, 2010a, 2010b], asdemonstrated in section 4. The subsequent cooling of thestratified core is addressed in section 5, and the generation ofa core dynamo in the convecting outer core is investigated insection 6. Reese and Solomatov [2010] suggested that theiron content of the impactor may descend and create asuperheated layer of iron on the core. Section 7 explores theeffect of such an iron layer on subsequent core cooling andregeneration of the core dynamo. The lack of magnetic sig-nature of the lowland as a whole and the presence of someweak anomalies over the lowland are explained in section 8.Concluding remarks are relegated to section 9.

2. Impact Heating of Mars

[4] This section estimates the shock pressure distributionand temperature increase in the interior of Mars induced byBorealis impact, closely following the procedure used byArkani‐Hamed and Olson [2010a]. An axisymmetricspherical Mars model is adopted and it is assumed that theimpact occurred vertically and created a circular basin. The

axis of symmetry passes through the impact site and thecenter of Mars. Although the axes of the ellipse fitted to thelowland are ∼8500 and 10,600 km [Andrews‐Hanna et al.,2008] I consider a circular basin diameter of either 7000or 8000 km to be conservative and also to account forpossible subsequent modifications of the basin. Two impactvelocities of 10 and 6 km/s are used. The former is theaverage of the impact velocities of Mars proposed byNeukum and Wise [1976] and the upper limit of the impactvelocity in the sweet spot of the parameter space investi-gated by Marinova et al. [2008]. The latter is the lower limitof the velocity in the sweet spot. The 10 km/s impactvelocity is probably more realistic (see below).[5] The impactor size is estimated on the basis of empir-

ical scaling laws of Holsapple [1993] and Melosh [1989].Briefly, the diameter of the model basin is related to thediameter of its transient cavity, which provides a means tocalculate the kinetic energy of the impactor. Using an impactvelocity and the impactor density, I then determine theimpactor size. Note that Holsapple’s [1993] scaling lawprobably underestimates the transient diameter [Stewart,2010], because the formation of a giant impact basin islargely controlled by dynamic weakening along impact‐induced faults and the transient diameter is closer to the finaldiameter of the basin than that derived from the scaling laws[e.g., Senft and Stewart, 2009]. The direct relationshipbetween the transient diameter and the energy of theimpactor indicates that the calculated impact effects are alsounderestimated. The shock pressure distribution in a Marsmodel is calculated using the average model of Pierazzo etal. [1997] and assuming constant but different acousticvelocities and densities in the core and the mantle. It isworth mentioning that Pierazzo et al. [1997] consideredimpact velocities of 10 km/s or higher. Their model may beless accurate for the low impact velocity of 6 km/s consid-ered in the present study. As a shock wave passes, the targetdecompresses adiabatically and a large percentage of thedeposited energy is released as kinetic energy (i.e., exca-vation of the basin). The remaining energy goes into heat[Bjorkman and Holsapple, 1987], increasing the tempera-ture of the impactor and target. The corresponding impact‐induced temperature increase is estimated using the “foun-dering” shock heating model of Watters et al. [2009]. Notethat the foundering model yields the least temperatureincrease in the lower mantle among the three shock heatingmodels investigated by Watters et al. [2009], emphasizingthat the temperature increases presented in this paper areprobably further underestimated. Table 1 lists the physicalparameters used in this study, and Table 2 gives the resultsof the scaling laws applied to the four Borealis impactmodels. At a reasonable impact velocity of 10 km/s, themass of an impactor capable of creating the giant northernlowland is an order of magnitude smaller than that of theimpactors considered during the accretion of Mars [e.g., Keand Solomatov, 2009].[6] Figure 1 shows the impact‐induced temperature

increase in Mars for impact model A. The results for theother models have similar characteristics in spatial varia-tions, though different temperature values. The shock wavepropagates as a spherical wave centered on the isobaricsphere located directly beneath the impact site. It is reflectedat the surface with a 180° phase change and no loss of

Table 1. Physical Parameters Common Among the Models

Parameter Value (Unit)

Mars radius (Rs) 3390 (km)Core radius (Rc) 1700 (km)Gravity at the surface (g) 3.72 (m/s2)Gravity at the core‐mantle boundary(gc)

3.56 (m/s2)

Mantle density (rm) 3500 (kg/m3)Core density (rc) 7500 (kg/m3)Melt density (rl) 2700 (kg/m3)Impactor density (rimp) 3000 (kg/m3)P wave velocity in the mantle (Vpm) 7.24 (km/s)P wave velocity in the core (Vpc) 4 (km/s)S wave velocity in the mantle (Vsm) 4 (km/s)Impact velocity (Vimp) 10 (km/s)The constant in Pierazzo et al.’s [1997]model for the mantle (Sm)

1.25

The constant in Pierazzo et al.’s [1997]model for the core (Sc)

1.6

Specific heat of the mantle (Cpm) 1200 (J/kg/K)Specific heat of the core (Cpc) 600 (J/kg/K)Thermal expansion coefficient of themantle at the surface (am)

3 × 10−5 (1/K)

Thermal expansion coefficient of thecore (ac)

10−5 (1/K)

Melting expansion coefficient of themantle (bm)

0.024a

Thermal conductivity of the core (Kc) 40 (W/m/K)Thermal conductivity of the mantle at273 K (Km)

4 (W/m/K)

The preimpact mean heat flux at thecore‐mantle boundary

40 (mW/m2)

Latent heat of melting (L) 400 kJ/kgSurface temperature (To) 230 KPresent average uranium content of themantle

16 ppb

Present average potassium content ofthe mantle

305 ppm

Present average thorium content of themantle

56 ppb

Reference viscosity at the core‐mantleboundary (ho)

1019 Pa s

Kinetic viscosity of the core (nc) 1 m2/s

aSparks and Parmentier [1994]

ARKANI‐HAMED: BOREALIS CRIPPLING OF THE DYNAMO OF MARS E12021E12021

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energy. The interference of the direct and reflected wavesreduces the resulting shock pressure near the surface. Uponimpinging the core‐mantle boundary, the direct shock waveis partly reflected back to the mantle and partly transmittedto the core. The reduction of temperature in the mantle nearthe core‐mantle boundary due to the interference of thedirect and reflected waves is small and ignored. Because theshock wave velocity in the liquid iron core is smaller thanthat in the overlying solid silicate mantle, the refractionangle, calculated on the basis of Snell’s law, is alwayssmaller than the incident angle at the core‐mantle boundary.Consequently, parts of the mantle and core do not receiveshock waves. Table 2 includes the colatitude relative to thesubimpact point on the core where the shock ray is tangentto the core. Beyond this point no shock wave directly im-pinges the core‐mantle boundary, and the mantle immedi-ately above the core receives no shock wave and thus is notheated at all. Only ∼20% of the core’s surface receives thedirect shock wave.[7] The kinetic energy of the impactor and the total impact

heat energy received by the mantle and the core are includedin Table 2. The heat inputs to the mantle and core areestimated by integrating Cpm rm dT over the domain ofcalculations in the mantle seen in Figure 1 and integratingCpc rc dT over the entire core. Here Cpm and Cpc are thespecific heats of the mantle and core, and rm and rc are themantle and core densities, respectively. The variable dT isthe impact‐induced temperature increase at a given point.The impactor energies are in the lower part of the energyrange, 3–6 × 1029 J, estimated by Marinova et al. [2008].The total impact heat input to Mars for the impact velocityof 10 km/s is 27–33% of the impactor energy, which is lessthan but comparable to the ∼35–55% suggested by O’Keefeand Ahrens [1977] for the same impact velocity but smallimpactors. Less than 10% of the heat energy is partitioned tothe core.[8] Figure 2 shows profiles of the shock pressure and the

impact‐induced temperature increase along the axis ofsymmetry for the four models considered. Also included inFigure 2a is the lithostatic pressure indicating that the shockpressure exceeds the lithostatic pressure, which is requiredby the foundering shock heating model. The isobaric sphereis not isothermal because the foundering model takes intoaccount the effect of the preimpact lithostatic pressure. Notethat the temperature increase occurring in the isobaric sphereis well above the melting temperature of the upper mantle,but no account is taken for the latent heat of fusion inFigures 1 and 2b, which present a “potential” temperatureincrease. The temperature will be modified by taking thelatent heat of fusion into account and allowing melting to

occur in estimating the impact effects on the mantledynamics in the next section. The high‐velocity impactsincrease the upper mantle temperature much more than thelow velocity ones. However, because the decay of the shockpressure with distance from the center of the isobaric sphereis faster for the high‐velocity impacts than for the low‐velocity impacts [Pierazzo et al., 1997], the temperatureincrease in the deeper parts of the core is higher for the low‐velocity impacts. The abrupt increase of the temperatureacross the core-mantle boundary is due to the smaller spe-cific heat of the iron core compared to that of the silicate

Table 2. Characteristics of the Scaling Lawsa

Model Db Dtr Diso Dimp Vimp M Po Eimp Em Ec Eheat/Eimp �o

A 8000 4498 1184 1614 10 7.7 2.4 3.8 1.0 0.03 0.27 52.6B 7000 3977 1012 1381 10 4.8 2.4 2.4 0.78 0.02 0.33 53.9C 8000 4498 1414 2148 6 18.2 1.2 3.3 0.4 0.04 0.13 50.7D 7000 3977 1210 1838 6 13.3 1.2 2.0 0.4 0.04 0.22 52.4

aDb is basin diameter, Dtr is the transient cavity diameter, Diso is the diameter of the isobaric sphere, and Dimp is the impactor diameter, all in km. Vimp isthe impact velocity in km/s and M is the mass of the impactor in 1021 kg. Po is the shock pressure in the isobaric sphere in 1011 Pa s. Eimp is the kineticenergy of the impactor, Em is the heat energy partitioned to the mantle, Ec is the heat energy partitioned to the core, Eheat is the total heat energy input toMars, and �o is the colatitude relative to the subimpact point on the core where the shock ray is tangent to the core, in degrees.

Figure 1. The temperature increase in the mantle and thecore of model A (Table 2) by shock heating following theBorealis impact. No attempt is made to incorporate the latentheat of melting and evaporation near the impact site. Theblack areas do not receive any shock wave. The heating ofthe mantle by the shock wave emerging out of the core inthe antipodal region is insignificant and ignored. Note thatthe maximum temperature increase in the antipodal part ofthe core is about 50 K. Upon emerging out of the core theshock wave suffers energy loss due to partial reflection intothe core. Also, because of the higher specific heat of thesilicate mantle compared to the iron core, the maximumimpact temperature increase directly above the core is in theorder of 25 K.


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mantle (see Table 1). The jump increases the outward heatflux of the core and does not allow the impact‐heatedlowermost mantle to reduce the heat flux.[9] Mantle heating by the shock wave emerging out of the

core in the antipodal region is small and ignored in Figure 1,

partly because the shock wave traveling the entire core losesa major amount of its energy and partly because a fraction ofthe shock wave impinging the antipodal region of the core‐mantle boundary is reflected back into the core. Figure 2bshows that the impact temperature increase at the antipo-

Figure 2. (a) Shock pressure and (b) impact‐induced temperature increase along the axis of symmetryfor models A–D (see Table 2). A negative radius means a radius in the antipode direction. The mantle inthis antipodal region is not shown in the horizontal axis. Note that shock pressure and temperatureincreases in the antipodal region of the mantle are not calculated, as explained in the Figure 1 caption,which explains the Figure 2 cut off at the −1700 km radius. The ray theory [Aki and Richards, 2002] isadopted for calculation of shock wave transmission across the core-mantle boundary.


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dal point in the core directly beneath the core‐mantleboundary is about 51 and 28 K for the high impact velocitymodels A and B, respectively, and about 290 and 265 K forthe low impact velocity models C and D, respectively. Asmentioned above Pierazzo et al.’s [1997] model is probablyless accurate for the low impact velocity of 6 km/s and thehigh temperature values of 290 and 265 K are likely over-estimated. Because only a fraction of the shock waveimpinging the antipodal region emerges out of the core, theshock pressure at the base of the mantle directly above thisregion is small. Moreover, the higher specific heat of thesilicate mantle compared to that of the iron core makes theimpact temperature increase at the base of the antipodalmantle even smaller.

3. Impact‐Induced Mantle Dynamics

[10] Borealis impact drastically changes the mantledynamics, by introducing a huge amount of impact heat inthe upper mantle as seen in Figure 1. This section isconcerned with the mantle dynamics caused by the impactheating. The effects of a large impact on the mantledynamics of terrestrial planets have been investigated on thebasis of convection in a rectangular coordinate [Watterset al., 2009], in an axisymmetric cylindrical coordinate[Monteux et al., 2007], in an axisymmetric spherical coor-dinate [Ghods and Arkani‐Hamed, 2007] and (Ghods, A.,and J. Arkani‐Hamed, Effects of the Borealis impact on thethermal evolution of Mars, submitted to Physics of the Earthand Planetary Interiors, 2010), and in a three‐dimensionalspherical coordinate [Roberts et al., 2009; Ke andSolomatov, 2009]. I follow the technique used by Ghodsand Arkani‐Hamed [2007] in their studies of the effects ofAitken impact on the thermal evolution of the Moon, partlybecause the heating of the mantle by a vertical impact isaxisymmetric and the geometry of the axisymmetric spher-ical coordinate is more relevant. Briefly, I adopt a self‐gravitating spherical mantle, with temperature‐dependentand melt depletion‐dependent viscosity, temperature‐dependent thermal conductivity, and a pressure‐dependentthermal expansion coefficient. The mantle dynamic equa-tions are solved in a spherical shell with an inner radius Rc =1700 km and an outer radius Rs = 3390 km. The temperatureat the surface is kept unchanged and a cooling core‐mantleboundary is adopted.[11] A preimpact model is calculated to establish a rea-

sonable temperature distribution prior to the impact. Themodel starts at 4.6 Ga, assumed to be after the accretion ofthe planet and the core formation and magma ocean solid-ification, with an adiabatic initial temperature distribution inthe mantle and core that reaches 2000 K at the core‐mantleboundary [Hauck and Phillips, 2002]. The temperaturedecreases linearly in the upper 100 km from ∼1600 K to thesurface temperature of 230 K. The core is assumed to beliquid with an adiabatic temperature distribution. Radioac-tive heat generation is taken into account in the mantle andthe crust, while no internal heating is considered for thecore. The radioactive elements concentration at presentfollows that ofWanke et al. [1994] with K, Th, and U valuesof 305 ppm, 56 ppb, and 16 ppb, respectively. Thirty per-cent of the radioactive elements are allocated to the crust andthe rest are uniformly distributed in the mantle. There is

good evidence that a stagnant lid has existed on Mars almostfrom day one [e.g., Breuer and Spohn, 2003; Williams andNimmo, 2004]. Note that a stagnant lid is produced due toboth the low temperature near the surface which increasesthe strength of the material, and the low density of the crustwhich increases the buoyancy of the lid. The estimates ofthe crustal thickness range in a very wide spectrum from 50to 250 km [Breuer and Spohn, 2003]. The interpretation ofthe gravity and topography suggests crustal thicknesses of40–80 km [Zuber et al., 2000]; the thickest crust underliesthe oldest regions. Because of very early chemical differ-entiation [e.g., Halliday et al., 2001], it is plausible that amajor part of the crust was formed while the magma oceanwas solidifying. The initial thickness of the crust is taken tobe 50 km in the models. A stagnant lid convection regime isadopted in the calculations of mantle dynamics. The initialthickness of the stagnant lid is taken to be 60 km, assumingthat the base of the stagnant lid is determined by an elastic‐to‐ductile transition temperature of ∼1070 K [e.g., Stevensonet al., 1983; Schubert and Spohn, 1990]. Because of inef-ficient heat transfer by thermal conduction through thestagnant lid, the radioactive heating gradually increases themantle temperature in the early history of the planet [e.g.,Breuer and Spohn, 2003]. Detailed study of the radioactiveheating of Martian mantle, considering different amounts ofpartitioning of the radioactive elements to the crust, sug-gests that the temperature in the mantle may increase by upto 250 K (e.g., see the nominal model of Arkani‐Hamed[2005a]). Adopting a higher initial temperature in themantle, such as solidus [Ke and Solomatov, 2009] willguarantee that the mantle remains partially molten for a longtime or even up to the present. Note that Ke and Solomatov[2009] did not include radioactive heating in their models.[12] The mantle is allowed to melt as its temperature

surpasses the solidus. I use McKenzie and Bickle’s [1988]batch melting model for fertile dry peridotite to calculatethe fractional melting at the end of each time step. Becauseof its lower density compared to that of solid residue, meltseparates from the solid residue and rapidly moves to thesurface. Only a small few percent of melt that is trapped inthe disconnected pores remains with the solid residue. Inthis study I assume that melt remains in the solid matrix andmoves with the matrix if it is less than or equal to 3% of avolume element. The excess melt is extracted and placed onthe surface instantaneously as a newly forming part of thecrust. I also take into account the enthalpy of melting in theenergy equation and calculate the temperature and meltdepletion fields accordingly. A melt depletion field specifiesthe solid residue after a certain amount of melting. Forexample, a melt depletion of 0.20 indicates a solid residueafter 20% melting. Melting is a chemical reaction whichdepletes the iron content of the solid residue, reducing itsdensity and increasing its viscosity [e.g., Hirth andKohlstedt, 1996]. Therefore the density of the solid resi-due is a function of temperature and the fractional melting.I consider both melt depletion buoyancy, due to the low‐density solid residue, and melt retention buoyancy, due tothe presence of low‐density melt in the pores, in themomentum equations. The density of the solid residue rs iscalculated by

�s ¼ �m 1� �m T � Toð Þ � �mM½ �; ð1Þ


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where rm is the density of the pristine mantle at surfacetemperature To (= 230 K), T is the temperature in kelvin, am

and bm are coefficients of thermal expansion and meltexpansion of the mantle, respectively, and M denotes themelt depletion. The effective density of the matrix (i.e., avolume element) r is determined by

� ¼ �s þ ’ �l � �sð Þ; ð2Þ

where ’ is the volumetric content of melt and rl (= 2700kg/m3) is the density of the melt.[13] The mantle viscosity is assumed to be temperature

and melt depletion dependent. The pristine mantle viscosityis calculated by

� ¼ �oD� exp�C T � Toð Þ ð3Þ

where the reference viscosity ho is the viscosity at the core‐mantle boundary, Dh is the viscosity contrast between thesurface and the core‐mantle boundary, and C = −ln [Dh/(TCMB − To)] denotes the temperature dependence of theviscosity where TCMB is the temperature at the core‐mantleboundary. Ghods and Arkani‐Hamed (submitted manu-script, 2010) examined reference viscosities of 1019, 1020,and 1021 Pa s, and viscosity contrasts of 1000, 2000, 5000,and 10000. It was found that for a given reference viscosity

the main characteristics of the mantle dynamics remainalmost unchanged as long as a stagnant lid exists on top, atleast during the 100 Myr investigated. A viscosity contractof 1000 is found sufficient to create a stagnant lithosphere,which is also adopted in this study along with the referenceviscosity of 1019 Pa s. Although the vigor of the mantleconvection decreases at high reference viscosities, themantle dynamics is still vigorous especially in the impact‐heated region. For the melt depletion dependency, the vis-cosity of the solid residue is increased linearly, by up to afactor of 10 for a maximum of 25% melting, which is themaximum melting that can be handled by the computer codeused in this study. Note the distinction between the meltcreated by partial melting, a maximum of 25%, and the meltretained in the pores of the matrix, a maximum of 3%. Theeffect of the pore melt on the viscosity of the matrix isusually small and is ignored in the models, assuming that theevolution of the mantle dynamics is dominated by solidrheology. The viscosity field is time varying and changesboth radially and laterally during the evolution because ofthe time and spatial variations of temperature and meltdepletion fields Figure 3 shows the spatial variations ofviscosity immediately after the impact, which is assumed tooccur at 4.5 Ga [e.g., Frey et al., 2002]. The viscositychanges significantly in the stagnant lithosphere andmoderately in the convecting part of the mantle, as sug-gested for the stagnant lid convection regime [e.g., Grassetand Parmentier, 1998]. The region directly beneath theimpact site which has experienced appreciable melting (seeFigure 4b) ends up having a relatively higher viscositybecause the melt has already moved up but left behind thehigh‐viscosity solid residue except for a small amount ofmelt in the pores. The decrease of the solid residue viscositydue to temperature increase is not sufficient to reduce theviscosity of the region appreciably. In the pristine mantleimmediately outside this region, the viscosity is decreasedbelow the viscosity of the preimpact model, because theimpact heating has elevated the temperature but has notcaused melting.[14] The temperature‐dependent thermal conductivity Km

of the mantle follows Schatz and Simmons [1972] experi-mental results:

Km ¼ 414:8= 30:6þ 0:21Tð Þ; T < 500K ð4aÞ

Km ¼ 414:8= 30:6þ 0:21Tð Þ þ 0:0023 T � 500ð Þ; T > 500K: ð4bÞ

The thermal expansion coefficient of the mantle am is 3 ×10−5 at the surface and decreases linearly with depth by 50%at the core‐mantle boundary.[15] A postimpact model starts after the very early stages

of impact‐induced melting [Nimmo et al., 2008; Marinovaet al., 2008], when the melt has already moved to the sur-face and the mantle can be treated as a viscous solid with no

Figure 3. The spatial variations of the normalized viscosityimmediately after impact.

Figure 4. Snapshots of (a) 2‐D temperature and (b) melt depletion distributions in model A (Table 2) at every 1 Myr afterthe Borealis impact. The 0 Myr shows the temperature distribution immediately after impact, which is modified (see thetext). Note that the impact‐induced mantle dynamics have not penetrated to the antipode hemisphere during this early stageof the thermal evolution.


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Figure 4


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more than 3% melt. However, to account for the thermaleffects of these early processes, the temperature is reset tocorrespond to the temperature of partial melt wherevermelting occurred, assuming that temperature in the partiallymolten region increases linearly from solidus to liquidus.The maximum temperature corresponds to 25% partialmelting. This approximation may underestimate the effectsof the impact heating on the mantle dynamics.[16] To better illustrate impact effects on the mantle

dynamics, I consider two models, one with impact and theother without impact, and compare their results. For a modelwith impact it is required to add the impact temperatureincrease to a preimpact temperature distribution developedby the preexisting mantle convection. However, such anaddition is not viable because of the lack of informationabout the impact site relative to the preexisting mantledynamics. An impact occurring over an upwelling buoyantmantle is expected to enhance the buoyancy and increase theascending velocity of the mantle directly beneath the impactsite, whereas the impact on top of a descending mantlereduces the negative buoyancy and the descending velocityof the mantle or even makes the buoyancy positive whichchanges the direction of the mantle convection. Therefore,the two‐dimensional (2‐D) axisymmetric impact‐inducedtemperature increase is directly added to the sphericallysymmetric part of the preimpact temperature. The resultingtemperature is then modified to account for the enthalpy ofmelting where it surpasses the solidus. The 2‐D axisym-metric temperature distribution thus obtained is regarded asthe initial temperature of the postimpact model. For themodel with no impact the spherically symmetric part of thepreimpact temperature is regarded as the initial temperature.Also the preimpact convection velocity is set to zeroimmediately before the impact in both models. This isolatesthe impact‐induced convection of the postimpact modelsfrom that of the preimpact convection. The postimpactthermal evolution models start at the impact time. Allmodels are calculated for a period of 100 Myr, but theresults of the first 11 Myr are presented here which issufficient to demonstrate the development of the impact‐induced mantle dynamics and the removal of the impact‐heated base of the mantle away from the core‐mantleboundary. The core temperature of a model with impact isspherically symmetric, but not adiabatic. The heat flux at thecore‐mantle boundary is estimated from the cooling historyof a stratified core (see below). On the other hand, the coretemperature is adiabatic in a model with no impact.[17] Figure 4a shows snapshots of the 2‐D temperature

distribution of model A with impact and illustrates details ofmantle dynamics at every 1 Myr interval. The upwelling ofthe highly buoyant hot upper mantle as a giant plumedominates the postimpact mantle dynamics. It developsupward motion of the entire column of the mantle directlybeneath the impact site down to the core‐mantle boundaryand results in appreciable lateral motion in the base of themantle, which brings the surrounding colder material to thesubimpact region. Moreover, the impact‐heated and strati-fied core with spherically symmetric temperature (seebelow) heats the entire base of the mantle and creates a low‐viscosity layer on the entire surface of the core, which fur-ther facilitates the lateral motion of the base of the mantle

and prevents the impact‐heated lowermost mantle to reducethe heat flux out of the core. The snapshots of the meltdepletion field (Figure 4b) better illustrate the mantledynamics. The impact‐heated, hot plume of low‐densitysolid residue ascends rapidly leaving almost no trace nearthe core‐mantle boundary by 4 Myr. The plume remains inthe subimpact hemisphere. The quiescence of the antipodalhemisphere characterizes the model with no impact,exhibiting negligible convection and rendering the temper-ature distribution almost spherically symmetric. For thisreason, the model with no impact is not presented. Note thatsetting the preimpact velocity to zero immediately before theimpact disentangles the effects of convection initiation fromthe effects of the impact‐heating to a very good extent. Theantipodal hemisphere exhibits negligible convection initia-tion. The postimpact mantle dynamics are almost entirelycontrolled by impact, at least for the 100 Myr investigated.[18] Figure 5 shows the temperature profiles along the

axis of symmetry directly beneath the impact site at every2 Myr and the solidus and liquidus of dry peridotite adoptedfor the mantle. The upper parts of the mantle melt exten-sively. The melt in excess of 3% is extracted and put on thesurface of Mars instantaneously, as mentioned before. Thetemperature at the core‐mantle boundary gradually reducestoward the preimpact value as the stratified core cools. Alsoincluded in Figure 5 is the radially averaged, sphericallysymmetric profile of the preimpact temperature distributionimmediately before the impact. It is clear that convection inthe preimpact model was effective enough to create a well‐defined thermal boundary layer near the core‐mantleboundary.

4. Direct Impact Heating of the Core

[19] Shock waves propagate in the mantle as sphericalwaves centered on the isobaric sphere. Upon impinging thecore‐mantle boundary part of the waves is transmitted to thecore. This section explains the direct heating of the core bythe transmitted shock waves. I closely follow the techniquedeveloped by Arkani‐Hamed and Olson [2010a]. Briefly,shock waves are traced using seismic ray theory [Aki andRichards, 2002] and the seismic velocities of the mantleand core listed in Table 1. The results obtained using theimpedance match method [Watters et al., 2009] or the shockdynamic method [Han and Yin, 1993] are similar to that ofthe ray theory. Shock heating in the core is calculated for thematerial properties of liquid iron (Table 1). Figure 6 showsthe resulting temperature increase in the core for the fourmodels. The black regions of the core do not receive shockwaves, because the shock wave velocity in the core is lessthan that in the mantle and Snell’s law prohibits the shockwaves to enter these regions, as mentioned before. Figure 6shows that the high velocity impact heats the shallower partsof the core in the subimpact region more than the lowvelocity impact, whereas the antipodal region of the coreis less heated by the high velocity impact. This is becausethe effective shock pressure Pd (= Ps − Po) used in thefoundering shock heating model of Watters et al. [2009]increases with radius in the antipode region. Although theshock pressure, Ps, decreases with distance from the center


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of the isobaric sphere, the lithostatic pressure Po decreaseseven faster with radius (Figure 2a).[20] The differentially heated core becomes quite unstable

and an energetic thermal adjustment takes place within avery short time and redistributes the shock‐heated fluid ontospherically symmetric isothermal surfaces with increasingtemperature as a function of distance from the center,resulting in a stable thermal stratification. The evolution ofthe temperature distribution during stratification inside acore with characteristics similar to those of the modelcore considered here [Arkani‐Hamed and Olson, 2010b,Figure 3] indicates that the core becomes stratified within ashort period of 1–2 kyr, which is also assumed in the presentstudy. The stratified temperature is calculated by determin-ing the volume fraction of the core versus the shock‐heatedtemperature increase. Assuming that the core was initiallyclose to a well‐mixed state the stable thermal stratification isthen calculated by adding the stratified impact temperatureincrease to the preimpact adiabatic temperature and refillingthe core according to temperature. Figure 7 shows thespherically symmetric temperature distributions in the strat-ified core for the four models thus calculated. The preimpactadiabatic temperature is assumed 2000 K at the core‐mantleboundary. The impact‐heated part of the core is concentratedin the upper ∼300 km. Note that the shock‐induced tem-perature perturbations are far larger than the temperature

perturbations associated with convection in iron‐rich plane-tary cores, estimated to be less than 1 K [e.g., Stevenson,1987; Christensen and Wicht, 2007]. The direct impactheating of the core and subsequent thermal stratification caneffectively suppress a preexisting thermally driven coreconvection for a limited time [Arkani‐Hamed and Olson,2010b].

5. Cooling of the Stratified Core

[21] The upward concentration of the impact heated, high‐temperature part in the stratified core suppresses core con-vection shortly after the impact. However, because of thevery low viscosity of the liquid iron, convection develops inthe outer parts and heat is transferred to the mantle byconvection. This section presents the poststratificationthermal evolution of the core calculated following the pro-cedure adopted by Arkani‐Hamed and Olson [2010a,Appendix A].[22] Figure 1 shows that about 20% of the core‐mantle

boundary receives direct shock wave and major shockheating actually occurs only on ∼10%. The base of themantle overlying the remaining 80% of the boundary is notimpact heated at all and it dominates subsequent cooling ofthe core which has a spherically symmetric temperature.Moreover, the fast upwelling of the buoyant upper mantledirectly beneath the basin pulls up the impact‐heated part of

Figure 5. Temperature profiles of model A (Table 2) along the axis of symmetry beneath the impact siteat certain times after the impact. The numbers on the curves denote time after the impact in Myr. Curves Sand L are the mantle solidus and liquidus. The “before” curve is the spherically symmetric temperaturedistribution immediately before impact. It shows that a pronounced thermal boundary layer was formed atthe core‐mantle boundary before the impact. Regions with temperatures higher than solidus are partiallymolten. Note the rapid upwelling of the impact‐heated regions and the temperature decrease in the lowerparts of the mantle to almost its preimpact condition, due to the lateral motion of the mantle to fill thespace drained by the upwelling. Note that the temperature at the core‐mantle boundary gradually reducesas the core cools.


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the mantle away from the core‐mantle boundary andreplaces it with the colder surrounding material in a shorttime as seen in Figures 4 and 5. Accordingly, the thermalevolution of the core is calculated assuming that it is over-lain by the preimpact thermal boundary layer of the mantle.The domain of calculation at a given time is divided intothree parts: A conducting inner core; a convecting outercore; and a conducting overlying mantle layer of 50 kmthickness. The preimpact temperature distribution in themantle layer is assumed linear and is obtained using a coreheat flux of 40 mW/m2, which is comparable to the heat fluxestimated at the impact time [Breuer and Spohn, 2003;Williams and Nimmo, 2004; Ke and Solomatov, 2009]. Thetemperature at the top of the mantle layer is kept unchanged,because the average interior temperature of the mantle doesnot change appreciably during the short cooling period ofthe stratified core.[23] The heat transfer in the conducting zones is deter-

mined by solving the heat conduction equation in a sphericalcoordinate

@T=@t ¼ 1=r2� �

@=@r r2�@T=@r� �

; ð5Þ

where r is the distance from the center, T is temperature, t istime, and � is the thermal diffusivity. The convective outercore is also subdivided into three sublayers: The lower andthe upper thermal boundary layers where heat is transferredby conduction and the middle convecting layer where heat istransferred by convection. The thermal boundary layers are

assumed to have identical thicknesses. The temperature inthe outer core is obtained through solving the enthalpyequation

4�R21q1 ¼ 4�R2

cqc þZ

4�r2drCpc�c@T=@t; ð6Þ

where the integration is over the entire outer core. q1 and qcare heat fluxes at the bottom and the top of the outer coreand Cpc is the specific heat of the core at constant pressure.For numerical simplicity a constant grid interval of Dr =100 m is used throughout the entire domain. However,because of very low viscosity of the liquid core, its thermalboundary layers are much thinner than the grid interval. Tocompensate for this difference and assure that heat transferthrough the thermal boundary layers of the convecting outercore is not affected by the gridding, the thermal diffusivityof the boundary layers is increased by a factor of Dr/d,where d is the thickness of a given boundary layer. The timeinterval Dt is determined at the beginning of each time stepusing the stability criterion

Dt ¼ 2=4 �c; ð7Þ

which assures that heat does not diffuse by more than d/2during that interval; �c denotes the thermal diffusivity of thecore. Note that the time steps are variable because of thetime varying thickness of the boundary layer (see below).[24] Figure 8 shows the temperature profiles in the core

and the overlying mantle layer at certain times after the corestratification for model A. The other models have similartemperature profiles but with different values. I use kine-matic viscosity of 1 m2/s for the outer core, which is higherthan the viscosity values suggested for the outer core of theEarth based on geodetic, geomagnetic, and seismic studies[Secco, 1995, Tables 1–3]. I also examined viscosity valuesof 10−2 and 10−4 m2/s for short time periods due to the hugecomputer time demand. The results were almost identical,emphasizing that the thermal evolution of the stratified coreis mainly controlled by the overlying mantle layer. Follow-ing the stratification there is a hot layer near the surface of thecore, specified by curve 0 in Figure 8, which makes thetemperature gradient positive and suppresses core convec-tion (the adiabatic temperature gradient in a convecting coreis negative). Note that while the impact heat is beingexhausted to the mantle through convection in the outer hotlayer, the middle part of the core between 1000 and 1650 kmradii is actually heated up, largely by the downward heatconduction from the outer hot layer and partly by upwardheat conduction along the adiabat from the central part. Thisincreases the temperature gradient and results in a sub-adiabatic core below the outer hot layer.[25] The thermal boundary layer thickness d of the con-

vecting outer core is determined at the beginning of eachtime step following King et al. [2009], as described byArkani‐Hamed and Olson [2010a]. The boundary remainsthinner than 20 m for a major part of the thermal evolutionof the stratified core (Figure 9a).[26] The convection in the outer core is penetrative with

gradual thickening of the convecting layer, as seen from thetime variations of its thickness (Figure 9b). However,shortly after the exhaustion of the major part of the impact

Figure 6. The shock‐induced temperature increase in thecore of models A–D (Table 2). The black region does notreceive the shock wave according to Snell’s law because theshockwave velocity in the liquid iron core is smaller than thatin the solid silicate mantle. The color is saturated at 700 K forbetter visualization. Temperature in the white region is morethan 700 K.


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heat the convection zone penetrates very rapidly to thecenter and global convection of the core resumes. This rapidpenetration is due to the fact that the temperature in thedeeper parts of the core remains close to the adiabatictemperature as seen in Figure 8. The rapid penetrationincreases the characteristic length of convection by a factorof ∼3 and the thermal Rayleigh number by a factor of ∼27,two orders of magnitude higher than that required forregeneration of dynamo as indicated by the numericalmodels of Kuang et al. [2008]. Figure 9b shows thatdepending on the size and the velocity of the impactor itmay take about 35–85 Myr for the convective layer toexceed the critical thickness and the core become capable ofregenerating a strong core dynamo.[27] Figure 10 shows the heat flux out of the core of the four

models. The heat flux starts at a very high value because thecore stratification places the most impact‐heated part of thecore directly beneath the core‐mantle boundary. However,this substantially heated part is quite thin and cools rapidlyallowing the heat flux to reduce appreciably. It is worthreminding that the heat flux shown in Figure 10 is used as thecooling boundary condition at the core‐mantle boundary inthe calculations of the mantle dynamics explained above.[28] The hemispheric dichotomy of the magnetization of

the Martian crust was recently related to a single hemisphericdynamo in the south [Stanley et al., 2008]. It was suggestedthat a 1° mantle convection or a giant Borealis impact raisedthe temperature at the core‐mantle boundary in the northernhemisphere and created a hemispheric temperature distribu-tion on the core. The colder core‐mantle boundary in thesouth allowed appreciable heat loss from the core which

powered a single hemispheric dynamo. The magneticsource bodies in the Martian crust reside in the upper 45–50 km [e.g., Voorhies et al., 2002] and they require 50–100 Myr to cool through their magnetic blocking tem-peratures and acquire strong magnetization enough to giverise to the magnetic anomalies of Mars, which are an orderof magnitude stronger than the magnetic anomalies of theEarth. Figures 4 and 5 emphasize that a single hemisphericdynamo which possibly resulted from the giant Borealisimpact does not last more than 5 Myr. It is worth notingthat although direct impact heating of the base of themantle is limited to less than 20% of the core’s surface, thethermally stratified core with a spherically symmetrictemperature substantially heats the entire base of themantle by over 200 K within the first 5 Myr (see Figure 8).This significantly reduces the viscosity of the mantleimmediately above the core‐mantle boundary and creates aglobe encircling, low‐viscosity layer overlying the entirecore. The low‐viscosity layer facilitates lateral motion of thelowermost mantle and the upwelling of the impact‐heatedbuoyant material, and further diminishes the lateral varia-tions of temperature at the base of the mantle. The timeestimated to suppress the lateral variations of temperature inthe base of the mantle is much shorter than the time requiredfor a hemispheric dynamo to stay active and magnetize thecrust in the southern hemisphere.

6. Regeneration of the Core Dynamo

[29] The thermal stratification quenches the core con-vection within a few thousand years and the preexisting

Figure 7. The spherically symmetric temperature distribution in the core of models A–D (Table 2)immediately after stratification. The stratified impact temperature increase is added to the preimpactspherically symmetric adiabatic temperature that starts at 2000 K at the core‐mantle boundary. The deeperpart of the core, with radius less than 1200 km, is not shown in Figure 7 for clarity. The temperature ofthis region follows the preimpact adiabatic temperature.


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magnetic field decreases by more than an order of magni-tude within one dipole decay time, ∼10 kyr [Arkani‐Hamedand Olson, 2010b]. However, the convecting outer core iscapable of generating a dynamo. Here I make a roughestimate of the dipole magnetic field intensity arising fromthe mean magnetic field that is expected to be generated inthe convecting outer core. Using the scaling equation (48)of Christensen and Aubert [2006], the mean magneticstrength inside the convecting outer core is determined by

B ¼ 0:91=2o �1=6c �cgcqadvRcdð Þ= CpcRi

� �� 1=3; ð8Þ

where mo (4p × 10−7 H/m) is the magnetic permeability, rc(7500 kg/m3) and gc (3.56 m/s2) are the core density and thegravitational acceleration at the core‐mantle boundary,respectively, ac (1 × 10−5(1/K)) and Cpc (600 J/kg/K) arethe thermal expansion coefficient and the specific heat ofthe core, respectively, and Rc (1700 km), Ri, and d (= Rc −Ri) are the outer radius (the core radius), the inner radius,and the thickness of the layer, respectively. Note that Ri andd are time‐dependent because of the penetrative nature ofthe convection. The buoyancy flow over the entire surfaceQB in equation (48) of Christensen and Aubert [2006] isexpressed in equation (8) in terms of the advective heat fluxper unit area qadv. In a thermally driven dynamo QB = 4 pRc2 ac qadv/Cpc. The advective heat flux in the core is

the heat flux at the core‐mantle boundary q, shown inFigure 10, minus the conductive heat flux, qcond along theadiabat. In a convective layer of highly conductive iron, theheat transfer by conduction is smaller than but comparableto the heat transfer by advection. I replace qadv by q toestimate an upper limit for B. Figure 11 shows the mean

magnetic field intensity generated inside the convectingouter core. The field intensity is mainly controlled by theheat flux q, which decreases in time, and by the thickness ofthe convecting layer d, which increases in time. The radiusto the bottom of the convecting layer Ri also decrease intime but relatively slowly. The rapid decrease of the fieldintensity in the first few million years is due to the fastdecrease of the heat flux, while the convecting layerremains thin (see Figure 9b). For a given core model, andexcept for the rapid decrease in the first few million years,the magnetic field intensity increases gradually with timeuntil the convecting layer penetrates to the center of thecore. The field intensity remains lower than 4–6 × 105 nTbefore global convection resumes. Note that the dipolecomponent of the magnetic field is probably 3–10 timesweaker than the mean field as estimated by Christensen andAubert [2006]. Also the dipole field decays by a factor of(Rc/Rs)

3 (∼0.13) as it reaches the surface of Mars at radiusRs. Therefore, the magnetic dipole field of the convectingouter core expected at the surface of Mars is at least twoorders of magnitude weaker than those shown in Figure 11.Higher‐degree harmonics decay even more rapidly. Esti-mates of the paleointensity of the magnetic field at thesurface of Mars at around 4.2 Ga, based on the oldestMartian meteorite ALH84001 [e.g., Weiss et al., 2008] andon the magnetostrophic force balance in its liquid core[Arkani‐Hamed, 2005b] indicate that the dipole core fieldintensity at the surface of Mars was comparable to that onpresent‐day Earth. This indicates that the dipole fieldgenerated by the convecting outer core at the surface ofMars is at least two orders of magnitude weaker than thatrequired to magnetize the magnetic source bodies in the

Figure 8. The thermal evolution of model A (Table 2). The numbers on the curves denote the time afterthe impact in Myr. Only the upper 200 km of the core is displayed for clarity. The temperature in thedeeper part is close to the initial adiabat. Note the region deeper than the 0 Myr curve is heated up and thetemperature gradient is positive.


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Figure 9. Time variations of the thickness of (a) the thermal boundary layer and (b) the convecting outercore of models A–D (Table 2). The dashed lines are for the case where the impactor iron layer is placed onthe core. Note that the thickness of the boundary layer is smaller than the grid interval adopted (see textfor details). The convecting layer gradually propagates to deeper parts of the core until the impact heat isexhausted and then it penetrates very rapidly.


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Martian crust before the rapid penetration of convectivelayer to the center. The present calculations suggest thatBorealis impact, if it occurred, was capable of crippling thecore dynamo of Mars for about 35–85 Myr.

7. Effects of an Impactor Iron Layer

[30] The giant Borealis impact is capable of increasing thetemperature of the mantle by about 3000 degrees down toabout 1000 km depth as seen in Figures 1 and 2. Thetemperature increase is enough to melt not only the uppermantle directly beneath the impact site but also the impactor.The upper mantle was already depleted in iron during earlycore formation prior, but the impactor may have an appre-ciable amount of iron which upon melting sinks due to itshigher density compared to the low density of the sur-rounding silicate mantle. Reese and Solomatov [2010]studied several sinking mechanisms of the impactor ironand concluded that the major part of the iron could sink tothe core‐mantle boundary and spread over the core directlybeneath the solid mantle, creating a super‐heated iron layeron the core. This is an interesting possibility and deservesfurther study.[31] Here I investigate the effects of the super‐heated

impactor iron layer on the cooling of the stratified corediscussed in the previous section, and determine the mag-netic field possibly generated in the layer. I consider modelA with an impactor of 1600 km diameter (see Table 2). Bytaking the particle velocity to be one half the impactvelocity, Reese and Solomatov [2010] implicitly assumedthe impactor and the target to be made of the similarmaterial, as also adopted here. Accordingly, I assume thatthe iron content comprises 1/8 of the total volume of theimpactor, and let its entire iron sink and spread on the core.

This amounts to an impactor iron layer ∼8 km thick.Depending on the sinking mechanism the impactor iron maytake several days to several thousand years to descend andcover the core, and it may cool or further heat up whilesinking [Reese and Solomatov, 2010]. I assume that the timeit takes for the total impactor iron to reach the core iscomparable with the time it takes for the core to be stratified(a few thousand years), a longer descent time would hampercore cooling by gradually replenishing hot impactor iron tothe surface of the core. I also assume no appreciable changesin the temperature of the sinking iron due to friction with thesurrounding mantle and set an initial temperature of 4270 Kfor the impactor iron layer placed on top of the stratifiedcore. This consists of the impact temperature increase in theisobaric sphere (Figure 2) plus the preimpact temperature inthe upper mantle. It also takes into account the adiabatictemperature increase from the upper mantle to the core‐mantle boundary. The resulting enlarged core is allowed tocool following the procedure described in the previoussection. Figure 12 shows the thermal evolution of theenlarged core. The super‐heated layer cools very rapidly. Itlargely loses its heat to the mantle but also appreciably to themiddle part of the core, which further delays exhaustion ofthe impact heat of the core. Included in Figure 11 is themean magnetic field intensity generated inside the con-vecting outer core of the enlarged core. The impactor ironlayer enhances the magnetic field intensity for about 2 Myr,but does not generate an appreciable core dynamo, while itdelays the regeneration of a strong core dynamo by anadditional ∼40 Myr.[32] The mean field to dipole field ratio of 3–10 estimated

by Christensen and Aubert [2006] is probably conservativeif applied to the magnetic field possibly generated inthe impactor iron layer. Stanley et al. [2005] numerically

Figure 10. Heat flux of models A–D (Table 2) at the core‐mantle boundary after the impact. The dashedline is for the case where the impactor iron layer is placed on the core.


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simulated the magnetic field generated inside a thinspherical shell overlying a conductive sphere, for the innerradius to outer radius ratios of up to 0.9, and concludedthat the magnetic field in the thin shells is dominated bymuch higher‐degree harmonics compared to the dipolefield. For the case of the impactor layer this ratio is about0.995, and the height of the tangent cylinder is only 330 km,too small to generate any appreciable dipole field at thesurface of Mars.

8. Magnetic Signature of the Lowland

[33] The giant Borealis impact excavates the entire crust atthe impact site and creates a very deep transient cavity,which is largely filled by the fall back, the collapse of thebasin rim, the isotatic upwelling of the impact‐heatedmantle, and partly by the superheated basaltic lava at tem-peratures well above the solidus of basalt which creates alava lake covering the northern lowland. The basaltic lavawould have acquired strong magnetization upon subsequentcooling below the magnetic blocking temperatures of itsmagnetic minerals if a strong core field existed.[34] To investigate this possibility, I determine the cooling

of the lava lake and estimate the downward propagation ofthe Curie temperature inside the lake. Volcanism usuallystacks thin layers of lava in the process of building a thickvolcanic construct. This allows a given lava layer to coolefficiently from the top before being covered by the nextlava layer. Here an extreme case scenario is considered, byassuming that the entire crust of ∼30 km thickness beneaththe lowland [Zuber et al., 2000] is the depth of the lava lake.For the lowland model of 8000 km diameter this amounts toabout 15 × 108 km3 of basaltic lava. It is also assumed thatall of the lava is emplaced at once immediately after theimpact. This elongates the magnetization time of the lava

lake. I take the initial temperature of the lava to be 2270 K,about 750 K higher than its solidus, and the underlyinglithosphere is at solidus of 1350 K. It is assumed that thelava cools by heat conduction alone, at a much lower ratethan cooling by convection. Note that these extreme mea-sures lead to an over estimate of the cooling time of the lavalake. As the lava cools it crosses the melting temperatureand acquires latent heat of melting, set to 4 × 105 J/kg. Idetermine the thermal evolution of the upper 100 km ofMars consisting of the 30 km thick lava and 70 km thickunderlying lithosphere. Except for the initial temperatures ofthe lava and the lithosphere other physical parameters areassumed to be identical for the two sublayers; for the solidand liquid phases a density of rb = 3000 kg/m3, a specificheat of Cpb = 1200 J/kg/K, and a temperature‐dependentthermal conductivity Kb following Schatz and Simmons[1972] in the experimental model, equations (4a) and (4b).Approximating the lake by a laterally uniform horizontallayer, because the lake is much thinner than the radius ofMars, the one‐dimensional heat conduction equation

�bCpb@T=@t ¼ @ Kb@T=@z½ �=@z; ð9Þ

is solved subject to the temperature boundary conditions of230 K at the surface (z = 0 km) and 1523 K at the base (z =100 km). No radioactive heating is taken into accountbecause of the short period of thermal evolution considered.Figure 13 shows the temperature profiles at 2 Myr intervals.Also included in Figure 13 is the range of the magneticblocking temperature of magnetite, which is likely the mainmagnetic carrier in the Martian crust [e.g., Dunlop andArkani‐Hamed, 2005], spanning from the Curie tempera-ture of 840 K down to 740 K. The lava lake cools from topand bottom, but largely from the top. The sharp temperaturedifference initially existing between the lake and the

Figure 11. The intensity of the mean magnetic field generated in the convecting outer core of modelsA–D (Table 2). The dashed curve is for the case where the impactor iron layer is placed on the core.


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underlying region diminishes within about 10 Myr. Theentire lake cools through the magnetic blocking temperaturerange within 45–80 Myr. Figure 14 shows the depth to theCurie temperature, indicating that the rapid cooling of thelake from the top can result in precipitation of singledomainor pseudosingle‐domain magnetic particles, which canacquire significant thermoremanent magnetization in thepresence of a core dynamo. Note that possible minor vol-canism occurred at later times would create thin layers oflava which cool rapidly to the atmosphere without thermallydemagnetizing the underlying magnetized magma oceansignificantly.[35] A spherical shell with a constant thickness and uni-

formly distributed magnetic particles which is magnetizedby an internal magnetic field produces no magnetic fieldoutside [e.g., Runcorn, 1975]. However, being punctured bysubsequent impacts it can create appreciable edge effectsstrong enough to be observable at satellite altitudes of 100–400 km. There have been many large impact basins such asUtopia (diameter 3380 km) and Isidis (diameter 1350 km)created at around 4 Ga [Frey, 2008] that most likely punc-tured the entire thickness of the solidified lava lake about400 Myr after Borealis impact. However, no edge effects ofthese punctured regions have been detected by Mars GlobalSurveyor [e.g., Acuña et al., 1999; Lillis et al., 2008],emphasizing that the magma ocean is not magnetized andprobably no strong core field existed when the lake wascooling below its magnetic blocking temperature range. It isworth noting that Hellas basin which has punctured themagnetized crust in the southern hemisphere shows distinctedge effects at satellite altitudes [e.g., Mohit and Arkani‐Hamed, 2004].

[36] Borealis impact constrains the period when the strongcore dynamo of Mars magnetized the crust. Assuming thatthe impact occurred at 4.5 Ga, the core dynamo of Marsmust have resumed no earlier than around 4.4 Ga. On theother hand, the lack of magnetic signatures associated withgiant impact basins such as Utopia and Hellas that werecreated at around 4.1 Ga implies that the core dynamo musthave ceased no later than 4.1 Ga [Lillis et al., 2008].Therefore, the core dynamo was likely active for about 100Myr prior to Borealis impact and for about 300 Myr oncethe crippled core became active again. The strong magneticanomalies of Mars require the source bodies to carry ther-moremanent magnetization [Arkani‐Hamed, 2003; Dunlopand Arkani‐Hamed, 2005], which is acquired as they cooledthrough their magnetic blocking temperatures in the pres-ence of a strong core field. Whether the source bodies areintrusive [e.g., Hood and Richmond, 2002] or are formed bystacking successive volcanic layers [Arkani‐Hamed, 2005b],it may take ∼100 Myr for them to acquire magnetization inthe presence of a strong core field. This indicates that eachactive period of the core is long enough to magnetize sourcebodies of the large and extensive magnetic anomalies in thesouthern hemisphere with horizontal dimensions of over1000 km and estimated thicknesses of over 30 km [e.g.,Connerney et al., 1999; Nimmo and Gilmore, 2001; Arkani‐Hamed, 2002; Voorhies et al., 2002; Langlais et al., 2004].The magnetic anomalies of the southern hemisphere couldbe due to magnetization acquired partly prior to Borealisimpact and partly after 100 Myr following the impact.[37] The large impacts that have created Hellas, Isidis, and

Argyre basins have completely demagnetized the preexistingcrust underlying about 80% of the basins [Mohit and Arkani‐

Figure 12. The thermal evolution of the enlarged core of model A. The numbers on the curves denotetime after impact in Myr. The enlarged core radius is 1708 km and only the upper 100 km of the core isshown for clarity. Note that, although the impactor iron layer cools rapidly, it conducts appreciable heatdown to the stratified part of the core during the first ∼5 Myr; compare to Figure 8.


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Hamed, 2004]. It is expected that a much larger Borealisimpact excavated a major part of the preexisting crust anddemagnetized the remaining part, which explains the lack ofstrong magnetic signature over the entire lowland. The very

weak localized magnetic anomalies observed over the low-land may arise from the bottom topography of the lava lake[Zuber et al., 2000, Figure 2], which was created by thecollapse of the transient cavity and subsequent isotatic uplift

Figure 14. The depth to Curie temperature of magnetite (840 K) in the first 80 Myr after emplacement ofthe magma ocean. The horizontal dashed line is the bottom of the magma ocean.

Figure 13. The temperature profiles inside the magma ocean and the underlying lithosphere. Thenumbers on the curves are time after emplacement of the magma in Myr. The horizontal dash‐dotted lineshows the lower boundary of the ocean. The two vertical dashed lines specify the magnetic blockingtemperature range of magnetite.


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of the mantle. Deeper parts of the lake must have cooled atlater times and very slowly (see Figure 13), allowing mag-netic particles to grow and become multidomain with weakermagnetic properties. It is possible that deeper parts of thelake cooled below the magnetic blocking temperatures andacquired weak magnetization at a later time and in thepresence of the regenerated core dynamo.

9. Conclusions

[38] I investigated the heating of the Martian interior bythe putative Borealis impact using Pierazzo et al.’s [1997]shock pressure distribution model and the founderingshock heating model of Watters et al. [2009]. The northernlowland is modeled by a circular basin, and the effects ofthe impact velocity and the size of the impactor were esti-mated by using impact velocities of 6 and 10 km/s andmodel basin diameters of 7000 and 8000 km. The investi-gation spans four different time scales ranging from a fewminutes, when the shock waves propagate and heat themantle and core, to a few thousand years that it takes for thedifferentially heated core to stratify, to a few tens of thou-sand years for the diminishing of a possible preexisting coredynamo, and, finally, to several tens of millions of years forthe stratified core to cool and reestablish a global convec-tion and possibly regenerate a strong core dynamo. Themodel calculations lead to the conclusions that (1) impactheating in the upper mantle can dominate postimpact mantledynamics; (2) impact heating of the deeper parts of themantle may not suppress a preexisting core dynamo; (3)direct impact heating causes the core to become stratified,resulting in an upward increasing temperature distributionin the upper ∼300 km, which suppresses the thermal con-vection in the core and diminishes a possible preimpactthermally driven core dynamo in a few tens of thousandyears; (4) during subsequent cooling of the stratified core adownward‐propagating convection develops in the outercore which efficiently transfers heat to the mantle; (5) theconvection zone thickens gradually while the impact heat isbeing exhausted to the mantle, but very rapidly once majorpart of the heat is exhausted; (6) depending on the size andvelocity of the impactor, it takes on the order of 35–85 Myrfor the core to exhaust the impact heat and reestablish aglobal thermal convection and likely regenerate a strongcore dynamo; (7) a plausible superheated iron layer pro-duced on the core by the sinking iron content of theimpacting body is found to be too thin to generate a sig-nificant dynamo and create appreciable magnetic field at thesurface of Mars (the layer, however, delays the cooling ofthe core and regeneration of a strong dynamo for an addi-tional ∼40 Myr); and (8) Borealis impact causes consider-able melting in the mantle and results in pervasivevolcanism, filling the basin and creating a thick lava lake.The entire lake, ∼30 km thickness, cools below the Curietemperature within about 40–70 Myr, during which the coredynamo is crippled. It does not acquire thermoremanentmagnetization in the absence of a core dynamo. However,because of appreciable topographic relief at the bottom ofthe lake, deeper parts of the lake may cool slowly and bemagnetized by the regenerated core dynamo and create the

localized weak magnetic anomalies observed over thelowland.[39] The above conclusions must be regarded indicators,

rather than rigorous. This is even more so for the modelswith impact velocity of 6 km/s, because the Pierazzo et al.[1997] pressure distribution model may be less accurate atimpact velocities less than 10 km/s. The physical para-meters entering the model calculations are poorly con-strained, especially during the first 100–200 Myr of thehistory of Mars considered in this study. Whether the hugeBorealis impact actually occurred and whether it occurredat 4.5 Ga is not clear. The initial temperature of the Martianinterior immediately after the accretion is not well con-strained. The mantle viscosity which controls mantledynamics both before and after the impact is not knownaccurately. It may differ from the model used in this studyby a few orders of magnitude. The 70% partitioning of theradioactive elements to the mantle has appreciable effect onthe radioactive heating of the mantle, which in turn controlsmantle rheology. The acoustic velocities adopted are basedon the interpolation of the seismic velocities of Earth. Thecore viscosity of 1 m2/s used in the calculations seemsmuch higher than expected which required considerableamount of computer time if adopted, a common short-coming of all core dynamo models of terrestrial planets.However, the conclusion that Borealis impact, if itoccurred, could have crippled the core dynamo of Mars forabout 100 Myr seems plausible. The absence of a sizablecore dynamo when the basaltic crust of the northern low-land was cooling is in good agreement with the lack ofmagnetic signature of the lowland as established by theMars Global Surveyor data.

[40] Acknowledgments. This research is supported by NaturalSciences and Engineering Research Council of Canada. I would like tothank S. Stanley (University of Toronto) for many discussions we had inthe early stages of this study and A. Ghods (Institute for Advanced Studiesin Basic Science, Iran) for preparing Figures 3 and 4. I would also like tothank Wes Watters (Cornell University) and an anonymous reviewer fortheir constructive comments.

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J. Arkani‐Hamed, Department of Earth and Planetary Sciences, McGillUniversity, 3450 University St., Montreal, QC H3A 2A7, Canada.([email protected])


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