strong remanent crustal magnetization inferred from magnetometer and electron reflectometer observations on mars global surveyor suggests that mars had a core dynamo in its early history , which stopped during the noachian era [ acua et al . , 1999 ; lillis et al . , 2008 ] . over 30 giant noachian impact basins of diameters > 1000 km ( exposed and buried ) based on the strength of postimpact remagnetization in the crustal rocks of these basins , lillis et al . [ , ] , for example , suggested that the global magnetic field vanished toward the end of this basin formation sequence . in particular , acidalia is strongly magnetized , whereas the younger utopia basin is completely demagnetized , indicating that the dynamo stopped sometime between the two impact events . these results raise the intriguing question of whether the timing of the basins was merely coincidental or the basin - forming impacts caused the death of the martian dynamo . several studies have been made to link these impacts and the energy for dynamo action . suggested that shock heating of the mantle by basin - forming impacts could retard core - mantle heat flow to a degree unfavorable for core convection , thus terminating the dynamo . arkani - hamed and olson , arkani - hamed , and roberts and arkani - hamed   argued that the impact heating of the core and the lateral mixing would result in stable stratification of the core material , thus reducing the buoyancy flux to a level insufficient to sustain an active dynamo for more than 100 myr . to interpret the sudden termination ( i.e. , in a period much shorter than its lifetime ) of the martian dynamo , kuang et al .   argued that the martian dynamo could be subcritical in its later stage , and perturbations to the heat flux across the core - mantle boundary ( cmb ) from the impacts could easily tip the delicate balances among the buoyancy force , the lorentz force and the coriolis force in the core , and thus destroy the subcritical dynamo instantly . the above interpretations focus only on one possible scenario that heating of the core by the impacts could reduce the energy to a level below that needed to drive a core dynamo [ roberts et al . , 2009 ; arkani - hamed and olson , 2010 ; arkani - hamed , 2012 ] . however , it is also possible that depending on the core properties and impact angles , the impacts may only create a significant thermal heterogeneity in the mantle , not a substantial heating of the entire core [ e.g. , schultz et al . 2008 ; sreenivasan and jellinek , 2012 ] demonstrated that cmb thermal heterogeneity can play a major role in a supercritical martian dynamo . since the martian dynamo could inevitably be subcritical toward its end [ kuang et al . , 2008 ] , and since subcritical dynamos differ substantially from supercritical dynamos [ sreenivasan and jones , 2011 ] , it is necessary to address a very important question : could the impact - induced thermal heterogeneity terminate a subcritical martian dynamo ? the answer will provide an important piece of the puzzle on the ending of the martian dynamo . here we investigate via numerical simulation of subcritical dynamos , whether the lateral heterogeneity , rather than the total magnitude of the impact - induced thermal perturbation , may be sufficient to terminate the dynamo . we use the same dynamo model as kuang et al .   and jiang and kuang   but with impact - induced heterogeneous heat flux across the cmb . in this model , the buoyancy force , the fluid viscosity , the magnetic diffusivity , and the thermal conductivity are given by the nondimensional rayleigh number rth , the ekman number e , the magnetic rossby number ro , and the modified prandtl number p , respectively . except rth , the numerical resolution is much higher , with the maximum 180 spherical harmonic degrees , and 160 radial grid points , but the subcritical dynamo region remains significant : the critical point to terminate a subcritical dynamo is rcr  1900 , and the critical point for the onset of the dynamo is rcf  2600 . impact - induced thermal perturbations in this study follow those of roberts et al . . the mantle is heated by a shock wave emanating from the impact location at the colatitude i and the longitude i on the surface . assuming that melt production does not consume any waste heat 2009 ] where p is the difference between the shock pressure ps and the lithostatic pressure p0 , c and s are the intercept and slope of the equation of state relating the shock and particle velocities , 0 is the mean density , and the shock pressure ps and thus t decay rapidly with the distance from the impact center [ e.g. , pierazzo et  al . , this t is added to a prevailing temperature field in mantle convection simulation with citcoms model [ zhong et al . , mathematically , the postimpact total heat flux , scaled by the uniform mean heat flux h0 , across the cmb can be written as where h is the normalized impact - induced heat flux perturbation ( as shown in figure  1 ) , i is the relative heterogeneity amplitude , and c.c . an example of the normalized impact - induced heat flux perturbation h in 3 at the cmb due to an impact centered at i=45. the blue and orange represent the negative and positive heat flux anomaly ( relative to the background uniform heat flux ) out of the cmb , respectively . for dynamo simulation , ht is assumed time invariant , since the dynamo timescales are much shorter than those of mantle convection . for example , the magnetic diffusion time 40,000 years , many orders of magnitude shorter than those of the mantle convection ( tens of myr ) . because dynamo solutions are periodic in azimuth ( with the z axis as the mean rotation axis ) , we can also assume without loss of generality that i=0 , i.e. , impact locations are specified only via i , which varies from 0 ( the north pole ) to 90 ( the equator ) . for easier numerical implementation , we divide the total temperature t into two parts : where ta is a steady , conducting distribution with the boundary condition ( ta/r)cmb=ht and the time varying  is solved via the energy equation with the boundary condition ( /r)cmb=0 . from now on , unless otherwise stated , all quantities are nondimensional . survivability of subcritical dynamos with 3 is examined as follows : all simulations start from the same initial state that is a well - established subcritical dynamo solution without the heterogeneity ( i=0 ) . this ensures that all subsequent changes of the dynamos are only caused by the implementation of 3 . the dynamo is terminated if , to leading order , the rms field strength decays exponentially in time , i.e. , b  b0e (  > 0 ) . given an impact location i , the amplitude i increases from 0 to a critical value  where the subcritical dynamo could no longer be sustained . to be consistent with the boussinesq approximation in our model thus , we set up an upper limit i  0.3 which can account for up to 90% of large basin - forming impacts [ see roberts et al . 
 2009 , figure 3 ] . we conclude that within our model capacity , the impact will not kill the subcritical dynamo if  > 0.3 . the effects of the impact - induced cmb thermal heterogeneity 3 on subcritical dynamos are summarized in figure  2 . in this figure , each circle represents a subcritical dynamo simulation result : filled circles are the dynamos that survived the impacts and the open circles are those disabled by the impacts . the heterogeneity 3 properties define the coordinates : the amplitude i is the radius , and the location ( 90i ) is the polar angle . from the figure one can observe that this suggests a critical boundary : if located outside the boundary , the heterogeneity 3 could not stop the subcritical dynamos ; otherwise , it could terminate the dynamos , provided that i  . in summary , subcritical dynamos could easily survive the impacts near the polar regions but will be more likely killed by those near the equator . for example , sreenivasan and jellinek   showed that ( supercritical ) dynamos are more easily killed by thermal heterogeneity near the equator than near the polar regions . the solid circles are the dynamos that survived the impacts , while the open circles are those killed by the impacts . the polar coordinates of the symbols describe the heterogeneity properties : the radius is the relative amplitude i of the heterogeneity , and the polar angle is the impact center latitude ( 90i ) . to better understand how the thermal heterogeneity 3 could terminate a subcritical dynamo , we examine the dynamo field properties and its generation mechanisms . as shown in figure  3 , the poloidal magnetic field of the subcritical dynamos is hemispherically asymmetric at the cmb : the temporal mean radial component   is very strong in the southern hemisphere ( see figure  3a ) , while its latitudinal rms distribution ( 6)is nearly an order of magnitude stronger in the southern hemisphere than in the northern hemisphere ( figure  3b ) . we can also observe from the figure that the thermal heterogeneity 3 reduces significantly the field strength but less so to the hemispherical asymmetry . for example ,   with the heterogeneity of i = 60 and i = 0.3 ( the dotted line in figure 3b ) is nearly one third of that without heterogeneity ( the solid line in the figure ) . but the latitudinal location of the maximum magnitude is only shifted by approximately 10 toward the equator . the properties of the radial magnetic field br at the cmb : ( a ) the temporal mean   with i = 0.3 and i = 60 and ( b ) the azimuthal rms field strength 
 7 with i = 0 ( the solid line ) , i = 0.05 and i=0 ( the dashed line ) , and i = 0.3 and i = 60 ( the dotted line ) . the field hemispherical asymmetry implies that of the dynamo action in the core and can be shown through the magnetic energy variation in the core derived from the magnetic induction where v is the fluid velocity and vr is its radial component . equation 8 shows that the total time variation of the magnetic energy   ( the left side ) is determined by the dynamo action fd  br(b)vr and the ohmic dissipation f  br(b)r . for an active dynamo , fd>0 in part of the core ( hereafter defined as the dynamo region ) . because the flow helicity h  v(v ) is critical for dynamo action [ e.g. , moffatt , 1978 ] , we analyze fd and h together . in figure  4 we show the temporal means   and   in the midcore with the heterogeneity i = 0.05 and i = 90 ( the equator ) . in addition , both display striking northeast - southwest stripes across midlatitudes , indicating strong correlations between h and fd . their latitudinal distributions 9are shown in figure  5 . from the figure we observe similar strong hemispherical asymmetries . in particular , as shown in figure  5b , 3 does not affect much the hemispherical asymmetry but reduces significantly the helicity   in the core and thus the effectiveness of the dynamo action . the dynamo action and the helicity of the subcritical dynamo with the heterogeneity i = 0.05 and i = 90 : ( a ) the temporal mean dynamo action   in midcore and ( b ) the temporal mean helicity   at the same radial position . the integrated ( a ) dynamo action   and ( b ) the helicity   defined in 9 of two subcritical dynamos : one without thermal heterogeneity i=0 ( the solid lines ) and the other with the heterogeneity i=0.05 and i=90 ( the dotted lines ) . our simulation results demonstrate clearly that subcritical dynamos are prone to impact - induced thermal heterogeneity 3 at the cmb , especially those centered near the equator . we examine the implications of our results for the termination of the martian dynamo by focusing on several known giant impact basins on mars . [ , ] , the martian dynamo likely ceased between the formation of acidalia and utopia basins : the postimpact remagnetization in the acidalia basin is likely more than an order of magnitude stronger than that in the utopia basin . thus , our results may suggest that utopia ( or an earlier large basin - forming impact ) could have killed the dynamo , since the dynamo magnetic decay timescales are much shorter than those of the uppermost crust to cool down below the curie point of any likely magnetic mineral [ dunlop and arkani - hamed , 2005 ] . however , utopia is currently centered approximately at i  46. if we consider only the impact - induced thermal heterogeneity , then based on our simulation results that i > 60 for terminating the subcritical dynamos , it would not be able to kill the martian dynamo . this could be invalid for two scenarios : either the utopia impact could have heated up the entire core substantially such that the available buoyancy force is insufficient to drive a subcritical dynamo or a polar reorientation could have occurred after the impact to move the impact center to the current high - latitude location . since the initial heterogeneous heating of the core can be well mixed convectively in a transient period t  /rm ( e.g. , 100  years with a typical magnetic reynolds number rm  400 in the core [ kuang et al . , 2008 ] ) , the core heating could be effectively described by a smaller mean heat flux h0 in 3 across the cmb after t . arkani - hamed and olson   found similar horizontal mixing timescales and a much longer lived stably stratified layer at the top of the core . the latter would not change our results qualitatively . for the second scenario , a lower bound since the subcritical dynamos will survive an impact more than 30 away from the equator , this suggests that a postimpact 16 northward polar reorientation is necessary for terminating the dynamo by utopia . it is interesting to note that studies of retention ages [ frey , 2008 ] indicate a systematic sawtooth time variation pattern in the latitudinal locations of the largest basins on mars ( see figure  6 ) , suggesting postimpact polar reorientations . basin center latitude versus n(300 ) crater retention age for 30 very large basins on mars ( with diameters larger than 1000  km ) [ frey , 2008 ] . these follow a systematic pattern in their latitudes that could be explained if the very largest impacts tried to reorient mars by migrating toward the poles and subsequent impacts occurred mostly near the equator . it is possible that events other than the large basin - forming impacts could end the martian dynamo . suggested an even larger polar reorientation from internal mass redistribution associated with , e.g. , formation of tharsis . the tharsis plateau is younger than the utopia basin , but its formation could start much earlier . provided that the tharsis plume was near the equator , the thermal heterogeneity associated with the plume could also kill the martian dynamo , as suggested by our results and by sreenivasan and jellinek . however , other studies also suggest tharsis plume migration during its uprising [ e.g. , rmek and zhong , 2012 ] . these certainly bring additional complications on the cause of the martian dynamo termination . there are also debates on the timing of the martian dynamo [ hood et al . , these may suggest that processes not related to impacts , e.g. , reduction of heat flux across the cmb over time , could eventually shut down the dynamo . regardless , our study finds that subcritical dynamos are very sensitive to small thermal heterogeneity across the cmb . if such heterogeneity kills the martian dynamo , then the magnetic timing will place a strong constraint on the location of the heterogeneity and on possible polar reorientation of mars . martian dynamo can be terminated by impact - induced thermal heterogeneity magnetic field morphology remains intact martian dynamo timing places a lower bound on paleopolar reorientation
the observed strong remanent crustal magnetization at the surface of mars suggests an active dynamo in the past and ceased to exist around early to middle noachian era , estimated by examining remagnetization strengths in extant and buried impact basins . 
 we investigate whether the martian dynamo could have been killed by these large basin - forming impacts , via numerical simulation of subcritical dynamos with impact - induced thermal heterogeneity across the core - mantle boundary . 
 we find that subcritical dynamos are prone to the impacts centered on locations within 30 of the equator but can easily survive those at higher latitudes . our results further suggest that magnetic timing places a strong constraint on postimpact polar reorientation , e.g. , a minimum 16 polar reorientation is needed if utopia is the dynamo killer .