Correction to “Possible crippling of the core dynamo of Mars by Borealis impact”

[1] In the paper “Possible crippling of the core dynamo of Mars by Borealis impact” by Jafar Arkani-Hamed (Journal of Geophysical Research, 115, E12021, doi:10.1029/2010JE003602, 2010) the impact heating of Mars by the Borealis impact, which likely created the northern lowland basin, was calculated. Using the crater scaling laws [Holsapple, 1993; Melosh, 1989] the basin diameter was related to the size of the impactor. Following the impact, a nearly uniform shock pressure was generated inside an isobaric region in the mantle, outside which the shock pressure decreased exponentially with distance from the isobaric center following the average model of Pierazzo et al. [1997]. After crossing the core-mantle boundary, the shock wave travelled in the core where the shock pressure again decayed with distance travelled from the isobaric center according to Pierazzo et al.'s average model but with the physical parameters of the core. The corresponding impact temperature increase is obtained using the Foundering model of Watters et al. [2009]. [2] The impact-heated core stratified within a few tens of years and the possible pre-existing core dynamo decayed with the characteristic time of 10–15 kyr [Arkani-Hamed and Olson, 2010]. Shortly after the stratification, convection started in a thin layer in the outer core, the thickness of which increased in time as convection penetrated to deeper parts of the core until the entire core convected on a global scale. It took ∼60 Myr for the core to develop global convection and power a new core dynamo. [3] Here I describe a correction required in the calculation of the shock pressure distribution in the core. This correction is important because it increases the crippling time of the Martian core dynamo by a factor of larger than 4. The source of the required correction is the transmission coefficient of the shock wave across the core-mantle boundary (CMB), the ratio of the shock pressure at the top of the core to that at the base of the mantle. The transmission coefficient was determined on the basis of seismic ray theory [Aki and Richards, 2002, section 5.2]. It resulted in a sudden drop of shock pressure as passing from the mantle to the core, in contrast to the sudden jump of the pressure according to recent Hydrocode models [Ivanov et al., 2010; Bierhaus et al., 2011]. [4] Here I only present the results for an impact velocity of 10 km/s and a resulting model basin diameter of 8000 km, and compare the results with those of the previous model in the original paper. The results for the basin diameter of 7000 km presented in the previous paper are also changed accordingly. Other physical parameters of the model and numerical procedures are identical to those of the previous model. The proper boundary conditions for the shock wave transmission from the mantle to the core are determined on the basis of Hugoniot equations (see Arkani-Hamed and Ghods [2011] for details), constrained by the continuity of particle velocity across the boundary as well as the equality of reflected and refracted shock pressures at the boundary. Figure 1 shows the shock pressure distribution and the impact temperature increase in Mars. The present results for the mantle are identical to those of the previous model. Also, the main characteristics of the shock pressure distribution and the corresponding impact temperature increase in the core of the present model are similar to those of the previous model, except that their present magnitudes are higher, reflecting the effects of the new boundary conditions used at CMB. Although the shock pressure dropped crossing from mantle to the core in the previous model the temperature still jumped because of the smaller, by a factor of 2, specific heat of iron core relative to that of the silicate mantle. In the present model the temperature increases in the core are even more pronounced because the shock pressure jumps across the boundary, similar to those presented by hydrocode models of Ivanov et al. [2010] and Bierhaus et al. [2011]. Note that the shock pressure decreases monotonically inside the core as shock wave propagates, whereas the impact temperature first decreases and then slightly increases in the antipodal hemisphere. This is because the lithostatic pressure decreases much faster with radius in the antipodal hemisphere than the shock pressure, and the foundering shock heating model of Watters et al. [2009] is sensitive to the difference between the shock pressure and lithostatic pressure. [5] The higher impact energy partitioned to the core in the present model requires longer time for the core to exhaust the heat to the mantle. While the outer core convects heat to the mantle, an appreciable amount of heat is also conducted downward to the deeper parts of the stratified core. This further enhances thermal stability deep in the core. The thickness of the convecting outer core increases in time as convection penetrates to deeper parts of the core until the entire core convects on a global scale (Figure 2). It takes ∼250 Myr in the present model, compared to ∼60 Myr of the previous model, for the core to cool and the temperature to become super adiabatic, allowing global convection to resume. [6] The strongly convecting outer core with high electrical conductivity is capable of generating magnetic field, which increases in intensity as the layer thickness increases. The mean magnetic field generated inside the convecting outer core (Figure 2) is calculated using the scaling equation of Christensen and Aubert [2006], as described in the previous paper. The dipole field at CMB is 3–10 times weaker than the mean field inside the layer and field decays by a factor of (Rc3/Rs3 ∼ 0.13) as it propagates from the core of radius Rc = 1700 km to reach the surface of Mars at radius Rs = 3390 km. The dipole field at the surface of Mars is very weak during the crippling period but becomes comparable to that of the Earth field at the surface when global core convection occurs. Figure 2 shows that Borealis impact could have crippled the core dynamo of Mars for ∼250 Myr, compared to ∼60 Myr of the previous estimate. [7] This research is supported by Natural Sciences and Engineering Research Council of Canada (NSERC).

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