Did tidal deformation power the core dynamo of Mars?

We first show that 7 out of the 20 giant impact basins of Mars recently reported by Frey [Frey, H., 2008. Geophys. Res. Lett. 35. L13203] trace a great circle on Mars. The other five basins trace another great circle and still the other three basins trace yet another great circle. The latter great circle is in good agreement with the pre-Tharsis equator of Mars that is estimated from modeling crustal magnetic anomalies [Arkani-Hamed, J., 2001. Geophys. Res. Lett. 28, 3409–3412] and diagonalizing the moment of inertia of Mars after removing the loading effects of Tharsis bulge [Sprenke, K.F., Baker, L.L., Williams, A.F., 2005. Icarus 174, 486–489]. It is shown in this paper that the three great circles were likely the equatorial plane of Mars at certain times and Mars experienced appreciable polar wander. The great circles also indicate that the asteroids that created the basins were satellites of Mars whose orbits decayed in time through spin–orbit coupling with tidally deforming Mars, and eventually impacted on the planet creating the giant basins at around 4 Ga. The orbital dynamics of four largest asteroids show that they could have orbited Mars for several hundred million years if they were retrograde satellites. Continual elliptical straining of otherwise circular fluid streamlines of the liquid core of Mars by tidal deformation could have exerted a strong strain that was large enough to overcome dissipation and excite the elliptical instability inside the core. We investigate the physical properties of the martian core that are required to allow the tidal deformation to power the core dynamo, i.e., the growth time of the elliptical instability to become shorter than the dissipation time. The tidal energy dissipation rate inside Mars caused by even only one of the 4 largest asteroids is found to be over two orders of magnitude greater than the magnetic energy dissipation rate in the core, indicating that if only one of the 4 largest asteroids were orbiting in retrograde sense, it would have likely powered the core dynamo of Mars for several hundred million years.