Impact chronology of leftover planetesimals

Abstract

After the formation of the Moon the terrestrial planets were pummelled by impacts from planetesimals left over from terrestrial planet formation. This work attempts to reproduce the impact rates set by modern crater chronologies using leftover planetesimals from three different dynamical models of terrestrial planet formation. I ran dynamical simulations for 1 billion years using leftover planetesimals from the Grand Tack, Depleted Disc and Implantation models of terrestrial planet formation with the GENGA N-body integrator. I fit the cumulative impacts on the Earth and Mars using a function that is a sum of exponentials with different weighing factors and e-folding times. Most fits require three or four terms. The fitted timescales cluster around t1=10 Myr, t2=35 Myr, t3=100 Myr and t4>200 Myr. I attribute them to dynamical losses of planetesimals through different mechanisms: high-eccentricity Earth crossers and the nu6 secular resonance, Earth crossers, Mars crossers, and objects leaking on to Mars crossing orbits from beyond Mars. I place a constraint on the initial population using the known Archean terrestrial spherule beds, and I conclude that the Archean impacts were mostly created by leftover planetesimals. The inferred mass in leftover planetesimals at the time of the Moon's formation was about 0.015 Earth masses. The third time constant is comparable to that of modern crater chronologies. As such, the crater chronologies are indicative of impacts by an ancient population of Mars crossers. The initial perihelion distribution of the leftovers is a major factor in setting the rate of decline: to reproduce the current crater chronologies the number of Earth crossers at the time of the Moon's formation had to be at most half of the Mars crossers. These results together place constraints on dynamical models of terrestrial planet formation.

Accepted in Astronomy and Astrophysics

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