  The timeline of the lunar bombardment in the first Gy of the Solar System
remains unclear. Some basin-forming impacts occurred 3.9-3.7Gy ago. Many other
basins formed before, but their exact ages are not precisely known. There are
two possible interpretations of the data: in the cataclysm scenario there was a
surge in the impact rate approximately 3.9Gy ago, while in the accretion tail
scenario the lunar bombardment declined since the era of planet formation and
the latest basins formed in its tail-end. Here, we revisit the work of
Morbidelli et al.(2012) that examined which scenario could be compatible with
both the lunar crater record in the 3-4Gy period and the abundance of highly
siderophile elements (HSE) in the lunar mantle. We use updated numerical
simulations of the fluxes of impactors. Under the traditional assumption that
the HSEs track the total amount of material accreted by the Moon since its
formation, we conclude that only the cataclysm scenario can explain the data.
The cataclysm should have started ~3.95Gy ago. However we show that HSEs could
have been sequestered from the lunar mantle due to iron sulfide exsolution
during magma ocean crystallization, followed by mantle overturn. Based on the
hypothesis that the lunar magma ocean crystallized about 100-150My after Moon
formation, and therefore that HSEs accumulated in the lunar mantle only after
this time, we show that the bombardment in the 3-4Gy period can be explained in
the accretion tail scenario. This hypothesis would also explain why the Moon
appears so depleted in HSEs relative to the Earth. We also extend our analysis
of the cataclysm and accretion tail scenarios to the case of Mars. The
accretion tail scenario requires a global resurfacing event on Mars ~4.4Gy ago,
possibly associated with the formation of the Borealis basin, and it is
consistent with the HSE budget of the planet.
