Can narrow discs in the inner Solar system explain the four terrestrial planets?

A successful Solar system model must reproduce the four terrestrial planets. Here, we focus on (1) the likelihood of forming Mercury and the four terrestrial planets in the same system (a 4-P system); (2) the orbital properties and masses of each terrestrial planet; and (3) the timing of Earth's last giant impact and the mass accreted by our planet thereafter. Addressing these constraints, we performed 450 N-body simulations of terrestrial planet formation based on narrow protoplanetary discs with mass confined to 0.7-1.0 au. We identified 164 analogue systems, but only 24 systems contained Mercury analogues, and eight systems were 4-P ones. We found that narrow discs containing a small number of embryos with individual masses comparable to that of Mars and the giant planets on their current orbits yielded the best prospects for satisfying those constraints. However, serious shortcomings remain. The formation of Mercury analogues and 4-P systems was too inefficient (5 per cent and 2 per cent, respectively), and most Venus-to-Earth analogue mass ratios were incorrect. Mercury and Venus analogues also formed too close to each other (similar to 0.15-0.21 au) compared to reality (0.34 au). Similarly, the mutual distances between the Venus and Earth analogues were greater than those observed (0.34 versus 0.28 au). Furthermore, the Venus-Earth pair was not reproduced in orbital-mass space statistically. Overall, our results suggest serious problems with using narrow discs to explain the inner Solar system. In particular, the formation of Mercury remains an outstanding problem for terrestrial planet formation models.