RESONANCES OF MULTIPLE EXOPLANETS AND IMPLICATIONS FOR THEIR FORMATION

Among ∼160 of the multiple exoplanetary systems confirmed, about 30% of them have neighboring pairs with a period ratio ≤2. A significant fraction of these pairs are around mean motion resonance (MMR), and, more interestingly, peak around 2:1 and 3:2, with a clear absence of more closely packed MMRs with period ratios less than 4:3, regardless of planet masses. Here, we report numerical simulations demonstrating that such MMR behavior places important constraints on the disk evolution stage out of which the observed planets formed. Multiple massive planets (with mass ≥0.8 M {sub Jup}) tend to end up with a 2:1 MMR mostly independent of the disk masses, but low-mass planets (with mass ≤30 M {sub ⊕}) can have MMRs larger than 4:3 only when the disk mass is quite small, suggesting that the observed dynamical architecture of most low-mass-planet pairs was established late in the disk evolution stage, just before it was dispersed completely.