Accepted for ApJ Letters 2014 May 29 Preprint typeset using LATEX style emulateapj v. 5/2/11 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), 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 sim-ulations 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 MJup) tend to end up with a 2:1 MMR mostly independent of the disk masses but low-mass planets (with mass ≤ 30 M⊕) 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. Subject headings: planet-disk interactions — planetary systems- protoplanetary disks 1