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While numerical simulations have been playing a key role in the studies ofplanet-disk interaction, testing numerical results against observations hasbeen limited so far. With the two directly imaged protoplanets embedded in itscircumstellar disk, PDS 70 offers an ideal testbed for planet-disk interactionstudies. Using two-dimensional hydrodynamic simulations we show that theobserved features can be well explained with the two planets in formation,providing strong evidence that previously proposed theories of planet-diskinteraction are in action, including resonant migration, particle trapping,size segregation, and filtration. Our simulations suggest that the two planetsare likely in 2:1 mean motion resonance and can remain dynamically stable overmillion-year timescales. The growth of the planets at $10^{-8}-10^{-7}~M_{\rmJup}~{\rm yr}^{-1}$, rates comparable to the estimates from H$\alpha$observations, does not destabilize the resonant configuration. Large grains arefiltered at the gap edge and only small, (sub-)$\mu$m grains can flow to thecircumplanetary disks and the inner circumstellar disk. With the sub-millimetercontinuum ring observed outward of the two directly imaged planets, PDS 70provides the first observational evidence of particle filtration by gap-openingplanets. The observed sub-millimeter continuum emission at the vicinity of theplanets can be reproduced when (sub-)$\mu$m grains survive over multiplecircumplanetary disk gas viscous timescales and accumulate therein. One suchpossibility is if (sub-)$\mu$m grains grow in size and remain trapped inpressure bumps, similar to what we find happening in circumstellar disks. Wediscuss potential implications to planet formation in the solar system andmature extrasolar planetary systems.

An Ideal Testbed for Planet-disk Interaction: Two Giant Protoplanets in Resonance Shaping the PDS 70 Protoplanetary Disk