Leaky Dust Traps in Planet-Embedded Protoplanetary Disks

From the survival of dust disks for a few Myr to the establishment of chemical dichotomy, dust traps are expected to play a pivotal role in sculpting protoplanetary disks and the early planet formation process. These traps however may not be perfect as evidenced by the detection of gas and dust inside the gaps and cavities of structured disks. Using two-fluid hydrodynamic global simulations in both two-dimensions (2D) and three-dimensions (3D), we directly compute the dynamics of dust grains as they aerodynamically interact with the disk gas that is being perturbed by an embedded planet of varying mass. In both 2D and 3D, we find the dust trap to be more leaky for lower mass planet and for higher turbulent $\alpha$. More crucially, we find the fraction of the dust mass that remain trapped within the pressure bump can be up to an order of magnitude more reduced in 3D vs. 2D with all else equal. Our simulations show a complex behavior of dust radial motion that is both azimuthally and poloidally non-uniform, with the overall dynamics dominated by the dust coupling to the gas flow even for relatively high St = 0.1. The leaky traps we find suggest pebble isolation mass is likely not truly isolating and that gap-opening planets do not establish as an unconditional impermeable barrier. Our findings have implications for recent JWST MINDS results, which show that volatiles, including water, are present in the inner regions of disks hosting outer dust rings.