We modeled the 3-D structure of the Kuiper Belt dust cloud at four different dust production rates , incorporating both planet-dust interactions and grain-grain collisions using the collisional grooming algorithm .
Simulated images of a model with a face-on optical depth of \sim 10 ^ { -4 } primarily show an azimuthally-symmetric ring at 40–47 AU in submillimeter and infrared wavelengths ; this ring is associated with the cold classical Kuiper Belt .
For models with lower optical depths ( 10 ^ { -6 } and 10 ^ { -7 } ) , synthetic infrared images show that the ring widens and a gap opens in the ring at the location of of Neptune ; this feature is caused by trapping of dust grains in Neptune ’ s mean motion resonances .
At low optical depths , a secondary ring also appears associated with the hole cleared in the center of the disk by Saturn .
Our simulations , which incorporate 25 different grain sizes , illustrate that grain-grain collisions are important in sculpting today ’ s Kuiper Belt dust , and probably other aspects of the Solar System dust complex ; collisions erase all signs of azimuthal asymmetry from the submillimeter image of the disk at every dust level we considered .
The model images switch from being dominated by resonantly-trapped small grains ( “ transport dominated ” ) to being dominated by the birth ring ( “ collision dominated ” ) when the optical depth reaches a critical value of \tau \sim v / c , where v is the local Keplerian speed .