By carrying out two-dimensional two-fluid global simulations , we have studied the response of dust to gap formation by a single planet in the gaseous component of a protoplanetary disk - the so-called “ dust filtration ” mechanism .
We have found that a gap opened by a giant planet at 20 AU in a \alpha =0.01 , \dot { M } = 10 ^ { -8 } M _ { \odot } yr ^ { -1 } disk can effectively stop dust particles larger than 0.1 mm drifting inwards , leaving a sub-millimeter dust cavity/hole .
However , smaller particles are difficult to filter by a planet-induced gap due to 1 ) dust diffusion , and 2 ) a high gas accretion velocity at the gap edge .
Based on these simulations , an analytic model is derived to understand what size particles can be filtered by the planet-induced gap edge .
We show that a dimensionless parameter T _ { s } / \alpha , which is the ratio between the dimensionless dust stopping time and the disk viscosity parameter , is important for the dust filtration process .
Finally , with our updated understanding of dust filtration , we have computed Monte-Carlo radiative transfer models with variable dust size distributions to generate the spectral energy distributions ( SEDs ) of disks with gaps .
By comparing with transitional disk observations ( e.g .
GM Aur ) , we have found that dust filtration alone has difficulties to deplete small particles sufficiently to explain the near-IR deficit of moderate \dot { M } transitional disks , except under some extreme circumstances .
The scenario of gap opening by multiple planets studied previously suffers the same difficulty .
One possible solution is by invoking both dust filtration and dust growth in the inner disk .
In this scenario , a planet induced gap filters large dust particles in the disk , and the remaining small dust particles passing to the inner disk can grow efficiently without replenishment from fragmentation of large grains .
Predictions for ALMA have also been made based on all these scenarios .
We conclude that dust filtration with planet ( s ) in the disk is a promising mechanism to explain submm observations of transitional disks but it may need to be combined with other processes ( e.g .
dust growth ) to explain the near-IR deficit of some systems .