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the effect of a planet in a gaseous disk has been well studied both analytically and numerically @xcite .
tidal torques resulting from the gravitational perturbation of the planet lead to an exchange in angular momentum which creates a gap around the planet . to sustain the gap in viscous disks , there needs to be a balance between the tidal torques , which clear the gap , and viscous torques , which fills the gap @xcite .
thus the gap criterion is given by @xmath1 where @xmath2 and @xmath3 are the mass of the planet and star , @xmath4 is the @xcite viscosity parameter , @xmath5 is the disk scale height and @xmath6 is the semi - major axis of the planet . our previous simulations ( * ? ? ?
* hereafter bf05 ) show the settling rate  and hence the thickness of the dust layer  depends on grain size .
since the gap criterion depends on the disk scale height , this would suggest that it is easier to create and sustain a gap in the dust layer than in the gas .
there are a variety of observational signature of planetary gaps , including mid - infrared dips ( e.g. * ? ? ?
* ; * ? ? ?
* ) and direct scattered light @xcite and sub - millimetre observations of protoplanetary disks @xcite .
recent models have indicated that alma will be able to detect planetary gaps at sub - millimetre wavelengths to distances of 100  pc @xcite .
however , these models assume that the gas and dust are well - mixed within the disk and yet we know the dust - to - gas ratio changes substantially as grains settle to the mid - plane and migrate radially ( bf05 ) . as well as the gas - to - dust ratio varying throughout the disk , we expect that the effects of planetary gaps will be stronger in the dust phase than in the gas phase , which will further affect observations .
in this paper we study the formation of a gap triggered by an embedded planet in the dust layer of a protoplanetary disk .
we will study the effects of planet mass and grain size on gap formation and evolution in 3d dusty - gas protoplanetary disks .
we use our 3d , two - phase ( gas@xmath0dust ) , locally isothermal , non - self - gravitating code based on the smoothed particles hydrodynamics ( sph ) algorithm .
the dusty gas is approximated by two inter - penetrating flows that interact by aerodynamic drag . for the nebula parameters used in this study , we are in the epstein drag regime and hence @xmath7 where @xmath8 is the gas density
, @xmath9 is the ( spherical ) grain radius , @xmath10 is the sound speed , and @xmath11 is the velocity difference between dust and gas . for details of how the equations of motion and the density of the two fluids are calculated , we refer the reader to bf05 .    the dust particles are incompressible ( @xmath12 = constant ) and there is no grain evaporation or coagulation , nor any gas condensation .
all simulations presented consider just one ( spherical ) grain size at a time .
we set up a disk of gas and dust with a total mass of @xmath13 around a @xmath14 star with an embedded planet of mass @xmath2 at a distance of @xmath6 .
the dust phase is 1% of the total disk mass and the system is evolved for about 100 planetary orbits .
the disk equation of state is isothermal with constant vertical temperature and radial profile @xmath15 .
code units are set by @xmath16 and the isothermal sound speed at @xmath17 is @xmath18 .
the initial density profile is constant and the dust density is @xmath19 ( see below for details ) . the planet is treated as a point mass particle which moves under the gravitational influence of the star on a fixed circular orbit ( i.e. no migration ) .
simulations start with 50,000 gas and 50,000 dust particles .
particles are removed from the simulations if they cross the hill radius of the planet , get closer than 0.4 code units of the central star ( which sets the inner disk edge ) , or if they escape past 4 code units ( which sets the outer disk edge ) .    in this work we present the results of two different disk models : ( 1 ) a small , low mass disk close to the minimum mass solar nebula ( mmsn model ) , and ( 2 ) a classical t  tauri star disk ( ctts model ) .
the mmsn disk has a mass of 2.9 10@xmath20  @xmath21 and extends from 2  au to 20  au .
the standard mmsn model has a 1 jupiter mass ( @xmath22 ) planet on a circular orbit of radius 5.2  au in a disk containing grains 1  m in size and @xmath23  g cm@xmath20 .
the ctts disk mass is 0.01 @xmath21 and spans 16  au to 150  au in radius .
the standard ctts model has a @xmath25 planet on a circular orbit of radius 40  au in a disk containing grains 1  mm in size and @xmath26 g cm@xmath20 .    for both disks we start by running the standard model and compare the evolution of the gap in the gas and dust phases .
we then run a series of experiments to study the effect of grain size in the dust disk for both models , with @xmath27 1  cm , 10  cm and 1  m for the mmsn disk and @xmath28  @xmath29 m , 1  mm and 1  cm for the ctts disk .
( because the nebula conditions and particularly the density in the ctts and mmsn models are different , the grain sizes used in the two models are different in order to obtain similar values for the gas drag and hence dust settling and migration rates . )
this is followed by a series of experiments that study the effects of planetary mass on gap formation and evolution , with @xmath30 and 1.0 @xmath22 for the mmsn model and @xmath310.1 , 0.5 , 1.0 and 5.0 @xmath22 for the ctts model .
the results of the standard mmsn model is shown in fig .
[ fig - mmsn - standard ] .
the left panel shows the top - down ( @xmath32 ) and side - on ( @xmath33 ) view of the gas and dust disk morphologies .
while the planet opens a gap in the gas , the gap in the dust layer is much more striking .
the right panel of fig .
[ fig - mmsn - standard ] compares the evolution of the azimuthally averaged surface density profile of the gas and dust after 8.4 and 104 planetary orbits .
recent observations have suggested that massive planets at large distances from the star may exist , such as a 5  @xmath22 planet 30  au from lkca 15 @xcite and a 12.5  @xmath22 planet 135  au from gg  tau @xcite .
our standard ctts model has a 5  @xmath22 planet at 40  au and the results are shown in fig .
[ fig - ctts - standard ] .
for the nebular parameters used , such a massive planet almost completely empties the inner disk of both gas and dust ( though this is likely due to the large inner disk radius - see * ? ? ? * ) .
since the gap criterion is partially governed by the disk scale height , and the dust scale height varies with grain size , we ran a series of simulations to determine the effect of grain size on the gap .
three grain sizes are tested in both disk models : 1  cm , 10  cm and 1  m for the mmsn disk and 100  @xmath29 m , 1  mm and 1  cm for the ctts disk .
[ fig - grains3d ] shows how the gap morphology of both the mmsn and ctts disks vary with dust grains size .
we find that both the width and depth of the gap increases with increasing grain size .
finally we investigate the effect of the planetary mass on the evolution of the gap . for our mmsn disk with 1  m grains
, @xmath34 varies from 0.05  @xmath22 to 1  @xmath22 , and for our ctts disk containing 1  mm grains , @xmath34 varies from 0.1 , 0.5 , 1 to 5  @xmath22 .
[ fig - planet-2ddens ] shows the comparison of the surface density profiles for both models . for the mmsn disk ,
the gap is more striking in the dust than the gas , while in the ctts disk the inner disk appears depleted of both gas and dust , while the dust pile - up at the outer gap edge is clearly seen . for the ctts disk ,
no change is seen in the surface density for a 0.1 @xmath22  planet in either the gas or dust phase .
these results are in general agreement with the minimum planet mass required to produce a gap in the disk models of @xcite .
structures created by planets in dusty disks are more diverse than those created in the gaseous disks . with only aerodynamic drag , we find that it is possible to create disks with a large central hole or a ring .
@xcite also found that the presence of a planet can produce disks with a central hole for certain grain sizes .
our results have implications for observational predictions of protoplanetary disks hosting planets . @xcite and @xcite use results of 2d hydrodynamic simulations to produce synthetic images of protoplanetary disks , but these simulations assume that the gas and dust are well mixed , which our results clearly demonstrate is not the case .    because our general findings show than the gap is generally more striking in the dust disk
, we suggest that predictions of observations of protoplanetary disks are too pessimistic .
our results show that the density contrast around the gap can be very strong ( and the volume density can actually be greater than the gas volume density ) and this would be detectable with alma .
our simulations support the results of @xcite , as we clearly see density enhancements in the outer gap edge of the ctts simulations , even for the smaller grains sizes which would be responsible for the majority of the sub - mm and mm emission .
our results also support the predictions of @xcite that gaps created by @xmath35 planets in mmsn disks should be visible with alma . for a more detailed analysis
, we refer the reader to fouchet et al .
( 2007 ) .
while we see a clear density increase in the vicinity of the external 3@xmath362 resonance of our standard mmsn disk , we do not believe that particles are trapped in the resonance . plotting the dust eccentricity against semi - major axis
when drag was neglected clearly shows resonances as thin vertical lines and a v - shaped pattern at the edges of the gap .
however when drag is included , we find that the drag efficiently damps high eccentricities and the resonant signatures disappear . furthermore , while the dust pile up appears to coincide with the 3@xmath362 external resonance for the mmsn disk ( when gas drag is included ) , this is not true for the standard ctts disk  see fig .
[ fig - ctts - standard ] .
thus the accumulation of dust that we and other authors @xcite notice close to the outer gap edge is not due to resonant trapping .
the accumulation of grains at the external edge of the gap may , however , favour the growth of planetesimals in this high density region .
we have conducted a series of 3d numerical simulations of two - phase ( dust@xmath0gas ) protoplanetary disks to study the behaviour of the dust in the presence of a planet .
we ran a series of experiments with a minimum mass solar nebula disk as well as a larger , more massive classical t  tauri star disk , varying the grain size and the planet mass .
we find that gap formation is more rapid and striking in the dust layer than in the gas layer .
varying the grain size alone results in a variety of different structures , and for the ctts disk these differences will be detectable with alma . for low mass planets in our mmsn disk ,
a gap was found to open in the dust layer while not in the gas layer .
simulations like these can be used to help interpret observations to constraint the planet mass and grain sizes in protoplanetary disks .
we numerically model the evolution of dust in a protoplanetary disk using a two - phase ( gas @xmath0 dust ) smoothed particle hydrodynamics ( sph ) code , which is non - self - gravitating and locally isothermal . 
 the code follows the three dimensional distribution of dust in a protoplanetary disk as it interacts with the gas via aerodynamic drag . in this work , 
 we present the evolution of a disk comprising 1% dust by mass in the presence of an embedded planet for two different disk configurations : a small , minimum mass solar nebular ( mmsn ) disk and a larger , more massive classical t tauri star ( ctts ) disk . 
 we then vary the grain size and planetary mass to see how they effect the resulting disk structure .    
 we find that gap formation is much more rapid and striking in the dust layer than in the gaseous disk and that a system with a given stellar , disk and planetary mass will have a different appearance depending on the grain size and that such differences will be detectable in the millimetre domain with alma . for low mass planets in our mmsn models , a gap can open in the dust disk while not in the gas disk . 
 we also note that dust accumulates at the external edge of the planetary gap and speculate that the presence of a planet in the disk may facilitate the growth of planetesimals in this high density region .