Imaging polarimetry is a powerful tool for imaging faint circumstellar material. For a correct analysis of observations we need to fully understand the effects of dust particle parameters, as well as the effects of the telescope, atmospheric seeing, and assumptions about the data reduction and processing of the observed signal. Here we study the major effects of dust particle structure, size-dependent grain settling, and instrumental properties. We performed radiative transfer modeling using different dust particle models and disk structures. To study the influence of seeing and telescope diffraction we ran the models through an instrument simulator for the ExPo dual-beam imaging polarimeter mounted at the 4.2m William Herschel Telescope (WHT). Particle shape and size have a strong influence on the brightness and detectability of the disks. In the simulated observations, the central resolution element also contains contributions from the inner regions of the protoplanetary disk besides the unpolarized central star. This causes the central resolution element to be polarized, making simple corrections for instrumental polarization difficult. This effect strongly depends on the spatial resolution, so adaptive optics systems are needed for proper polarization calibration. We find that the commonly employed homogeneous sphere model gives results that differ significantly from more realistic models. For a proper analysis of the wealth of data available now or in the near future, one must properly take the effects of particle types and disk structure into account. The observed signal depends strongly on the properties of these more realistic models, thus providing a potentially powerful diagnostic. We conclude that it is important to correctly understand telescope depolarization and calibration effects for a correct interpretation of the degree of polarization.
We apply the theory of radiative torque (RAT) alignment for studying protoplanetary disks around a T-Tauri star and perform 3D radiative transfer calculations to provide the expected maps of polarized radiation to be compared with observations, such as with ALMA. We revisit the issue of grain alignment for large grains expected in the protoplanetary disks and find that mm-sized grains at midplane do not align with the magnetic field as the Larmor precession timescale for such large grains becomes longer than the gaseous damping timescale. Hence, for these grains the RAT theory predicts that th…
Small solids embedded in gaseous protoplanetary disks are subject to strong dust-gas friction. Consequently, tightly-coupled dust particles almost follow the gas flow. This near conservation of dust-to-gas ratio along streamlines is analogous to the near conservation of entropy along flows of (dust-free) gas with weak heating and cooling. We develop this thermodynamic analogy into a framework to study dusty gas dynamics in protoplanetary disks. We show that an isothermal dusty gas behaves like an adiabatic pure gas; and that finite dust-gas coupling may be regarded as an effective heating/cool…
We study the dynamics of a viscous protoplanetary disc hosting a population of dust grains with a range of sizes. We compute steady-state solutions, and show that the radial motion of both the gas and the dust can deviate substantially from those for a single-size dust population. Although the aerodynamic drag from the dust on the gas is weaker than in the case where all grains are optimally coupled to the gas, the cumulative "back-reaction" of the dust particles can still alter the gas dynamics significantly. In typical protoplanetary discs, the net effect of the dust back-reaction decreases …
Tidal interactions between the embedded planets and their surrounding protoplanetary disks are often postulated to produce the observed complex dust substructures, including rings, gaps, and asymmetries. In this Letter, we explore the consequences of dust coagulation on the dust dynamics and ring morphology. Coagulation of dust grains leads to dust size growth which, under typical disk conditions, produces faster radial drifts, potentially threatening the dust ring formation. Utilizing 2D hydrodynamical simulations of protoplanetary disks which include a full treatment of dust coagulation, we …
More than a decade of dedicated experimental work on the collisional physics of protoplanetary dust has brought us to a point at which the growth of dust aggregates can - for the first time - be self-consistently and reliably modelled. In this article, the emergent collision model for protoplanetery dust aggregates (Güttler et al. 2010) as well as the numerical model for the evolution of dust aggregates in protoplanetary disks (Zsom et al. 2010) are reviewed. It turns out that, after a brief period of rapid collisional growth of fluffy dust aggregates to sizes of a few centimeters, the protopl…
The Earth is known to be depleted in volatile lithophile elements in a fashion that defies easy explanation. We resolve this anomaly with a model that combines the porosity of collisionally grown dust grains in protoplanetary disks with heating from FU Orionis events that dramatically raise protoplanetary disk temperatures. The heating from an FU Orionis event alters the aerodynamical properties of the dust while evaporating the volatiles. This causes the dust to settle, abandoning those volatiles. The success of this model in explaining the elemental composition of the Earth is a strong argum…
Dust growth is often neglected when building models of protoplanetary disks due to its complexity and computational expense. However, it does play a major role in shaping the evolution of protoplanetary dust and planet formation. In this paper, we present a numerical model coupling 2-D hydrodynamic evolution of a protoplanetary disk, including a Jupiter-mass planet, and dust coagulation. This is obtained by including multiple dust fluids in a single grid-based hydrodynamic simulation and solving the Smoluchowski equation for dust coagulation on top of solving for the hydrodynamic evolution. We…
Planet formation is thought to begin with the growth of dust particles in protoplanetary disks from micrometer to millimeter and centimeter sizes. Dust growth is hindered by a number of growth barriers, according to dust evolution theory, while observational evidence indicates that somehow these barriers must have been overcome. The observational evidence of dust traps, in particular the Oph IRS 48 disk, with the Atacama Large Millimeter/submillimeter Array (ALMA) has changed our view of the dust growth process. In this article I review the history of dust trapping in models and observations.
The formation of planetesimals via gravitational instability of the dust layer in a protoplanetary disks demands that there be local patches where dust is concentrated by a factor of $\sim$ a few $\times 10^3$ over the background value. Vortices in protoplanetary disks may concentrate dust to these values allowing them to be the nurseries of planetesimals. The concentration of dust in the cores of vortices increases the dust-gas ratio of the core compared to the background disk, creating a "heavy vortex." In this work, we show that these vortices are subject to an instability which we have cal…
We carried out two-dimensional high-resolution simulations to study the effect of dust feedback on the evolution of vortices induced by massive planets in protoplanetary disks. Various initial dust to gas disk surface density ratios ($0.001$ -- $0.01$) and dust particle sizes (Stokes number $4\times10^{-4}$ -- $0.16$) are considered. We found that while dust particles migrate inwards, vortices are very effective in collecting them. When dust density becomes comparable to gas density within the vortex, a dynamical instability is excited and it alters the coherent vorticity pattern and destroys …
Telescopes mounted with polarizers can study the neutral points of the Earths atmosphere, the solar corona, the surface of planets/moons of the Solar System, distant stars, galaxies and nebulae. These examples demonstrate well that polarimetry is a useful technique to gather astronomical information from spatially extended phenomena. There are two enigmatic celestial objects that can also effectively be studied with imaging polarimetry, namely the Kordylewski dust clouds (KDCs) positioned around the L4 and L5 triangular Lagrangian libration points of the Earth-Moon system. Although in 1961 the…
In this paper, we reexamine the possibility of shear-driven turbulence during sedimentation of dust grains in the protoplanetary disk. The shear-driven turbulence is expected to occur before the onset of the gravitational instability for MMSN model. While according to previous studies without taking account of growth of dust grains, with the larger abundance of dust grains, the gravitational instability is indicated to occur before shear-driven turbulence. In this paper, the case with dust growth is considered, and it is found that the Kelvin-Helmholtz instability tends to occur before the gra…
Aims. We aim to constrain the size and porosity of ejected dust particles from comet 252P/LINEAR and their evolution near the perihelion via near-infrared multiband polarimetry. A close approach of the comet to the Earth in March 2016 (~0.036 au) provided a rare opportunity for the sampling of the comet with a high spatial resolution. Methods. We made NIR JHKS bands polarimetric observations of the comet for 12 days near perihelion, interspersed between broadband optical imaging observations over four months. In addition, dynamical simulation of the comet was performed 1000 yr backward in time…
We identify two distinct physical mechanisms for dust gap opening by embedded planets in protoplanetary discs based on the symmetry of the drag-induced motion around the planet: I) A mechanism where low mass planets, that do not disturb the gas, open gaps in dust by tidal torques assisted by drag in the inner disc, but resisted by drag in the outer disc; and II) The usual, drag assisted, mechanism where higher mass planets create pressure maxima in the gas disc which the drag torque then acts to evacuate further in the dust. The first mechanism produces gaps in dust but not gas, while the seco…
We revisit, via a very simplified set of equations, a linear streaming instability (technically an overstability), which is present in, and potentially important for, dusty protoplanetary disks (Youdin & Goodman 2005). The goal is a better understanding of the physical origin of such instabilities, which are notoriously subtle. Rotational dynamics seem to be essential to this type of instability, which cannot be captured by one-dimensional Cartesian models. Dust `pileups' in moving pressure maxima are an important triggering mechanism of the instability, and drag feedback of dust upon the gas …
We present a possible correlation between the properties of scattered and thermal radiation from dust and the principal dust characteristics responsible for this relationship. To this end, we use the NASA/PDS archival polarimetric data on cometary dust in the Red (0.62--0.73 $μ$m) and K (2.00--2.39 $μ$m) domains to leverage the relative excess of the polarisation degree of a comet to the average trend at the given phase angle ($P_{\rm excess}$) as a metric of the dust's scattered light characteristics. The flux excess of silicate emissions to the continuum around 10 $μ$m ($F_{\rm Si}/F_{\rm co…
We identify a new hydrodynamical instability in protoplanetary discs that may arise due to variations in the dust-to-gas ratio and may lead to concentration of dust grains within a disc. The instability can arise due to dust settling, which produces a vertical compositional entropy gradient. The entropy gradient drives a baroclinic instability that is capable of creating toroidal gas vortices that gather dust into rings. Such dust rings are potentially observable via continuum emission of the dust or scattered light. Indeed, this instability may offer an explanation for the rings recently obse…
We study drag-driven instability in a protoplanetary disc consisting of a layer of single-sized dust particles which are coupled to the magnetized gas aerodynamically and the particle-to-gas feedback is included. We find a dispersion relation for axisymmetric linear disturbances and growth rate of the unstable modes are calculated numerically. While the secular gravitational instability in the absence of particle-to-gas feedback predicts the dust layer is unstable, magnetic fields significantly amplifies the instability if the Toomre parameter for the gas component is fixed. We also show that …
ALMA has revolutionized our view of protoplanetary disks, revealing structures such as gaps, rings and asymmetries that indicate dust trapping as an important mechanism in the planet formation process. However, the high resolution images have also shown that the optically thin assumption for millimeter continuum emission may not be valid and the low values of the spectral index may be related to optical depth rather than dust growth. Longer wavelength observations are essential to properly disentangle these effects. The high sensitivity and spatial resolution of the next-generation Very Large …
Enhancing the local dust-to-gas ratio in protoplanetary discs is a necessary first step to planetesimal formation. In laminar discs, dust settling is an efficient mechanism to raise the dust-to-gas ratio at the disc midplane. However, turbulence, if present, can stir and lift dust particles, which ultimately hinders planetesimal formation. In this work, we study dust settling in protoplanetary discs with hydrodynamic turbulence sustained by the vertical shear instability. We perform axisymmetric numerical simulations to investigate the effect of turbulence, particle size, and solid abundance o…
After 25 years of laboratory research on protoplanetary dust agglomeration, a consistent picture of the various processes that involve colliding dust aggregates has emerged. Besides sticking, bouncing and fragmentation, other effects, like, e.g., erosion or mass transfer, have now been extensively studied. Coagulation simulations consistently show that $\rm μ$m-sized dust grains can grow to mm- to cm-sized aggregates before they encounter the bouncing barrier, whereas sub-$\rm μ$m-sized water-ice particles can directly grow to planetesimal sizes. For siliceous materials, other processes have t…
We investigate the impact of a highly eccentric 10 $M_{\rm \oplus}$ (where $M_{\rm \oplus}$ is the Earth mass) planet embedded in a dusty protoplanetary disk on the dust dynamics and its observational implications. By carrying out high-resolution 2D gas and dust two-fluid hydrodynamical simulations, we find that the planet's orbit can be circularized at large radii. After the planet's orbit is circularized, partial gap opening and dust ring formation happen close to the planet's circularization radius, which can explain the observed gaps/rings at the outer region of disks. When the disk mass a…
Disc-driven planet migration is integral to the formation of planetary systems. In standard, gas-dominated protoplanetary discs, low-mass planets or planetary cores undergo rapid inwards migration and are lost to the central star. However, several recent studies indicate that the solid component in protoplanetary discs can have a significant dynamical effect on disc-planet interaction, especially when the solid-to-gas mass ratio approaches unity or larger and the dust-on-gas drag forces become significant. As there are several ways to raise the solid abundance in protoplanetary discs, for exam…
We investigate the dynamics of dust grains with various sizes in protoplanetary disk winds driven by magnetorotational turbulence, by simulating the time evolution of the dust grain distribution in the vertical direction. Small dust grains, which are well coupled to the gas, are dragged upward with the upflowing gas, while large grains remain near the midplane of a disk. Intermediate--size grains float at several scale heights from the midplane in time-averated force balance between the downward gravity and the upward gas drag. For the minimum mass solar nebula at 1 AU, dust grains with size o…
Instabilities of the dust layer in a protoplanetary disk are investigated. It is known that the streaming instability develops and dust density concentration occurs in a situation where the initial dust density is uniform. This work considers the effect of initial dust density gradient vertical to the midplane. Dust and gas are treated as different fluids. Pressure of dust fluid is assumed to be zero. The gas friction time is assumed to be constant. Axisymmetric two-dimensional numerical simulation was performed using the spectral method. We found that an instability develops with a growth rat…
Dust coagulation in a protoplanetary disk is the first step of planetesimal formation. However, a pathway from dust aggregates to planetesimals remains unclear. Both numerical simulations and laboratory experiments have suggested the importance of dust structure in planetesimal formation, but it is not well constrained by observations. We study how dust structure and porosity alters polarimetric images at millimeter wavelength by performing 3D radiative transfer simulations. Aggregates with different porosity and fractal dimension are considered. As a result, we find that dust aggregates with …
We study dust concentration in axisymmetric gas rings in protoplanetary disks. Given the gas surface density, we derived an analytical total dust surface density by taking into account the differential concentration of all the grain sizes. This model allows us to predict the local dust-to-gas mass ratio and the slope of the particle size distribution, as a function of radius. We test this analytical model comparing it with a 3D magneto-hydrodynamical simulation of dust evolution in an accretion disk. The model is also applied to the disk around HD 169142. By fitting the disk continuum observat…
We aim to derive a simple analytic model to understand the essential properties of vertically settling growing dust grains in laminar protoplanetary discs. Separating the vertical dynamics from the motion in the disc midplane, we integrate the equations of motion for both a linear and an exponential grain growth rate. Numerical integrations are performed for more complex growth models. We find that the settling efficiency depends on the value of the dimensionless parameter gamma, which characterises the relative efficiency of grain growth with respect to the gas drag. Since gamma is expected t…
Dust gaps and rings appear ubiquitous in bright protoplanetary disks. Disk-planet interaction with dust-trapping at the edges of planet-induced gaps is one plausible explanation. However, the sharpness of some observed dust rings indicate that sub-mm-sized dust grains have settled to a thin layer in some systems. We test whether or not such dust around gas gaps opened by planets can remain settled by performing three-dimensional, dust-plus-gas simulations of protoplanetary disks with an embedded planet. We find planets massive enough to open gas gaps stir small, sub-mm-sized dust grains to hig…
We examine the consequences of a model for the circulation of solids in a protoplanetary nebula in which aerodynamic drag is counterbalanced by the recycling of material to the outer disc by a protostellar outflow or a disc wind. This population of circulating dust eventually becomes unstable to the formation of planetesimals by gravitational instability, and results in the ultimate deposition of 30--50 earth masses in planetesimals on scales R< 1 AU. Such a model may provide an appropriate justification for the approximately power law initial conditions needed to reproduce observed planetary …
Planetesimal formation is a crucial yet poorly understood process in planet formation. It is widely believed that planetesimal formation is the outcome of dust clumping by the streaming instability (SI). However, recent analytical and numerical studies have shown that the SI can be damped or suppressed by external turbulence, and at least the outer regions of protoplanetary disks are likely weakly turbulent due to magneto-rotational instability (MRI). We conduct high-resolution local shearing-box simulations of hybrid particle-gas magnetohydrodynamics (MHD), incorporating ambipolar diffusion a…
Context. Multiple mechanisms are known to give rise to turbulence in protoplanetary disks, which facilitates the accretion onto the central star. Small dust particles that are well coupled to the gas undergo diffusion due to this turbulent motion. Aims. This paper investigates the influence of turbulence induced dust diffusion on the equilibrium of protoplanetary disks. Methods. The model accounts for dust sublimation, radiative transfer with the flux-limited diffusion approximation and dust diffusion. It predicts the density and temperature profiles as well as the dust-to-gas ratio of the dis…
Dust particles need to grow efficiently from micrometre sizes to thousands of kilometres to form planets. With the growth of millimetre to meter sizes being hindered by a number of barriers, the recent discovery that dust evolution is able to create `self-induced' dust traps shows promises. The condensation and sublimation of volatile species at certain locations, called snow lines, is also thought to be an important part of planet formation scenarios. Given that dust sticking properties change across a snow line, this raises the question: how do snow lines affect the self-induced dust trap fo…
When a planet forms a deep gap in a protoplanetary disk, dust grains cannot pass through the gap. As a consequence, the density of the dust grains can increase up to the same level of the density of the gas at the outer edge. The feedback on the gas from the drifting dust grains is not negligible, in such a dusty region. We carried out two-dimensional two-fluid (gas and dust) hydrodynamic simulations. We found that when the radial flow of the dust grains across the gap is halted, a broad ring of the dust grains can be formed because of the dust feedback and the diffusion of the dust grains. Th…
We study scattered light properties of protoplanetary discs at near-infrared wavelengths for various dust size and structure by performing radiative transfer simulations. We show that different dust structures might be probed by measuring disk polarisation fraction as long as the dust radius is larger than the wavelength. When the radius is larger than the wavelength, disc scattered light will be highly polarised for highly porous dust aggregates, whereas more compact dust structure tends to show low polarisation fraction. Next, roles of monomer radius and fractal dimension for scattered light…
The aim of this paper is to study the vertical profile of small dust particles in protoplanetary discs in which angular momentum transport is due to MHD turbulence driven by the magnetorotational instability. We consider particle sizes that range from approximately 1 micron up to a few millimeters.We use a grid--based MHD code to perform global two-fluid simulations of turbulent protoplanetary discs which contain dust grains of various sizes. In quasi--steady state, the gravitational settling of dust particles is balanced by turbulent diffusion. Simple and standard models of this process fail …
Turbulence acting on mixes of gas and particles generally evenly diffuses the latter through the former. However, in the presence of background gas temperature gradients a phenomenon known as turbulent thermal diffusion appears as a particle drift velocity (rather than a diffusive term). This process moves particles from hot regions to cold ones. We rederive turbulent thermal diffusion using astrophysical language and demonstrate that it could play a major role in protoplanetary discs by concentrating particles by factors of tens. Such a concentration would set the stage for collective behavio…
In protoplanetary disks, the differential gravity-driven settling of dust grains with respect to gas and with respect to grains of varying sizes determines the observability of grains, and sets the conditions for grain growth and eventually planet formation. In this work we explore the effect of photophoresis on the settling of large dust grains in the inner regions of actively accreting protoplanetary disks. Photophoretic forces on dust grains result from the collision of gas molecules with differentially heated grains. We undertake one dimensional dust settling calculations to determine the …
In a set of 16 drop tower experiments the motion of sub-mm to mm-sized particles under microgravity was observed. Illumination by a halogen lamp induced acceleration of the particles due to photophoresis. Photophoresis on dust-free chondrules, on chondrules, glass spheres and metal spheres covered with SiC dust and on pure SiC dust aggregates was studied. This is the first time that photophoretic motion of mm-sized particles has been studied experimentally. The absolute values for the photophoretic force are consistent with theoretical expectations for spherical particles. The strength of the …
Transporting solids of different sizes is an essential process in the evolution of protoplanetary disks and planet formation. Large solids are supposed to drift inward; high-temperature minerals found in comets are assumed to have been transported outward. From low-gravity experiments on parabolic flights we studied the light-induced erosion of dusty bodies caused by a solid-state greenhouse effect and photophoresis within a dust bed's upper layers. The gravity levels studied were 0.16g, 0.38g, 1g, and 1.7g. The light flux during the experiments was 12 +/- 2 kW/m^2 and the ambient pressure was…
We observe the dust continuum at 225 GHz and CO isotopologue (12CO, 13CO, and C18O) J=2-1 emission lines toward the CR Cha protoplanetary disk using the Atacama Large Millimeter/Submillimeter Array (ALMA). The dust continuum image shows a dust gap-ring structure in the outer region of the dust disk. A faint dust ring is also detected around 120 au beyond the dust gap. The CO isotopologue lines indicate that the gas disk is more extended than the dust disk. The peak brightness temperature of the 13CO line shows a small bump around 130 au while 12CO and C18O lines do not show. We investigate two…
The streaming instability is one of the most promising pathways to the formation of planetesimals from pebbles. Understanding how this instability operates under realistic conditions expected in protoplanetary disks is therefore crucial to assess the efficiency of planet formation. Contemporary models of protoplanetary disks show that magnetic fields are key to driving gas accretion through large-scale, laminar magnetic stresses. However, the effect of such magnetic fields on the streaming instability has not been examined in detail. To this end, we study the stability of dusty, magnetized gas…
We propose the possibility of a new phenomenon affecting the settling of dust grains at the terrestrial region in early protoplanetary disks. Sinking dust grains evaporate in a hot inner region during the early stage of disk evolution, and the effects of condensation and evaporation on vertical dust settling can be significant. A 1-D dust settling model considering both physical and chemical aspects is presented in this paper. Modeling results show that dust grains evaporate as they descend into the hotter interior and form a "condensation front," above which dust-composing major elements, Mg,…
A consensus view on the formation of planetesimals is now exposed to a threat, since recent numerical studies on the mechanical properties of dust aggregates tend to dispute the conceptual picture that submicrometer-sized grains conglomerate into planetesimals in protoplanetary disks. With the advent of precise laboratory experiments and extensive computer simulations on the interaction between elastic spheres comprising dust aggregates, we revisit a model for the tensile strength of dust aggregates consisting of small elastic grains. In the framework of contact mechanics and fracture mechanic…
In order to understand how the chemical and isotopic compositions of dust grains in a gaseous turbulent protoplanetary disk are altered during their journey in the disk, it is important to determine their individual trajectories. We study here the dust-diffusive transport using lagrangian numerical simulations using the the popular "turbulent diffusion" formalism. However it is naturally expressed in an Eulerian form, which does not allow the trajectories of individual particles to be studied. We present a simple stochastic and physically justified procedure for modeling turbulent diffusion in…
We study the turbulence induced in the dust layer of a protoplanetary disk based on the energetics of dust accretion due to gas drag. We estimate turbulence strength from the energy supplied by dust accretion, using the radial drift velocity of the dust particles in a laminar disk. Our estimate of the turbulence strength agrees with previous analytical and numerical research on the turbulence induced by Kelvin-Helmholtz and/or streaming instabilities for particles whose stopping time is less than the Keplerian time. For such small particles, the strongest turbulence is expected to occur when t…
The size and density of dust grains determine their response to gas drag in protoplanetary discs. Aerodynamical (size x density) sorting is one of the proposed mechanisms to explain the grain properties and chemical fractionation of chondrites. However, the efficiency of aerodynamical sorting and the location in the disc in which it could occur are still unknown. Although the effects of grain sizes and growth in discs have been widely studied, a simultaneous analysis including dust composition is missing. In this work we present the dynamical evolution and growth of multicomponent dust in a pr…
We study details of the UV radiation transfer in a protoplanetary disk, paying attention to the influence of dust growth and sedimentation on the disk density and temperature. Also, we show how the dust evolution affects photoreaction rates of key molecules, like CN and CS.
Small (sub)-micron dust is present over the entire lifetime of protoplanetary disks. As aggregation readily depletes small particles, one explanation might be that dust is continuously generated by larger bodies in the midplane and transported to the surface of the disks. In general, in a first step of this scenario, the larger bodies have to be destroyed again and different mechanisms exist with the potential to accomplish this. Possible destructive mechanisms are fragmentation in collisions, erosion by gas drag or light induced erosion. In laboratory experiments we find that the latter, ligh…
The streaming instability and Kelvin--Helmholtz instability are considered the two major sources causing clumping of dust particles and turbulence in the dust layer of a protoplanetary disk as long as we consider the dead zone where the magneto-rotational instability does not grow. Extensive numerical simulations have been carried out in order to elucidate the condition for the development of particle clumping caused by the streaming instability. In this paper, a set of two parameters suitable for classifying the numerical results is proposed. One is the Stokes number that has been employed in…
Relatively large dust grains (referred to as pebbles) accumulate at the outer edge of the gap induced by a planet in a protoplanetary disk, and a ring structure with a high dust-to-gas ratio can be formed. Such a ring has been thought to be located right outside of the planet orbit. We examined the evolution of the dust ring formed by a migrating planet, by performing two-fluid (gas and dust) hydrodynamic simulations. We found that the initial dust ring does not follow the migrating planet and remains at the initial location of the planet in the cases with a low viscosity of $α\sim 10^{-4}$. T…
