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Register a new userDust trapping around Lagrangian points in protoplanetary disks
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Trojans are defined as objects that share the orbit of a planet at the stable Lagrangian points $L_4$ and $L_5$. In the Solar System, these bodies show a broad size distribution ranging from micrometer($mu$m) to centimeter(cm) particles (Trojan dust) and up to kilometer (km) rocks (Trojan asteroids). It has also been theorized that earth-like Trojans may be formed in extra-solar systems. The Trojan formation mechanism is still under debate, especially theories involving the effects of dissipative forces from a viscous gaseous environment. We perform hydro-simulations to follow the evolution of a protoplanetary disk with an embedded 1--10 Jupiter-mass planet. On top of the gaseous disk, we set a distribution of $mu$m--cm dust particles interacting with the gas. This allows us to follow dust dynamics as solids get trapped around the Lagrangian points of the planet. We show that large vortices generated at the Lagrangian points are responsible for dust accumulation, where the leading Lagrangian point $L_4$ traps a larger amount of submillimeter (submm) particles than the trailing $L_5$, which traps mostly mm--cm particles. However, the total bulk mass, with typical values of $sim M_{rm moon}$, is more significant in $L_5$ than in $L_4$, in contrast to what is observed in the current Solar System a few gigayears later. Furthermore, the migration of the planet does not seem to affect the reported asymmetry between $L_4$ and $L_5$. The main initial mass reservoir for Trojan dust lies in the same co-orbital path of the planet, while dust migrating from the outer region (due to drag) contributes very little to its final mass, imposing strong mass constraints for the in situ formation scenario of Trojan planets.
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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.
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 Array (ngVLA) will open up the possibilities to spatially resolve disk continuum emission at centimeter wavelengths and beyond, which allows the study of dust growth in disks in the optically thin regime and further constrain models of planet formation.
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 find that if the planet does not open a gap quickly enough, the formation of an inner ring is impeded due to dust coagulation and subsequent radial drift. Furthermore, we find that a buildup of sub-mm sized grains often appears in the dust emission at the outer edge of the dust disk.
Protoplanetary disks often appear as multiple concentric rings in dust continuum emission maps and scattered light images. These features are often associated with possible young planets in these disks. Many non-planetary explanations have also been suggested, including snow lines, dead zones and secular gravitational instabilities in the dust. In this paper we suggest another potential origin. The presence of copious amounts of dust tends to strongly reduce the conductivity of the gas, thereby inhibiting the magneto-rotational instability, and thus reducing the turbulence in the disk. From viscous disk theory it is known that a disk tends to increase its surface density in regions where the viscosity (i.e. turbulence) is low. Local maxima in the gas pressure tend to attract dust through radial drift, increasing the dust content even more. We investigate mathematically if this could potentially lead to a feedback loop in which a perturbation in the dust surface density could perturb the gas surface density, leading to increased dust drift and thus amplification of the dust perturbation and, as a consequence, the gas perturbation. We find that this is indeed possible, even for moderately small dust grain sizes, which drift less efficiently, but which are more likely to affect the gas ionization degree. We speculate that this instability could be triggered by the small dust population initially, and when the local pressure maxima are strong enough, the larger dust grains get trapped and lead to the familiar ring-like shapes. We also discuss the many uncertainties and limitations of this model.
In this work, we study how the dust coagulation/fragmentation will influence the evolution and observational appearances of vortices induced by a massive planet embedded in a low viscosity disk by performing global 2D high-resolution hydrodynamical simulations. Within the vortex, due to its higher gas surface density and steeper pressure gradients, dust coagulation, fragmentation and drift (to the vortex center) are all quite efficient, producing dust particles ranging from micron to $sim 1.0 {rm cm}$, as well as overall high dust-to-gas ratio (above unity). In addition, the dust size distribution is quite non-uniform inside the vortex, with the mass weighted average dust size at the vortex center ($sim 4.0$ mm) being a factor of $sim10$ larger than other vortex regions. Both large ($sim$ mm) and small (tens of micron) particles contribute strongly to affect the gas motion within the vortex. As such, we find that the inclusion of dust coagulation has a significant impact on the vortex lifetime and the typical vortex lifetime is about 1000 orbits. After the initial gaseous vortex is destroyed, the dust spreads into a ring with a few remaining smaller gaseous vortices with a high dust concentration and a large maximum size ($sim$ mm). At late time, the synthetic dust continuum images for the coagulation case show as a ring inlaid with several hot spots at 1.33 mm band, while only distinct hot spots remain at 7.0 mm.
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