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The observed dust rings and gaps in protoplanetary disks could be imprints of forming planets. Even low-mass planets in the 1--10 Earth-mass regime, which have not yet carved deep gas gaps, can generate such dust rings and gaps by driving a radially-outward gas flow, as shown in previous work. However, understanding the creation and evolution of these dust structures is challenging due to dust drift and diffusion, requiring an approach beyond previous steady state models. Here we investigate the time evolution of the dust surface density influenced by the planet-induced gas flow based on post-processing three-dimensional hydrodynamical simulations. We find that planets larger than a dimensionless thermal mass of $m=0.05$ corresponding to $0.3$ Earth mass at 1 au or 1.7 Earth masses at 10 au generate dust rings and gaps provided that solids have small Stokes numbers St and that the disk midplane is weakly turbulent ($ diff As dust particles pile up outside the orbit of the planet, the interior gap expands with time when the advective flux dominates over diffusion. Dust gap depths range from a factor of a few to several orders of magnitude, depending on planet mass and the level of midplane particle diffusion. We constructed a semi-analytic model describing the width of the dust ring and gap, and then compared it with the observational data. We find that up to 65<!PCT!> of the observed wide-orbit gaps could be explained as resulting from the presence of a low-mass planet, assuming diff and St However, it is more challenging to explain the observed wide rings, which in our model would require the presence of a population of small particles ($ Further work is needed to explore the role of pebble fragmentation, planet migration, and the effect of multiple planets.
The observed dust rings and gaps in protoplanetary disks could be imprints of forming planets. Even low-mass planets in the 1--10 Earth-mass regime, which have not yet carved deep gas gaps, can generate such dust rings and gaps by driving a radially-outward gas flow, as shown in previous work. However, understanding the creation and evolution of these dust structures is challenging due to dust drift and diffusion, requiring an approach beyond previous steady state models. Here we investigate the time evolution of the dust surface density influenced by the planet-induced gas flow based on post-processing three-dimensional hydrodynamical simulations. We find that planets larger than a dimensionless thermal mass of $m=0.05$ corresponding to $0.3$ Earth mass at 1 au or 1.7 Earth masses at 10 au generate dust rings and gaps provided that solids have small Stokes numbers St and that the disk midplane is weakly turbulent ($ diff As dust particles pile up outside the orbit of the planet, the interior gap expands with time when the advective flux dominates over diffusion. Dust gap depths range from a factor of a few to several orders of magnitude, depending on planet mass and the level of midplane particle diffusion. We constructed a semi-analytic model describing the width of the dust ring and gap, and then compared it with the observational data. We find that up to 65<!PCT!> of the observed wide-orbit gaps could be explained as resulting from the presence of a low-mass planet, assuming diff and St However, it is more challenging to explain the observed wide rings, which in our model would require the presence of a population of small particles ($ Further work is needed to explore the role of pebble fragmentation, planet migration, and the effect of multiple planets.
Planets form in the disks surrounding young stars. The time at which the planet formation process begins is still an open question. Annular substructures such as rings and gaps in disks are intertwined with planet formation, and thus their presence or absence is commonly used to investigate the onset of this process. Current observations show that a limited number of disks surrounding protostars exhibit annular substructures, all of them in the Class I stage. The lack of observed features in most of these sources may indicate a late emergence of substructures, but it could also be an artifact of these disks being optically thick. To mitigate the problem of optical depth, we investigated substructures within a very young Class 0 disk characterized by low inclination using observations at longer wavelengths. We used 3 mm ALMA observations tracing dust emission at a resolution of 7 au to search for evidence of annular substructures in the disk around the deeply embedded Class 0 protostar Oph A SM1. The observations reveal a nearly face-on disk (inclinationsim 16$^ circ $) extending up to 40 au. The radial intensity profile shows a clear deviation from a smooth profile near 30 au, which we interpret as the presence of either a gap at 28 au or a ring at 34 au with Gaussian widths of $ $ au and $ $ au, respectively. Crucially, the 3 mm emission at the location of the possible gap or ring is determined to be optically thin, precluding the possibility that this feature in the intensity profile is due to the emission being optically thick. Annular substructures resembling those in the more evolved Class I and II disks could indeed be present in the Class 0 stage, which is earlier than suggested by previous observations. Similar observations of embedded disks in which the high-optical-depth problem can be mitigated are clearly needed to better constrain the onset of substructures in the embedded stages.
Atacama Large Millimeter/submillimeter Array surveys have suggested that protoplanetary disks are not massive enough to form the known exoplanet population, based on the assumption that the millimeter continuum emission is optically thin. In this work, we investigate how the mass determination is influenced when the porosity of dust grains is considered in radiative transfer models. The results show that disks with porous dust opacities yield similar dust temperatures, but systematically lower millimeter fluxes, as compared to disks that incorporate compact dust grains. Moreover, we have recalibrated the relation between dust temperature and stellar luminosity for a wide range of stellar parameters. We also calculated the dust masses of a large sample of disks using the traditionally analytic approach. The median dust mass from our calculation is about six times higher than the literature result, and this is mostly driven by the different opacities of porous and compact grains. A comparison of the cumulative distribution function between disk dust masses and exoplanet masses shows that the median exoplanet mass is about two times lower than the median dust mass when grains are assumed to be porous and there are no exoplanetary systems with masses higher than the most massive disks. Our analysis suggests that adopting porous dust opacities may alleviate the mass budget problem for planet formation. As an example illustrating the combined effects of optical depth and porous dust opacities on the mass estimation, we conducted new IRAM/NIKA-2 observations toward the IRAS\,04370+2559 disk and performed a detailed radiative transfer modeling of the spectral energy distribution (SED). The best-fit dust mass is roughly 100 times higher than the value given by a traditionally analytic calculation. Future spatially resolved observations at various wavelengths are required to better constrain the dust mass.
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