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Register a new userUsing Ice and Dust Lines to Constrain the Surface Densities of Protoplanetary Disks
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We present a novel method for determining the surface density of protoplanetary disks through consideration of disk dust lines which indicate the observed disk radial scale at different observational wavelengths. This method relies on the assumption that the processes of particle growth and drift control the radial scale of the disk at late stages of disk evolution such that the lifetime of the disk is equal to both the drift timescale and growth timescale of the maximum particle size at a given dust line. We provide an initial proof of concept of our model through an application to the disk TW Hya and are able to estimate the disk dust-to-gas ratio, CO abundance, and accretion rate in addition to the total disk surface density. We find that our derived surface density profile and dust-to-gas ratio are consistent with the lower limits found through measurements of HD gas. The CO ice line also depends on surface density through grain adsorption rates and drift and we find that our theoretical CO ice line estimates have clear observational analogues. We further apply our model to a large parameter space of theoretical disks and find three observational diagnostics that may be used to test its validity. First we predict that the dust lines of disks other than TW Hya will be consistent with the normalized CO surface density profile shape for those disks. Second, surface density profiles that we derive from disk ice lines should match those derived from disk dust lines. Finally, we predict that disk dust and ice lines will scale oppositely, as a function of surface density, across a large sample of disks.
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We present new determinations of disk surface density, independent of an assumed dust opacity, for a sample of 7 bright, diverse protoplanetary disks using measurements of disk dust lines. We develop a robust method for determining the location of dust lines by modeling disk interferometric visibilities at multiple wavelengths. The disks in our sample have newly derived masses that are 9-27% of their host stellar mass, substantially larger than the minimum mass solar nebula. All are stable to gravitational collapse except for one which approaches the limit of Toomre-Q stability. Our mass estimates are 2-15 times larger than estimates from integrated optically thin dust emission. We derive depleted dust-to-gas ratios with typical values of ~$10^{-3}$ in the outer disk. Using coagulation models we derive dust surface density profiles that are consistent with millimeter dust observations. In these models, the disks formed with an initial dust mass that is a factor of ~10 greater than is presently observed. Of the three disks in our sample with resolved CO line emission, the masses of HD 163296, AS 209, and TW Hya are roughly 3, 115, and 40 times more massive than estimates from CO respectively. This range indicates that CO depletion is not uniform across different disks and that dust is a more robust tracer of total disk mass. Our method of determining surface density using dust lines is robust even if particles form as aggregates and is useful even in the presence of dust substructure caused by pressure traps. The low Toomre-Q values observed in this sample indicate that at least some disks do not accrete efficiently.
Recent high angular resolution observations of protoplanetary disks at different wavelengths have revealed several kinds of structures, including multiple bright and dark rings. Embedded planets are the most used explanation for such structures, but there are alternative models capable of shaping the dust in rings as it has been observed. We assume a disk around a Herbig star and investigate the effect that ice lines have on the dust evolution, following the growth, fragmentation, and dynamics of multiple dust size particles, covering from 1 $mu$m to 2 m sized objects. We use simplified prescriptions of the fragmentation velocity threshold, which is assumed to change radially at the location of one, two, or three ice lines. We assume changes at the radial location of main volatiles, specifically H$_2$O, CO$_2$, and NH$_3$. Radiative transfer calculations are done using the resulting dust density distributions in order to compare with current multiwavelength observations. We find that the structures in the dust density profiles and radial intensities at different wavelengths strongly depend on the disk viscosity. A clear gap of emission can be formed between ice lines and be surrounded by ring-like structures, in particular between the H$_2$O and CO$_2$ (or CO). The gaps are expected to be shallower and narrower at millimeter emission than at near-infrared, opposite to model predictions of particle trapping. In our models, the total gas surface density is not expected to show strong variations, in contrast to other gap-forming scenarios such as embedded giant planets or radial variations of the disk viscosity.
Dust evolution in protoplanetary disks from small dust grains to pebbles is key to the planet formation process. The gas in protoplanetary disks should influence the vertical distribution of small dust grains ($sim$1 $mu m$) in the disk.Utilizing archival near-infrared polarized light and millimeter observations, we can measure the scale height and the flare parameter $beta$ of the small dust grain scattering surface and $^{12}$CO gas emission surface for three protoplanetary disks IM Lup, HD 163296, and HD 97048 (CU Cha). For two systems, IM Lup and HD 163296, the $^{12}$CO gas and small dust grains at small radii from the star have similar heights but at larger radii ($>$100 au) the dust grain scattering surface height is lower than the $^{12}$CO gas emission surface height. In the case of HD 97048, the small dust grain scattering surface has similar heights to the $^{12}$CO gas emission surface at all radii. We ran a protoplanetary disk radiative transfer model of a generic protoplanetary disk with TORUS and showed that there is no difference between the observed scattering surface and $^{12}$CO emission surface. We also performed analytical modeling of the system and found that gas-to-dust ratios larger than 100 could explain the observed difference in IM Lup and HD 163296. This is the first direct comparison of observations of gas and small dust grain heights distribution in protoplanetary disks. Future observations of gas emission and near-infrared scattered light instruments are needed to look for similar trends in other protoplanetary disks.
Theoretical models of the ionization state in protoplanetary disks suggest the existence of large areas with low ionization and weak coupling between the gas and magnetic fields. In this regime hydrodynamical instabilities may become important. In this work we investigate the gas and dust structure and dynamics for a typical T Tauri system under the influence of the vertical shear instability (VSI). We use global 3D radiation hydrodynamics simulations covering all $360^circ$ of azimuth with embedded particles of 0.1 and 1mm size, evolved for 400 orbits. Stellar irradiation heating is included with opacities for 0.1- to 10-$mu$m-sized dust. Saturated VSI turbulence produces a stress-to-pressure ratio of $alpha simeq 10^{-4}$. The value of $alpha$ is lowest within 30~au of the star, where thermal relaxation is slower relative to the orbital period and approaches the rate below which VSI is cut off. The rise in $alpha$ from 20 to 30~au causes a dip in the surface density near 35~au, leading to Rossby wave instability and the generation of a stationary, long-lived vortex spanning about 4~au in radius and 40~au in azimuth. Our results confirm previous findings that mm size grains are strongly vertically mixed by the VSI. The scale height aspect ratio for 1mm grains is determined to be 0.037, much higher than the value $H/r=0.007$ obtained from millimeter-wave observations of the HL~Tau system. The measured aspect ratio is better fit by non-ideal MHD models. In our VSI turbulence model, the mm grains drift radially inwards and many are trapped and concentrated inside the vortex. The turbulence induces a velocity dispersion of $sim 12$~m/s for the mm grains, indicating that grain-grain collisions could lead to fragmentation.
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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