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Register a new userGaps and Rings in Protoplanetary Disks with Realistic Thermodynamics: The Critical Role of In-Plane Radiation Transport
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Ryan Miranda IAS
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Many protoplanetary disks exhibit annular gaps in dust emission, which may be produced by planets. Simulations of planet-disk interaction aimed at interpreting these observations often treat the disk thermodynamics in an overly simplified manner, which does not properly capture the dynamics of planet-driven density waves driving gap formation. Here we explore substructure formation in disks using analytical calculations and hydrodynamical simulations that include a physically-motivated prescription for radiative effects associated with the planet-induced density waves. For the first time, our treatment accounts not only for cooling from the disk surface, but also for radiation transport along the disk midplane. We show that this in-plane cooling, with a characteristic timescale typically an order of magnitude shorter than the one due to surface cooling, plays a critical role in density wave propagation and dissipation (we provide a simple estimate of this timescale). We also show that viscosity, at the levels expected in protoplanetary disks ($alpha lesssim 10^{-3}$), has a negligible effect on density wave dynamics. Using synthetic maps of dust continuum emission, we find that the multiplicity and shape of the gaps produced by planets are sensitive to the physical parameters---disk temperature, mass, and opacity---that determine the damping of density waves. Planets orbiting at $lesssim 20$ au produce the most diverse variety of gap/ring structures, although significant variation is also found for planets at $gtrsim 50$ au. By improving the treatment of physics governing planet-disk coupling, our results present new ways of probing the planetary interpretation of annular substructures in disks.
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High resolution ALMA observations of protoplanetary disks have revealed that many, if not all primordial disks consist of ring-like dust structures. The origin of these dust rings remains unclear, but a common explanation is the presence of planetary companions that have cleared gaps along their orbit and trapped the dust at the gap edge. A signature of this scenario is a decrease of gas density inside these gaps. In recent work, Isella et al. 2016 derived drops in gas density consistent with Saturn-mass planets inside the gaps in the HD163296 disk through spatially resolved CO isotopologue observations. However, as CO abundance and temperature depends on a large range of factors, the interpretation of CO emission is non-trivial. We use the physical-chemical code DALI to show that the gas temperature increases inside dust density gaps, implying that any gaps in the gas, if present, would have to be much deeper, consistent with planet masses higher than a Jupiter mass. Furthermore, we show that a model with increased grain growth at certain radii, as expected at a snowline, can reproduce the dust rings in HD163296 equally well without the need for companions. This scenario can explain both younger and older disks with observed gaps, as gaps have been seen in systems as young <1 Myr. While the origin of the rings in HD163296 remains unclear, these modeling results demonstrate that care has to be taken when interpreting CO emission in protoplanetary disk observations.
It has been recently suggested that the multiple concentric rings and gaps discovered by ALMA in many protoplanetary disks may be produced by a single planet, as a result of the complex propagation and dissipation of the multiple spiral density waves it excites in the disk. Numerical efforts to verify this idea have largely utilized the so-called locally isothermal approximation with a prescribed disk temperature profile. However, in protoplanetary disks this approximation does not provide an accurate description of the density wave dynamics on scales of tens of au. Moreover, we show that locally isothermal simulations tend to overestimate the contrast of ring and gap features, as well as misrepresent their positions, when compared to simulations in which the energy equation is evolved explicitly. This outcome is caused by the non-conservation of the angular momentum flux of linear perturbations in locally isothermal disks. We demonstrate this effect using simulations of locally isothermal and adiabatic disks (with essentially identical temperature profiles) and show how the dust distributions, probed by mm wavelength observations, differ between the two cases. Locally isothermal simulations may thus underestimate the masses of planets responsible for the formation of multiple gaps and rings on scales of tens of au observed by ALMA. We suggest that caution should be exercised in using the locally isothermal simulations to explore planet-disk interaction, as well as in other studies of wave-like phenomena in astrophysical disks.
Since the discovery of the multi-ring structure of the HL Tau disk, ALMA data suggest that the dust continuum emission of many, if not all, protoplanetary disks consists of rings and gaps, no matter their spectral type or age. The origin of these gaps so far remains unclear. We present a sample study of 16 disks with multiple ring-like structures in the continuum, using published ALMA archival data, to compare their morphologies and gap locations in a systematic way. The 16 targets range from early to late type stars, from <0.5 Myr to >10 Myr, from ~0.2 to 40 L_Sun and include both full and transitional disks with cleared inner dust cavities. Stellar ages are revised using new Gaia distances. Gap locations are derived using a simple radial fit to the intensity profiles. Using a radiative transfer model, the temperature profiles are computed. The gap radii generally do not correspond to the orbital radii of snow lines of the most common molecules. A snow line model can likely be discarded as a common origin of multi-ring systems. In addition, there are no systematic trends in the gap locations that could be related to resonances of planets. Finally, the outer radius of the disks decreases for the oldest disks in the sample, indicating that if multi-ring disks evolve in a similar way, outer dust rings either dissipate with the gas or grow into planetesimal belts.
It has recently been shown that the inner region of protoplanetary disks (PPDs) is governed by wind-driven accretion, and the resulting accretion flow showing complex vertical profiles. Such complex flow structures are further enhanced due to the Hall effect, especially when the background magnetic field is aligned with disk rotation. We investigate how such flow structures impact global dust transport via Monte-Carlo simulations, focusing on two scenarios. In the first scenario, the toroidal magnetic field is maximized in the miplane, leading to accretion and decretion flows above and below. In the second scenario, the toroidal field changes sign across the midplane, leading to an accretion flow at the disk midplane, with decretion flows above and below. We find that in both cases, the contribution from additional gas flows can still be accurately incorporated into the advection-diffusion framework for vertically-integrated dust transport, with enhanced dust radial diffusion up to an effective $alpha^{rm eff}sim10^{-2}$ for strongly coupled dust, even when background turbulence is weak $alpha<10^{-4}$. Dust radial drift is also modestly enhanced in the second scenario. We provide a general analytical theory that accurately reproduces our simulation results, thus establishing a framework to model global dust transport that realistically incorporates vertical gas flow structures. We also note that the theory is equally applicable to the transport of chemical species.
We present new Atacama Large Millimeter/submillimeter Array (ALMA) observations for three protoplanetary disks in Taurus at 2.9,mm and comparisons with previous 1.3,mm data both at an angular resolution of $sim0.1$ (15,au for the distance of Taurus). In the single-ring disk DS Tau, double-ring disk GO Tau, and multiple-ring disk DL Tau, the same rings are detected at both wavelengths, with radial locations spanning from 50 to 120,au. To quantify the dust emission morphology, the observed visibilities are modeled with a parametric prescription for the radial intensity profile. The disk outer radii, taken as 95% of the total flux encircled in the model intensity profiles, are consistent at both wavelengths for the three disks. Dust evolution models show that dust trapping in local pressure maxima in the outer disk could explain the observed patterns. Dust rings are mostly unresolved. The marginally resolved ring in DS Tau shows a tentatively narrower ring at the longer wavelength, an observational feature expected from efficient dust trapping. The spectral index ($alpha_{rm mm}$) increases outward and exhibits local minima that correspond to the peaks of dust rings, indicative of the changes in grain properties across the disks. The low optical depths ($tausim$0.1--0.2 at 2.9,mm and 0.2--0.4 at 1.3,mm) in the dust rings suggest that grains in the rings may have grown to millimeter sizes. The ubiquitous dust rings in protoplanetary disks modify the overall dynamics and evolution of dust grains, likely paving the way towards the new generation of planet formation.
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