Protoplanetary disk simulations show that a single planet can excite more than one spiral arm, possibly explaining the recent observations of multiple spiral arms in some systems. In this paper, we ...explain the mechanism by which a planet excites multiple spiral arms in a protoplanetary disk. Contrary to previous speculations, the formation of both primary and additional arms can be understood as a linear process when the planet mass is sufficiently small. A planet resonantly interacts with epicyclic oscillations in the disk, launching spiral wave modes around the Lindblad resonances. When a set of wave modes is in phase, they can constructively interfere with each other and create a spiral arm. More than one spiral arm can form because such constructive interference can occur for different sets of wave modes, with the exact number and launching position of the spiral arms being dependent on the planet mass as well as the disk temperature profile. Nonlinear effects become increasingly important as the planet mass increases, resulting in spiral arms with stronger shocks and thus larger pitch angles. This is found to be common for both primary and additional arms. When a planet has a sufficiently large mass ( 3 thermal masses for (h/r)p = 0.1), only two spiral arms form interior to its orbit. The wave modes that would form a tertiary arm for smaller mass planets merge with the primary arm. Improvements in our understanding of the formation of spiral arms can provide crucial insights into the origin of observed spiral arms in protoplanetary disks.
We examine whether various characteristics of planet-driven spiral arms can be used to constrain the masses of unseen planets and their positions within their disks. By carrying out two-dimensional ...hydrodynamic simulations varying planet mass and disk gas temperature, we find that a larger number of spiral arms form with a smaller planet mass and a lower disk temperature. A planet excites two or more spiral arms interior to its orbit for a range of disk temperatures characterized by the disk aspect ratio , whereas exterior to a planet's orbit multiple spiral arms can form only in cold disks with . Constraining the planet mass with the pitch angle of spiral arms requires accurate disk temperature measurements that might be challenging even with ALMA. However, the property that the pitch angle of planet-driven spiral arms decreases away from the planet can be a powerful diagnostic to determine whether the planet is located interior or exterior to the observed spirals. The arm-to-arm separations increase as a function of planet mass, consistent with previous studies; however, the exact slope depends on disk temperature as well as the radial location where the arm-to-arm separations are measured. We apply these diagnostics to the spiral arms seen in MWC 758 and Elias 2-27. As shown in Bae et al., planet-driven spiral arms can create concentric rings and gaps, which can produce a more dominant observable signature than spiral arms under certain circumstances. We discuss the observability of planet-driven spiral arms versus rings and gaps.
As spiral waves driven by a planet in a gaseous disk steepen into a shock, they deposit angular momentum, opening a gap in the disk. This has been well studied using both linear theory and numerical ...simulations, but so far only for the primary spiral arm: the one directly attached to the planet. Using 2D hydrodynamic simulations, we show that the secondary and tertiary arms driven by a planet can also open gaps as they steepen into shocks. The depths of the secondary/tertiary gaps in surface density grow with time in a low-viscosity disk ( ), so even low-mass planets (e.g., super-Earth or mini-Neptune-mass) embedded in the disk can open multiple observable gaps, provided that sufficient time has passed. Applying our results to the HL Tau disk, we show that a single 30 Earth-mass planet embedded in the ring at 68.8 au (B5) can reasonably well reproduce the positions of the two major gaps at 13.2 and 32.3 au (D1 and D2), and roughly reproduce two other major gaps at 64.2 and 74.7 au (D5 and D6) seen in the mm continuum. The positions of secondary/tertiary gaps are found to be sensitive to the planetary mass and the disk temperature profile, so with accurate observational measurements of the temperature structure, the positions of multiple gaps can be used to constrain the mass of the planet. We also comment on the gaps seen in the TW Hya and HD 163296 disk.
We present the first kinematical detection of embedded protoplanets within a protoplanetary disk. Using archival Atacama Large Millimetre Array (ALMA) observations of HD 163296, we demonstrate a new ...technique to measure the rotation curves of CO isotopologue emission to sub-percent precision relative to the Keplerian rotation. These rotation curves betray substantial deviations caused by local perturbations in the radial pressure gradient, likely driven by gaps carved in the gas surface density by Jupiter-mass planets. Comparison with hydrodynamic simulations shows excellent agreement with the gas rotation profile when the disk surface density is perturbed by two Jupiter-mass planets at 83 and 137 au. As the rotation of the gas is dependent upon the pressure of the total gas component, this method provides a unique probe of the gas surface density profile without incurring significant uncertainties due to gas-to-dust ratios or local chemical abundances that plague other methods. Future analyses combining both methods promise to provide the most accurate and robust measures of embedded planetary mass. Furthermore, this method provides a unique opportunity to explore wide-separation planets beyond the mm continuum edge and to trace the gas pressure profile essential in modeling grain evolution in disks.
Combining hydrodynamic planet-disk interaction simulations with dust evolution models, we show that protoplanetary disks with a giant planet can reveal diverse morphology in (sub)millimeter ...continuum, including a full disk without significant radial structure, a transition disk with an inner cavity, a disk with a single gap and a central continuum peak, and a disk with multiple rings and gaps. Such diversity originates from (1) the level of viscous transport in the disk, which determines the number of gaps a planet can open; (2) the size and spatial distributions of grains determined by the coagulation, fragmentation, and radial drift, which in turn affects the emissivity of the disk at (sub)millimeter wavelengths; and (3) the angular resolution used to observe the disk. In particular, our results show that disks with the same underlying gas distribution can have very different grain size/spatial distributions and thus appearance in continuum, depending on the interplay among coagulation, fragmentation, and radial drift. This suggests that proper treatments for the grain growth have to be included in models of protoplanetary disks concerning continuum properties and that complementary molecular line observations are highly desired in addition to continuum observations to reveal the true nature of disks. The fact that a single planet can produce diverse disk morphology emphasizes the need to search for more direct, localized signatures of planets in order to confirm (or dispute) the planetary origin of observed ringed substructures.
Abstract
Besides the spirals induced by the Lindblad resonances, planets can generate a family of tightly wound spirals through buoyancy resonances. The excitation of buoyancy resonances depends on ...the thermal relaxation timescale of the gas. By computing timescales of various processes associated with thermal relaxation, namely, radiation, diffusion, and gas–dust collision, we show that the thermal relaxation in protoplanetary disks’ surface layers (
Z
/
R
≳ 0.1) and outer disks (
R
≳ 100 au) is limited by infrequent gas–dust collisions. The use of the isothermal equation of state or rapid cooling, common in protoplanetary disk simulations, is therefore not justified. Using three-dimensional hydrodynamic simulations, we show that the collision-limited slow thermal relaxation provides favorable conditions for buoyancy resonances to develop. Buoyancy resonances produce predominantly vertical motions, whose magnitude at the
12
CO emission surface is of the order of 100 m s
−1
for Jovian-mass planets, sufficiently large to detect using molecular line observations with ALMA. We generate synthetic observations and describe characteristic features of buoyancy resonances in Keplerian-subtracted moment maps and velocity channel maps. Based on the morphology and magnitude of the perturbation, we propose that the tightly wound spirals observed in TW Hya could be driven by a (sub-)Jovian-mass planet at 90 au. We discuss how non-Keplerian motions driven by buoyancy resonances can be distinguished from those driven by other origins. We argue that observations of multiple lines tracing different heights, with sufficiently high spatial/spectral resolution and sensitivity to separate the emission arising from the near and far sides of the disk, will help constrain the origin of non-Keplerian motions.
Abstract
As host to two accreting planets, PDS 70 provides a unique opportunity to probe the chemical complexity of atmosphere-forming material. We present ALMA Band 6 observations of the PDS 70 disk ...and report the first chemical inventory of the system. With a spatial resolution of 0.″4–0.″5 (∼50 au), 12 species are detected, including CO isotopologs and formaldehyde, small hydrocarbons, HCN and HCO
+
isotopologs, and S-bearing molecules. SO and CH
3
OH are not detected. All lines show a large cavity at the center of the disk, indicative of the deep gap carved by the massive planets. The radial profiles of the line emission are compared to the (sub)millimeter continuum and infrared scattered light intensity profiles. Different molecular transitions peak at different radii, revealing the complex interplay between density, temperature, and chemistry in setting molecular abundances. Column densities and optical depth profiles are derived for all detected molecules, and upper limits obtained for the nondetections. Excitation temperature is obtained for H
2
CO. Deuteration and nitrogen fractionation profiles from the hydrocyanide lines show radially increasing fractionation levels. Comparison of the disk chemical inventory to grids of chemical models from the literature strongly suggests a disk molecular layer hosting a carbon-to-oxygen ratio C/O > 1, thus providing for the first time compelling evidence of planets actively accreting high C/O ratio gas at present time.
We present an improved method to measure the rotation curves for disks with nonaxisymmetric brightness profiles initially published in Teague et al. Application of this method to the well studied AS ...209 system shows substantial deviations from Keplerian rotation of up to 5%. These deviations are most likely due to perturbations in the gas pressure profile, including a perturbation located at 250 au and spanning up to 50 au that is only detected kinematically. Modeling the required temperature and density profiles required to recover the observed rotation curve, we demonstrate that the rings observed in micrometer scattered light are coincident with the pressure maxima, and are radially offset from the rings observed in millimeter continuum emission. This suggests that if rings in the NIR are due to submicrometer grains trapped in pressure maxima, then there is a vertical dependence on the radius of the pressure minima.
ABSTRACT The disk surrounding SAO 206462, an 8 Myr old Herbig Ae star, has recently been reported to exhibit spiral arms, an asymmetric dust continuum, and a dust-depleted inner cavity. By carrying ...out two-dimensional, two-fluid hydrodynamic calculations, we find that a planetary-mass companion located at the outer disk could be responsible for these observed structures. In this model, the planet excites primary and secondary arms interior to its orbit. It also carves a gap and generates a local pressure bump at the inner gap edge where a vortex forms through Rossby wave instability. The vortex traps radially drifting dust particles, forming a dust-depleted cavity in the inner disk. We propose that the vortex is responsible for the brightest southwestern peak seen in infrared scattered light and sub-millimeter dust continuum emission. In particular, it is possible that the scattered light is boosted as one of the spiral arms passes through the high density vortex region, although the vortex alone may be able to explain the peak. We suggest that a planetary companion with a mass of 10-15 is orbiting SAO 206462 at 100-120 au. Monitoring of the brightest peak over the next few years will help reveal its origin because the spiral arms and vortex will show distinguishable displacement.
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