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 two-dimensional hydrodynamic simulations of self-gravitating protostellar disks subject to axisymmetric, continuing mass loading from an infalling envelope and irradiation from the central ...star to explore the growth of gravitational instability (GI) and disk fragmentation. We assume that the disk is built gradually and smoothly by the infall, resulting in good numerical convergence. We confirm that for disks around solar-mass stars, infall at high rates at radii beyond ~50 AU leads to disk fragmentation. At lower infall rates, however, irradiation suppresses fragmentation. We find that, once formed, the fragments or clumps migrate inward on typical type I timescales of ~2 x 10 super(3) yr initially, but with a stochastic component superimposed due to their interaction with the GI-induced spiral arms. Migration begins to deviate from the type I timescale when the clump becomes more massive than the local disk mass, and/or when the clump begins to form a gap in the disk. As they migrate, clumps accrete from the disk at a rate between 10 super(-3) and 10 super(-1) M sub(J) yr super(-1), consistent with analytic estimates that assume a 1-2 Hill radii cross section. The eventual fates of these clumps, however, diverge depending on the migration speed: 3 out of 13 clumps in our simulations become massive enough (brown dwarf mass range) to open gaps in the disk and essentially stop migrating; 4 out of 13 are tidally destroyed during inward migration; and 6 out of 13 migrate across the inner boundary of the simulated disks. A simple analytic model for clump evolution explains the different fates of the clumps and reveals some limitations of two-dimensional simulations. Overall, our results indicate that fast migration, accretion, and tidal destruction of the clumps pose challenges to the scenario of giant planet formation by GI in situ, although we cannot address whether or not remnant solid cores can survive after tidal stripping. The models where the massive clumps are not disrupted and open gaps may be relevant to the formation of close binary systems similar to Kepler 16. A clump formed by GI-induced fragmentation can be as large as 10 AU and as luminous as 2 x 10 super(-3) L sub(middot in circle), which will be easily detectable with ALMA, but its lifetime before dynamically collapsing is only ~1000 years.
By carrying out two-dimensional two-fluid global simulations, we have studied the response of dust to gap formation by a single planet in the gaseous component of a protoplanetary disk-the so-called ...dust filtration mechanism. We have found that a gap opened by a giant planet at 20 AU in an alpha = 0.01, M = 10 super(-8) M sub(middot in circle) yr super(-1) disk can effectively stop dust particles larger than 0.1 mm drifting inward, leaving a submillimeter (submm) dust cavity/hole. However, smaller particles are difficult to filter by a gap induced by a several MJ planet due to (1) dust diffusion and (2) a high gas accretion velocity at the gap edge. Based on these simulations, an analytic model is derived to understand what size particles can be filtered by the planet-induced gap edge. We show that a dimensionless parameter T sub(s)/ alpha , which is the ratio between the dimensionless dust stopping time and the disk viscosity parameter, is important for the dust filtration process. Finally, with our updated understanding of dust filtration, we have computed Monte Carlo radiative transfer models with variable dust size distributions to generate the spectral energy distributions of disks with gaps. By comparing with transitional disk observations (e.g., GM Aur), we have found that dust filtration alone has difficulties depleting small particles sufficiently to explain the near-IR deficit of moderate M transitional disks, except under some extreme circumstances. The scenario of gap opening by multiple planets studied previously suffers the same difficulty. One possible solution is to invoke both dust filtration and dust growth in the inner disk. In this scenario, a planet-induced gap filters large dust particles in the disk, and the remaining small dust particles passing to the inner disk can grow efficiently without replenishment from fragmentation of large grains. Predictions for ALMA have also been made based on all these scenarios. We conclude that dust filtration with planet(s) in the disk is a promising mechanism to explain submm observations of transitional disks but it may need to be combined with other processes (e.g., dust growth) to explain the near-IR deficit of some systems.
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 It has been suggested that the gaps and cavities recently discovered in transitional disks are opened by planets. To explore this scenario, we combine two-dimensional two fluid (gas + ...particle) hydrodynamical calculations with three-dimensional Monte Carlo Radiative Transfer simulations and study the observational signatures of gaps opened by one or several planets, making qualitative comparisons with observations. We find that a single planet as small as 0.2 can produce a deep gap at millimeter wavelengths and almost no features at near-infrared (NIR) wavelengths, while multiple planets can open up a few ×10 AU wide common gap at both wavelengths. Both the contrast ratio of the gaps and the wavelength dependence of the gap sizes are broadly consistent with data. We also confirm previous results that NIR gap sizes may be smaller than millimeter gap sizes due to dust-gas coupling and radiative transfer effects. When viewed at a moderate inclination angle, a physically circular on-centered gap could appear to be off-centered from the star due to shadowing. Planet-induced spiral arms are more apparent at NIR than at millimeter wavelengths. Overall, our results suggest that the planet-opening-gap scenario is a promising way to explain the origin of the transitional disks. Finally, inspired by the recent Atacama Large Millimeter Array release of the image of the HL Tau disk, we show that multiple narrow gaps, well separated by bright rings, can be opened by planets soon after their formation in a relatively massive disk.
Nonsteady Accretion in Protostars Zhu, Zhaohuan; Hartmann, Lee; Gammie, Charles
The Astrophysical journal,
04/2009, Volume:
694, Issue:
2
Journal Article
Peer reviewed
Open access
Observations indicate that mass accretion rates onto low-mass protostars are generally lower than the rates of infall to their disks; this suggests that much of the protostellar mass must be accreted ...during rare, short outbursts of rapid accretion. We explore when protostellar disk accretion is likely to be highly variable. While constant a disks can in principle adjust their accretion rates to match infall rates, protostellar disks are unlikely to have constant a. In particular, we show that neither models with angular momentum transport due solely to the magnetorotational instability (MRI) nor gravitational instability (GI) are likely to transport disk mass at protostellar infall rates over the large range of radii needed to move infalling envelope material down to the central protostar. We show that the MRI and GI are likely to combine to produce outbursts of rapid accretion starting at a few AU. Our analysis is consistent with the time-dependent models of Armitage et al. and agrees with our observational study of the outbursting object FU Ori.
ABSTRACT Direct imaging observations have revealed spiral structures in protoplanetary disks. Previous studies have suggested that planet-induced spiral arms cannot explain some of these spiral ...patterns, due to the large pitch angle and high contrast of the spiral arms in observations. We have carried out three-dimensional (3D) hydrodynamical simulations to study spiral wakes/shocks excited by young planets. We find that, in contrast with linear theory, the pitch angle of spiral arms does depend on the planet mass, which can be explained by the nonlinear density wave theory. A secondary (or even a tertiary) spiral arm, especially for inner arms, is also excited by a massive planet. With a more massive planet in the disk, the excited spiral arms have larger pitch angle and the separation between the primary and secondary arms in the azimuthal direction is also larger. We also find that although the arms in the outer disk do not exhibit much vertical motion, the inner arms have significant vertical motion, which boosts the density perturbation at the disk atmosphere. Combining hydrodynamical models with Monte-Carlo radiative transfer calculations, we find that the inner spiral arms are considerably more prominent in synthetic near-IR images using full 3D hydrodynamical models than images based on two-dimensional models assuming vertical hydrostatic equilibrium, indicating the need to model observations with full 3D hydrodynamics. Overall, companion-induced spiral arms not only pinpoint the companion's position but also provide three independent ways (pitch angle, separation between two arms, and contrast of arms) to constrain the companion's mass.
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