Identifying Anticyclonic Vortex Features Produced by the Rossby Wave Instability in Protoplanetary Disks

Draft version July 12, 2021 Typeset using LATEX twocolumn style in AASTeX62 Identifying Anticyclonic Vortex Features Produced by the Rossby Wave Instability in Protoplanetary Disks Pinghui Huang,1, 2, 3 Andrea Isella,4 Hui Li,3 Shengtai Li,3 and Jianghui Ji1 1CAS Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China 2University of Chinese Academy of Sciences, Beijing 100049, China 3Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA 4Department of Physics & Astronomy, Rice University, 6100 Main Street, Houston, TX 77005, USA ABSTRACT Several nearby protoplanetary disks have been observed to display large scale crescents in the (sub)millimeter dust continuum emission. One interpretation is that these structures correspond to anticyclonic vortices generated by the Rossby wave instability within the gaseous disk. Such vortices have local gas over-densities and are expected to concentrate dust particles with Stokes number around unity. This process might catalyze the formation of planetesimals. Whereas recent observations showed that dust crescent are indeed regions where millimeter-size particles have abnormally high concentration relative to the gas and smaller grains, no observations have yet shown that the gas within the crescent region counter-rotates with respect to the protoplanetary disk. Here we investi- gate the detectability of anticyclonic features through measurement of the line-of-sight component of the gas velocity obtained with ALMA. We carry out 2D hydrodynamic simulations and 3D radiative transfer calculation of a protoplanetary disk characterized by a vortex created by the tidal interaction with a massive planet. As a case study, the disk parameters are chosen to mimic the IRS 48 system, which has the most prominent crescent observed to date. We generate synthetic ALMA observations of both the dust continuum and 12CO emission around the frequency of 345 GHz. We find that the anticyclonic features of vortex are weak but can be detected if both the source and the observational setup are properly chosen. We provide a recipe for maximizing the probability to detect such vortex features and present an analysis procedure to infer their kinematic properties. Keywords: detectability and sensitivity | vorticity | ALMA: protoplanetary disks 1. INTRODUCTION gration of solid particles in the direction of the gas pres- Protoplanetary systems such as IRS48 (van der Marel sure gradient (see, e.g., Weidenschilling 1977; Birnstiel et al. 2013), LkHα 330 (Isella et al. 2013), HD 142527 et al. 2013). This interpretation is supported by the fact (Muto et al. 2015), MWC 758 (Isella et al. 2010), and that gas-dust decoupling is most efficient for grains with SAO 206462 (Pérezet al. 2014) exhibit large cavities Stokes number around unity, which, for typical densities and prominent crescents in the (sub-)millimeter dust of protoplanetary disks, correspond indeed to grains that continuum emission. In systems where spatially re- emit mostly at (sub-)millimeter wavelengths. solved multi-wavelength observations of both dust and Whereas the motion of dust particles in gaseous disks is relatively well understood, the origin of gas pres- arXiv:1809.07001v1 [astro-ph.EP] 19 Sep 2018 gas emission exist, namely IRS 48, HD 142527, and MWC 758, the continuum crescents appear to originate sure maxima is not. A commonly accepted explana- from the azimuthal and radial concentration of solid par- tion for the existence of asymmetric pressure maxima ticles toward local maxima of the gas pressure (Casas- in protoplanetary disks is that they originate from large sus et al. 2015; Boehler et al. 2017; van der Marel et al. scale vortices resulting from hydrodynamic instabilities. 2015). Such concentration is believed to result from the Specifically, vortices can be generated by planets (Li decoupling between dust and gas, and subsequent mi- et al. 2005; Zhu et al. 2014; Fu et al. 2014b) or viscosity transitions (Regályet al. 2013; Miranda et al. 2017). A massive planet or a sharp radial viscosity transition cre- Corresponding author: Pinghui Huang ate a steep radial gradient in the gas density which trig- [email protected] gers the Rossby Wave Instability (RWI, Lovelace et al. 2 Huang P. et al. 1999; Li et al. 2000) which at nonlinear stage can pro- to properly account for observational noise. Synthetic duce large-scale vortices (Li et al. 2001, 2005; Ou et al. observations are then analyzed to search for the signa- 2007). Numerical simulations show that the formation ture of the vortex in the intensity moments of the gas and evolution of a vortex strongly depend on the disk intensity. We find that kinematic signatures of a vor- viscosity. In particular, a vortex can form and survive tex in a disk like IRS 48 can be detected by ALMA. for hundreds to thousands orbits only if the viscosity is We provide the observational set up required to achieve low (α ' 10−3 s 10−5, Fu et al. 2014a). Taken at face such a detection. Our analysis is complementary and ex- value, this result is in conflict with the typical α ' 0:01 tends the recent study of the effect of planet-disk inter- required to explain mass accretion rates found in proto- action on the CO line emission presented by Pérezet al. planetary disks (Hartmann et al. 1998). However, the- (2018). Note that our analysis should be applicable to oretical models suggest that disk viscosity might vary vortices excited via different mechanisms as described with the distance from the star, and that the innermost above, because the typical velocity variations associated disk regions (<1 AU), those responsible for the accretion with vortices are similar, with their magnitudes reaching onto the star, might be more viscous than the disk re- a fraction of the local sound speed (Li et al. 2001). gions probed by current spatially resolved observations The outline of this paper is as follows. In Section 2, (>10 AU). Lacking direct measurements (but see Fla- we describe our numerical model setup and methods. In herty et al. 2017), the level of viscosity in protoplanetary Section 3, we present the results of the numerical simu- disks remains highly debated. lations and the synthetic images obtained. In section 4, In addition to informing about disk viscosity, vortices we discuss and summarize our results. might be pivotal in the formation of planets: they can speed up the dust coagulation and the formation of plan- 2. MODELING PROCEDURE etesimals (Barge & Sommeria 1995), stop the radial in- 2.1. Planet-disk interaction model ward drift of dust particles (Weidenschilling 1977), and We use the two-fluid hydrodynamic 2D code LA- help overcome the fragmentation barrier (Brauer et al. COMPASS (Li et al. 2005, 2008; Fu et al. 2014b) to 2008). Vortices generated at the edges of low ioniza- simulate the formation and evolution of a large scale tion regions could perhaps lead to the formation of the vortex in a protoplanetary disk caused by the interac- planetesimals needed by core accretion model (Pollack tion with a massive planet. The hydrodynamic model et al. 1996) to form giant planets. Moreover, vortices is initialized using properties similar to that of the IRS generated by giant planets could perhaps control the 48 system, though our results apply to protoplanetary formation and migration of rocky planets in their region disks in general. We adopt a stellar mass M = 2 M of influence (see, e.g., Liu et al. 2018). Studying the ? (van der Marel et al. 2013) and a stellar effective tem- presence of vortices in protoplanetary disks is therefore perature T = 9400 K (Follette et al. 2015). The initial important to understand the architecture of the Solar ? gas surface density profile is Σ (r) = Σ (r=r )−1 systems and of the multitude of planetary systems dis- gas gas;0 0 where Σ = 1:73 g cm−2 and r = 35 au. The in- covered so far. gas;0 0 ner and outer boundaries of the disk are 0:4r = 14 au In this paper, we study the direct detectability of vor- 0 and 6:68r = 233:8 au, respectively. Modeling by Brud- tices from spatially and spectrally resolved observations 0 erer et al. (2014) have indicated that the inner gaseous of the molecular line emission at millimeter-wavelengths. disk of IRS 48 is depleted between 0:4 − 20 au. Here Observations of dust continuum crescents support the we have chosen the initial inner gas disk boundary at vortex hypothesis and, when combined with molecular 14 au and, with disk-planet interaction, the inner gas line data, provide indication of the efficiency of the dust disk will be significantly depleted over time. Overall, concentration process. However, direct measurements of we find that our results on vortices do not depend on the gas vorticity are necessary to i) confirm that the ob- the choice of the inner disk boundary. At the beginning served dust crescents correspond to gas vortices and ii) of the simulation, gas and dust are well coupled with study the mechanisms related to the vortex formation a gas-to-dust ratio of 100. Dust grains are modeled as and evolution. Here, we focus on the scenario in which compact spheres with a diameter of s = 0:20 mm and a vortex is created by a massive planet and simulate its d internal density of ρ = 1:2 g cm−3. The corresponding density and velocity structure through high resolution d Stokes number at r is 0.022. The choice of the grain 2D hydrodynamic calculations of the disk-planet inter- 0 size has little effect on our results and is motivated by action. We then perform radiative transfer calculation the fact that these are the grains that emit most the to generate synthetic images of the dust and CO emis- thermal radiation observed at λ = 2πs ≈ 1 mm.

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