Parametric Study of the Rossby Wave Instability in a Two-dimensional Barotropic Disk. II. Nonlinear Calculations

Abstract

Vortices in protoplanetary disks have attracted attention since the discovery of lopsided structures. One of the possible mechanisms for producing vortices is the Rossby Wave Instability (RWI). In our previous work, we have performed detailed linear stability analyses of the RWI with various initial conditions. In this paper, we perform numerical simulations of the vortex formation by the RWI in 2D barotropic disks using the Athena++ code. As initial conditions, we consider axisymmetric disks with a Gaussian surface density bump of various contrasts and half-widths. Perturbations grow as expected from the linear stability analyses in the linear and weakly non-linear regimes. After the saturation, multiple vortices are formed in accordance with the most unstable azimuthal mode and coalesce one after another. In the end, only one quasi-stationary vortex (the RWI vortex) remains, which migrates inward. During the RWI evolution, the axisymmetric component approaches the stable configuration. We find that the axisymmetric component reaches the marginally stable state for the most unstable azimuthal mode at the saturation and the marginally stable state for the m = 1 mode at the final vortex merger. We investigate the structure and evolution of the RWI vortices. We obtain some empirical relations between the properties of the RWI vortices and the initial conditions. Using tracer particle analyses, we find that the RWI vortex can be considered as a physical entity like a large fluid particle. Our results provide a solid theoretical ground for quantitative interpretation of the observed lopsided structures in protoplanetary disks.

Meso-scale Instability Triggered by Dust Feedback in Dusty Rings: Origin and Observational Implications

“…Figures 7 -9 indicate that the dust feedback is essential in producing the sharp features in the P V pro-files near the edges of the dusty rings in all cases. We speculate that such profiles will render the flow unstable to the Rossby wave instability (Lovelace et al 1999;Li et al 2000Li et al , 2001Ono et al 2016Ono et al , 2018. In fact, Figure 3 to 6 show that the linear development of unstable modes have an azimuthal mode number between 3 and 5, similar to the predictions given in Li et al (2000) for the most unstable modes.…”

Boundary Layers of Accretion Disks: Discovery of Vortex-Driven Modes and Other Waves

“…It was subsequently studied by a number of authors both analytically (Li et al 2000;Ono et al 2016) and numerically (Li et al 2001;Johnson & Gammie 2005;Ono et al 2018). A natural outcome of the nonlinear stage of the RWI is the formation of multiple vortices (each of them launching their individual spiral arms) with their subsequent merger into a single major vortex (Ono et al 2018). This sequence of events is precisely what we observe in our simulations.…”

“…The importance of RWI in astrophysical disks has been pointed out by Lovelace et al (1999) who demonstrated, in particular, that infinitesimal perturbations can grow exponentially provided that the underlying radial profile of ζ has an extremum. It was subsequently studied by a number of authors both analytically (Li et al 2000;Ono et al 2016) and numerically (Li et al 2001;Johnson & Gammie 2005;Ono et al 2018). A natural outcome of the nonlinear stage of the RWI is the formation of multiple vortices (each of them launching their individual spiral arms) with their subsequent merger into a single major vortex (Ono et al 2018).…”

Discovery of An au-scale Excess in Millimeter Emission from the Protoplanetary Disk around TW Hya

“…The gas disk may be full of such "weak vortices" if the PPD is moderately turbulent. A chain of vortices in the same radial location will merge into one vortex (e.g., Ono et al 2018), but there may be more vortices at different radii. In this sense, the emission feature could be a "tip of the iceberg" of even smaller dust concentrations.…”