Gravitoturbulence and the excitation of small-scale parametric instability in astrophysical discs

Abstract

Young protoplanetary discs and the outer radii of active galactic nucleii may be subject to gravitational instability and, as a consequence, fall into a 'gravitoturbulent' state. While in this state, appreciable angular momentum can be transported. Alternatively, the gas may collapse into bound clumps, the progenitors of planets or stars. In this paper, we numerically characterize the properties of 3D gravitoturbulence, focussing especially on its dependence on numerical parameters (resolution, domain size) and its excitation of small-scale dynamics. Via a survey of vertically stratified shearing box simulations with PLUTO and RODEO, we find (a) evidence that certain gravitoturbulent properties are independent of horizontal box size only when the box is larger than 40H, where H is the height scale, (b) at high resolution, small-scale isotropic turbulence appears off the midplane around z 0.5 − 1H 0 , and (c) this small-scale dynamics results from a parametric instability, involving the coupling of inertial waves with a large-scale axisymmetric epicyclic mode. This mode oscillates at a frequency close to Ω and is naturally excited by gravito-turbulence, via a nonlinear process to be determined. The small-scale turbulence we uncover has potential implications for a wide range of disc physics, e.g. turbulent saturation levels, fragmentation, turbulent mixing, and dust settling.

Dust dynamics and vertical settling in gravitoturbulent protoplanetary discs

“…Our unit of time is Ω −1 = 1, our unit of length is H = 1, while the surface density is fixed equal to Σ = 1.88. For details of how we calculate the 3D self-gravitating potential see Riols et al (2017) and Riols & Latter (2018a). The method was tested on the computations of 1D stratified disc equilibria, as well as their linear stability, to ensure that the implementation is correct (see appendices in Riols et al (2017)).…”

“…For τc = 20 Ω −1 , the turbulence is supersonic, highly compressible and characterized by large-scale spiral density waves, particularly strong in this cooling time regime. On top of these structures, small-scale motions driven by a parametric instability involving inertial waves attack the spiral wave fronts (see Riols et al 2017). Note that the resolution required to capture this instability is about 10 points per H. However, we emphasize that even for a resolution of 26 points per H, the smallest scales of the parasitic inertial modes are probably not resolved, given that it favours the smallest of scales.…”

“…The factor 1/2 comes from a rough estimate of Hg H/2 based on self-gravitating equilibria (see for instance Appendix A of Riols et al 2017).…”

“…In this paper we focus on the case τc = 20 Ω −1 . The reader may refer to Riols et al (2017) and Riols & Latter (2018a) (Section 3.1) to obtain a detailed analysis of related simulations and more information about the turbulent properties. For τc = 20 Ω −1 , the turbulence is supersonic, highly compressible and characterized by large-scale spiral density waves, particularly strong in this cooling time regime.…”

“…Of particular concern are additional vertical flows that may hinder dust sedimentation and/or the accumulation of dust in spirals. Very strong spiral shocks induce hydraulic jumps and accompanying fountain flows (Boley et al 2005) but, in fact, (less violent) vertical flows accompany spiral waves generically: recent high-resolution simulations by Riols et al (2017) and Riols & Latter (2018b) demonstrated that GI spiral waves (a) are subject to parasitic instabilities that produce small-scale inertial-wave turbulence, and (b) induce coherent large-scale vertical circulations mediated by g-modes. Both flows are necessarily absent in 2D simulations, and also potentially difficult to describe in global 3D simulations.…”