Linear stability of magnetized massive protoplanetary disks

Magneto-rotational instability (MRI) and gravitational instability (GI) are the two principle routes to turbulent angular momentum transport in accretion disks. Protoplanetary disks may develop both. This paper aims to reinvigorate interest in the study of magnetized massive protoplanetary disks, starting from the basic issue of stability. The local linear stability of a self-gravitating, uniformly magnetized, differentially rotating, three-dimensional stratified disk subject to axisymmetric perturbations is calculated numerically. The formulation includes resistivity. It is found that the reduction in the disk thickness by self-gravity can decrease MRI growth rates; the MRI becomes global in the vertical direction, and MRI modes with small radial length scales are stabilized. The maximum vertical field strength that permits the MRI in a strongly self-gravitating polytropic disk with polytropic index $\Gamma=1$ is estimated to be $B_{z,\mathrm{max}} \simeq c_{s0}\Omega\sqrt{\mu_0/16\pi G}$, where $c_{s0}$ is the midplane sound speed and $\Omega$ is the angular velocity. In massive disks with layered resistivity, the MRI is not well-localized to regions where the Elsasser number exceeds unity. For MRI modes with radial length scales on the order of the disk thickness, self-gravity can enhance density perturbations, an effect that becomes significant in the presence of a strong toroidal field, and which depends on the symmetry of the underlying MRI mode. In gravitationally unstable disks where GI and MRI growth rates are comparable, the character of unstable modes can transition smoothly between MRI and GI. Implications for non-linear simulations are discussed briefly.Comment: Accepted by ApJ; project source code available at https://github.com/minkailin/sgmr

Gravitational instability of planetary gaps and its effect on orbital migration

Gap formation by giant planets in self-gravitating disks may lead to a gravitational edge instability (GEI). We demonstrate this GEI with global 3D and 2D self-gravitating disk-planet simulations using the ZEUS, PLUTO and FARGO hydrodynamic codes. High resolution 2D simulations show that an unstable outer gap edge can lead to outwards orbital migration. Our results have important implications for theories of giant planet formation in massive disks.Comment: Published in the proceedings of IAUS 299. Associated paper is arXiv:1306.2514. Poster can be found at http://cita.utoronto.ca/~mklin924/IAUposter.pd

Steady state of dust distributions in disk vortices: Observational predictions and applications to transitional disks

The Atacama Large Millimeter Array (ALMA) has been returning images of transitional disks in which large asymmetries are seen in the distribution of mm-sized dust in the outer disk. The explanation in vogue borrows from the vortex literature by suggesting that these asymmetries are the result of dust trapping in giant vortices, excited via Rossby wave instability (RWI) at planetary gap edges. Due to the drag force, dust trapped in vortices will accumulate in the center, and diffusion is needed to maintain a steady state over the lifetime of the disk. While previous work derived semi-analytical models of the process, in this paper we provide analytical steady-state solutions. Exact solutions exist for certain vortex models. The solution is determined by the vortex rotation profile, the gas scale height, the vortex aspect ratio, and the ratio of dust diffusion to gas-dust friction. In principle, all these quantities can be derived from observations, which would give validation of the model, also giving constrains on the strength of the turbulence inside the vortex core. Based on our solution, we derive quantities such as the gas-dust contrast, the trapped dust mass, and the dust contrast at the same orbital location. We apply our model to the recently imaged Oph IRS 48 system, finding values within the range of the observational uncertainties.Comment: 11 pages, 3 figures, accepted by Ap

The effect of self-gravity on vortex instabilities in disc-planet interactions

We study the effect of disc self-gravity on vortex-forming instabilities associated with gaps opened by a Saturn mass planet in a protoplanetary disc. It is shown analytically and confirmed through linear calculations that vortex modes with low azimuthal mode number $,m,$ are stabilised by increasing self-gravity if the basic state is fixed. However, linear calculations show that the combined effect of self-gravity through the background and through the linear response shifts the most unstable vortex mode to higher $m.$ Nonlinear hydrodynamic simulations of planetary gaps show more vortices develop with increasing strength of self-gravity. For sufficiently large disc mass the vortex instability is suppressed and replaced by a new global instability, consistent with analytical expectations. In the nonlinear regime, vortex merging is increasingly delayed as the disc mass increases and multiple vortices may persist until the end of simulations. With self-gravity, the post-merger vortex is localised in azimuth and has similar structure to a Kida-like vortex. This is unlike the case without self-gravity where vortices merge to form a single vortex extended in azimuth. We also performed a series of supplementary simulations of co-orbital Kida-like vortices and found that self-gravity enables such vortices to execute horseshoe turns upon encountering each other. As a result vortex merging is avoided on time-scales where it would occur without self-gravity. Thus we suggest that mutual repulsion of self-gravitating vortices in a rotating flow is responsible for the delayed vortex merging above. The effect of self-gravity on vortex-induced migration is briefly discussed. We found that when self-gravity is included, the vortex-induced type III migration of Lin & Papaloizou (2010) is delayed but the extent of migration is unchanged.Comment: 21 pages, 19 figures. Accepted by MNRAS. Displayed abstract is shortene