THE SPIRAL WAVE INSTABILITY INDUCED BY A GIANT PLANET. I. PARTICLE STIRRING IN THE INNER REGIONS OF PROTOPLANETARY DISKS

We have recently shown that spiral density waves propagating in accretion disks can undergo a parametric instability by resonantly coupling with and transferring energy into pairs of inertial waves (or inertial-gravity waves when buoyancy is important). In this paper, we perform inviscid three-dimensional global hydrodynamic simulations to examine the growth and consequence of this instability operating on the spiral waves driven by a Jupiter-mass planet in a protoplanetary disk. We find that the spiral waves are destabilized via the spiral wave instability (SWI), generating hydrodynamic turbulence and sustained radially-alternating vertical flows that appear to be associated with long wavelength inertial modes. In the interval $0.3~R_p \leq R \leq 0.7~R_p$, where $R_p$ denotes the semi-major axis of the planetary orbit (assumed to be 5~au), the estimated vertical diffusion rate associated with the turbulence is characterized by $\alpha_{\rm diff} \sim (0.2-1.2) \times 10^{-2}$. For the disk model considered here, the diffusion rate is such that particles with sizes up to several centimeters are vertically mixed within the first pressure scale height. This suggests that the instability of spiral waves launched by a giant planet can significantly disperse solid particles and trace chemical species from the midplane. In planet formation models where the continuous local production of chondrules/pebbles occurs over Myr time scales to provide a feedstock for pebble accretion onto these bodies, this stirring of solid particles may add a time constraint: planetary embryos and large asteroids have to form before a gas giant forms in the outer disk, otherwise the SWI will significantly decrease the chondrule/pebble accretion efficiency.Comment: Accepted for publication in the The Astrophysical Journal, 19 pages, 12 figures, 1 tabl

Saving Super-Earths:Interplay between Pebble Accretion and Type I Migration

Overcoming type I migration and preventing low-mass planets from spiralling into the central star is a long-studied topic. It is well known that outward migration is possible in viscously heated disks relatively close to the central star because the entropy gradient can be sufficiently steep for the positive corotation torque to overcome the negative Lindblad torque. Yet efficiently trapping planets in this region remains elusive. Here we study disk conditions that yield outward migration for low-mass planets under specific planet migration prescriptions. In a steady-state disk model with a constant α-viscosity, outward migration is only possible when the negative temperature gradient exceeds ∼0.87. We derive an implicit relation for the highest mass at which outward migration is possible as a function of viscosity and disk scale height. We apply these criteria, using a simple power-law disk model, to planets that have reached their pebble isolation mass after an episode of rapid accretion. It is possible to trap planets with the pebble isolation mass farther than the inner edge of the disk provided that α crit 0.004 for disks older than 1 Myr. In very young disks, the high temperature causes the planets to grow to masses exceeding the maximum for outward migration. As the disk evolves, these more massive planets often reach the central star, generally only toward the end of the disk lifetime. Saving super-Earths is therefore a delicate interplay between disk viscosity, the opacity profile, and the temperature gradient in the viscously heated inner disk