Planetary waves can activate resonant drag instabilities in 3D dusty gaseous discs

Resonant Drag Instabilities (RDIs) in protoplanetary discs are driven by the aerodynamic back-reaction of dust on gas and occur when the relative dust-gas motion resonate with a wave mode intrinsic to the gas fluid. Axisymmetric models indicate that the RDI generates filamentary perturbations, leading to grain clumping and planetesimal formation. Motivated by these findings, we investigate the dust-gas interaction in a non-axisymmetric inviscid protoplanetary disc with an embedded low-mass planet (𝑀p ∈ [0.3, 3]𝑀⊕, here 𝑀⊕ is the Earth mass).We conduct global 3D high-resolution two-fluid simulations, with the dust being parametrized by the Stokes number St ∈ [0.01, 0.5]. We find that planetary waves (PWs; also known as Rossby waves), which propagate along the downstream separatrices of the horseshoe region, resonate with the streaming motion and trigger the RDI. The consequent development of a global-scale filamentary dust distribution does not sensitively depend on the Stokes number, nor does it depend on the fast dust settling that takes place in an inviscid disc. The rapid onset of this instability, which is comparable to the dynamical orbital time-scale, suppresses the formation of asymmetric structures in the dust in the vicinity of the planet (such as dust voids and filaments). Additionally, we find that the dust feedback enables buoyancy resonances in an otherwise non-buoyant (globally isothermal) disc. Therefore, our results provide the first numerical evidence of RDIs generation driven by planetary waves.

原行星盘中的共振阻力不稳定性（Resonant Drag Instabilities, RDIs）由尘埃对气体的气动反作用驱动，当尘埃与气体的相对运动与气体流体固有的波动模式发生共振时，该不稳定性便会被激发。轴对称模型研究表明，共振阻力不稳定性会产生丝状扰动，进而推动颗粒聚团与星子的形成。受此研究发现的启发，我们针对内嵌低质量行星（行星质量$M_p in [0.3, 3]M_oplus$，其中$M_oplus$代表地球质量）的无粘非轴对称原行星盘，开展尘埃-气体相互作用的相关数值研究。我们开展了全局三维高分辨率双流体模拟，其中尘埃的参数化表征采用斯托克斯数$St in [0.01, 0.5]$。研究发现，沿马蹄区下游分界面传播的行星波（Planetary Waves, PWs，又称罗斯贝波）会与尘埃流运动发生共振，进而触发共振阻力不稳定性。由此形成的全局尺度丝状尘埃分布，既不敏感依赖于斯托克斯数，也不受无粘盘中发生的尘埃快速沉降过程的影响。该不稳定性的快速发展时标与动力学轨道时标相当，能够抑制行星附近区域尘埃中非对称结构（如尘埃空洞与丝状结构）的形成。此外，我们还发现尘埃的反作用可在原本无浮力的全局等温盘中诱发浮力共振。因此，本研究结果首次提供了由行星波驱动的共振阻力不稳定性产生的数值证据。