Dust-void evolution driven by turbulent dust flux can induce runaway migration of Earth-mass planets

Torques from asymmetric dust structures (so-called dust-void and filamentary structures) formed around low-mass planets embedded in a non turbulent dust-gas disk can exceed the torques produced by the gas disk component, then governing the planet's orbital dynamics. Here, we investigate how these structures (hence the dust torque) change when the effect of turbulent dust diffusion and dust feedback are included, and the direct implications on the migration of Earth-like planets. Using the \textsc{Fargo3D} code, we perform 2D and 3D multifluid hydrodynamic simulations, focusing on a non-migrating planet with the mass $M_p=1.5\,M_\oplus$ in 2D and on migrating planets with $M_p\in[1.5,12]\,M_\oplus$ in 3D. We vary the $\delta$-dimensionless diffusivity parameter in the range $[0,3\times10^{-3}]$ and consider three different Stokes numbers $\mathrm{St}=\{0.04,0.26,0.55\}$, which are representative of the gas, transitional and gravity-dominated regimes, respectively. In our 2D models, we find that turbulent diffusion of dust prevents the formation of the dust-void and filamentary structures when $\delta>3\times10^{-4}$. Otherwise, dust structures survive turbulent diffusion flow. However, dust and total torques become positive only in transitional and gravity-dominated regimes. In our 3D models, we find that the dust-void is drastically modified and the high-density ring-shaped barrier delineating the dust-void disappears if $\delta\gtrsim10^{-4} $, due to the effect of dust turbulent diffusion along with the back-reaction of the dust. For all values of $\delta$, the filament in front of the planet is replaced by a low-density trench. Remarkably, as we allow the planets to migrate, the evolving dust-void can drive either runaway migration or outward (inward) oscillatory-torque migration. Our study thus suggests that low-mass Earth-like planets can undergo runaway migration in dusty disks.