Quantifying the Impact of the Dust Torque on the Migration of Low-mass Planets

Disk solids are critical in many planet formation processes, however, their effect on planet migration remains largely unexplored. Here we assess for the first time this important issue by building on the systematic measurements of dust torques on an embedded planet by Benitez-Llambay & Pessah (2018). Adopting standard models for the gaseous disk and its solid content, we quantify the impact of the dust torque for a wide range of conditions describing the disk/planet system. We show that the total torque can be positive and revert inward planet migration for planetary cores with $M_{\rm p} \lesssim 10 M_\oplus$. We compute formation tracks for low-mass embryos for conditions usually invoked when modeling planet formation processes. Our most important conclusion is that dust torques can have a significant impact on the migration and formation history of planetary embryos. The most important implications of our findings are: $\it{i})$ For nominal dust-to-gas mass ratios $\epsilon \simeq 0.01$, low-mass planets migrate outwards beyond the water ice-line if most of the mass in solids is in particles with Stokes numbers St $\simeq 0.1$. $\it{ii})$. For $\epsilon \gtrsim 0.02-0.05$, solids with small Stokes numbers, St $\simeq 0.01$, can play a dominant role if most of the mass is in those particles. $\it{iii})$ Dust torques have the potential to enable low-mass planetary cores formed in the inner disk to migrate outwards and act as the seed for massive planets at distances of tens of au.