The impact of dust evolution on the dead zone outer edge in magnetized protoplanetary disks

Abstract

Context. The dead zone outer edge corresponds to the transition from the magnetically dead to the magnetorotational instability (MRI) active regions in the outer protoplanetary disk midplane. It has been previously hypothesized to be a prime location for dust particle trapping. A more consistent approach to access such an idea has yet to be developed, since the interplay between dust evolution and MRI-driven accretion over millions of years has been poorly understood. Aims. We provide an important step toward a better understanding of the MRI–dust coevolution in protoplanetary disks. In this pilot study, we present a proof of concept that dust evolution ultimately plays a crucial role in the MRI activity. Methods. First, we study how a fixed power-law dust size distribution with varying parameters impacts the MRI activity, especially the steady-state MRI-driven accretion, by employing and improving our previous 1+1D MRI-driven turbulence model. Second, we relax the steady-state accretion assumption in this disk accretion model, and partially couple it to a dust evolution model in order to investigate how the evolution of dust (dynamics and grain growth processes combined) and MRI-driven accretion are intertwined on million-year timescales, from a more sophisticated modeling of the gas ionization degree. Results. Dust coagulation and settling lead to a higher gas ionization degree in the protoplanetary disk, resulting in stronger MRI-driven turbulence as well as a more compact dead zone. On the other hand, fragmentation has an opposite effect because it replenishes the disk in small dust particles which are very efficient at sweeping up free electrons and ions from the gas phase. Since the dust content of the disk decreases over millions of years of evolution due to radial drift, the MRI-driven turbulence overall becomes stronger and the dead zone more compact until the disk dust-gas mixture eventually behaves as a grain-free plasma. Furthermore, our results show that dust evolution alone does not lead to a complete reactivation of the dead zone. For typical T-Tauri stars, we find that the dead zone outer edge is expected to be located roughly between 10 au and 50 au during the disk lifetime for our choice of the magnetic field strength and configuration. Finally, the MRI activity evolution is expected to be crucially sensitive to the choice made for the minimum grain size of the dust distribution. Conclusions. The MRI activity evolution (hence the temporal evolution of the MRI-induced α parameter) is controlled by dust evolution and occurs on a timescale of local dust growth, as long as there are enough dust particles in the disk to dominate the recombination process for the ionization chemistry. Once that is no longer the case, the MRI activity evolution is expected to be controlled by gas evolution and occurs on a viscous evolution timescale.