Steady-state accretion in magnetized protoplanetary disks

Abstract

Context. The transition between magnetorotational instability (MRI)-active and magnetically dead regions corresponds to a sharp change in the disk turbulence level, where pressure maxima may form, hence potentially trapping dust particles and explaining some of the observed disk substructures. Aims. We aim to provide the first building blocks toward a self-consistent approach to assess the dead zone outer edge as a viable location for dust trapping, under the framework of viscously driven accretion. Methods. We present a 1+1D global magnetically driven disk accretion model that captures the essence of the MRI-driven accretion, without resorting to 3D global nonideal magnetohydrodynamic (MHD) simulations. The gas dynamics is assumed to be solely controlled by the MRI and hydrodynamic instabilities. For given stellar and disk parameters, the Shakura–Sunyaev viscosity parameter, α, is determined self-consistently under the adopted framework from detailed considerations of the MRI with nonideal MHD effects (Ohmic resistivity and ambipolar diffusion), accounting for disk heating by stellar irradiation, nonthermal sources of ionization, and dust effects on the ionization chemistry. Additionally, the magnetic field strength is numerically constrained to maximize the MRI activity. Results. We demonstrate the use of our framework by investigating steady-state MRI-driven accretion in a fiducial protoplanetary disk model around a solar-type star. We find that the equilibrium solution displays no pressure maximum at the dead zone outer edge, except if a sufficient amount of dust particles has accumulated there before the disk reaches a steady-state accretion regime. Furthermore, the steady-state accretion solution describes a disk that displays a spatially extended long-lived inner disk gas reservoir (the dead zone) that accretes a few times 10−9 M⊙ yr−1. By conducting a detailed parameter study, we find that the extent to which the MRI can drive efficient accretion is primarily determined by the total disk gas mass, the representative grain size, the vertically integrated dust-to-gas mass ratio, and the stellar X-ray luminosity. Conclusions. A self-consistent time-dependent coupling between gas, dust, stellar evolution models, and our general framework on million-year timescales is required to fully understand the formation of dead zones and their potential to trap dust particles.

Massive Compact Dust Disk with a Gap around CW Tau Revealed by ALMA Multiband Observations

“…At the dead-zone outer edge, the turbulent viscosity arising from the magnetorotational instability increases from inside out. This results in a steep decrease in the gas surface density (e.g., Delage et al 2022), which can also be seen in the dust distribution (e.g., Kretke et al 2009;Ueda et al 2021c). If this is the case, a similar transition in the gas surface density, as well as the transition in the turbulence strength, should be observed.…”

Distributions of gas and small and large grains in the LkHα 330 disk trace a young planetary system,

“…Furthermore, variations of the disk viscosity can also trigger spiral arms (Lyra et al 2015), but in this case numerous spiral arms would be expected, while only two are detected in current observations. However, the extension of a dead zone for a star such as LkHα 330 is expected to be around 20 au (Delage et al 2022), which is much smaller than the observed cavity. A clear way to distinguish this scenario from the planet scenario is to actually detect potential planet(s) or their circumplanetary disks inside the cavity, as in the case of PDS 70 (Keppler et al 2018;Benisty et al 2021).…”

Architecture of Planetary Systems Predicted from Protoplanetary Disks Observed with ALMA. II. Evolution Outcomes and Dynamical Stability

“…A higher viscosity α may explain the observed accretion rate, but it is not observationally favored, as the recent study (e.g., Flaherty et al 2015) suggests that the disk viscosity may be rather low. This inconsistency is mainly due to our simplified viscous model that assumes a constant α viscosity, and more sophisticated viscous accretion (Delage et al 2022) or disk-wind accretion (Bai 2016;Suzuki et al 2016;Ida et al 2018) models are required to address this inconsistency.…”