The interplay of gas, dust and magnetorotational instability in magnetized protoplanetary disks

The rich diversity of exoplanets discovered in various physical environments clearly shows that planet formation is an efficient process with multiple outcomes. To understand the emergence of newborn planets, one can rewind the clock of planetary systems by investigating the formation and evolution of their natal environment, the so-called protoplanetary disks. In the core accretion scenario, rocky planets such as the Earth are thought to be formed from cosmic dust particles that grow into pebbles and planetesimals, the building blocks of planets, later assembling together. An intricate puzzle in this theory is how exactly these building blocks are formed and kept long enough in the natal protoplanetary disk. Protoplanetary disks are weakly magnetized accretion disks that are subject to the magnetorotational instability (MRI). It is to date one of the main candidates for explaining their turbulence and angular momentum transport. The nonideal magnetohydrodynamic (MHD) effects prevent the MRI from operating everywhere in the protoplanetary disk, leading to MRI active regions with high turbulence and non-MRI regions with low turbulence. It has been hypothesized that these variations in the disk turbulence can lead to pressure maxima where dust particles can be trapped. In these so-called dust traps, dust particles can grow efficiently into pebbles and potentially planetesimals. Yet, it is still an open question how this MRI-powered mechanism shapes the secular evolution of protoplanetary disks, and how it is involved in the first steps of planet formation. It is because the interplay of gas evolution, dust evolution (dynamics and grain growth processes combined) and MRI-driven turbulence over millions of years has never been investigated. The central goal of this thesis is to bridge the gap in the core accretion scenario of planet formation by building the very first unified disk evolution framework that captures self-consistently this interplay. The unique approach adopted in this thesis leads to an exciting new pathway for the generation of spontaneous dust traps everywhere in the protoplanetary disk, which can be potential birth-sites for planets by forming and keeping their necessary building blocks.

There are four key milestones to my work. I describe them below. My PhD thesis can be found at this URL.

Figure: Simulated ALMA continuum emission at 1.3mm of a protoplanetary disk around a solar mass star at 0.7Myr of evolution. The observed dust ring resembles those of commonly observed protoplanetary disks in surveys (e.g., Andrews et al. 2018). To generate such an image, the dust size distribution has been obtained by employing our unified 1D disk evolution framework, post-processed with the radiative transfer code RADMC-3D (Dullemond et al. 2012) and the software SIMIO (Kurtovic submitted). Here it is assumed that the protoplanetary disk has a similar geometry, angular resolution, and sensitivity as Elias 24 (Huang et al. 2018), which represents the high angular resolution observations observed with ALMA. 

Spontaneous formation of long-lived dust traps during the secular evolution of magnetized protoplanetary disks

Based on the previous studies, we have built the very first unified 1D disk evolution framework that combines self-consistently the following key processes, whose interplay is key: (1) detailed MRI calculations to derive the gas turbulence; (2) gas advection/diffusion; (3) dust advection/diffusion including grain growth processes; and (4) stellar bolometric and X-ray luminosity evolutionary tracks. This is achieved by fully coupling the 1+1D MRI-driven disk accretion model described below to the code DustPy

This unique framework is fast enough to simulate protoplanetary disks over a few million years (their typical age), and run hundreds of simulations post-processed with radiative transfer calculations to compare with surveys of protoplanetary disks.

With this tool, we are now in position to provide a more consistent approach to assess whether the dead zone outer edge is a viable location for dust trapping in protoplanetary disks. The simulations demonstrate, for the first time, that observable spontaneous dust rings can be  formed at the dead zone outer edge under certain conditions, as well as within the dead zone. Planetesimal formation may be triggered in some of these dust rings, hence being potential birth-sites for planets.

Figure: Sole impact of dust evolution on the dead zone outer edge.

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

In this pilot study, we provide an important step toward a better understanding of the MRI-dust coevolution in protoplanetary disks. 

We employed and improved the 1+1D MRI-driven disk accretion model described below, and implemented the effect of dust evolution (dynamics and growth processes included) by partially coupling it to the code DustPy (Stammler & Birnstiel 2022). Doing so allowed, for the first time, to unveil some insights about how the evolution of dust and MRI-driven accretion are intertwined on million-year timescales, accounting for a careful modeling of the gas ionization degree. One should note that there is no gas evolution accounted for to isolate the effect of dust evolution on the MRI activity. 

We find that the MRI-induced gas turbulence changes on a timescale of local dust growth as long as there is enough dust particles in the protoplanetary disk to dominate the ionization chemistry. Once it is no longer the case, the change in the MRI-induced gas turbulence is controlled by gas evolution and occurs on a viscous evolution timescale. This demonstrates that the feedback of dust evolution into the gas ionization degree is crucial to accurately describe the MRI activity. Furthermore, the dead zone appears to be long-lived and to survive dust evolution over a few million years. In the case of typical T-Tauri stars, the dead zone outer edge is expected to be located between 10au and 50au for "strong enough" magnetic field strengths. 

Figure: Local MRI-induced gas turbulence computed both as function of radius and height by the 1+1D MRI-driven disk accretion model, for the fiducial model.

Steady-state MRI-driven accretion in magnetized protoplanetary disks

In this study, we applied the 1+1D MRI-driven disk accretion model described below to investigate the structure of a steadily accreting protoplanetary disk. To obtain the steady-state MRI-driven accretion solution the gas surface density, gas ionization degree, magnetic field, accretion rate, and MRI-induced gas turbulence are calculated self-consistently.

For the fiducial protoplanetary disk model considered, we find that no long-lived gas pressure maximum forms at the dead zone outer edge, unless a sufficient amount of dust particles has locally accumulated there. Furthermore, there is a steep decrease in the gas surface density coexisting with a steep increase in the MRI-induced gas turbulence where the dead zone outer edge is located. 

Additionally, we performed a comprehensive parameter study to investigate what model parameters the MRI-driven accretion in protoplanetary disks depends on, as well as the extent to which the accretion is efficient. We demonstrate that the MRI activity is crucially set by the local dust and gas properties, the stellar X-ray luminosity, and the magnetic field strength. This result strongly motivates the need of a time-dependent framework that captures the interplay between gas, dust, stellar and MRI evolution.

Figure: Flowchart of the 1+1D MRI-driven disk accretion model (figure from Delage et al. 2023).

New 1+1D global MRI-driven disk accretion model for magnetized protoplanetary disks

I have developed a code (to be publicly available soon) whose main output is an effective radial profile for the MRI-induced gas turbulence, self-consistently determined given stellar, gas and dust properties, under the framework of viscously driven accretion. 

The code implements a new 1+1D global magnetically driven disk accretion model built to study the outer region of protoplanetary disks  (> 1AU), which accretes viscously solely due to the MRI and hydrodynamic instabilities. Such a model has the advantage to capture the essence of the MRI-driven accretion in a non-computionally expensive way, making further coupling with 1D gas and dust evolution models feasible on million-year timescales

It includes the key following physical processes to obtain detailed considerations of the MRI activity: (1) disk heating by passively absorbing stellar irradiation; (2) dust settling; (3) nonthermal ionization (stellar X-rays, galactic cosmic rays, decay of short- and long-lived radionuclides); (4) ionization chemistry based on a semi-analytical model that captures the charge state of the disk dust-gas mixture, hence carefully modeling the gas ionization degree; and (5) nonideal magnetohydrodynamic (MHD) effects (Ohmic resistivity and ambipolar diffusion).