Numerical Insights into Disk Accretion, Eccentricity, and Kinematics in the Class 0 phase

TL;DR

This study addresses how Class 0 protoplanetary disks form and evolve under gravitational collapse when eccentric fluid motions are included. It uses two high-resolution 3D radiative MHD simulations with ambipolar diffusion (R1: 1 solar mass; R2: 3 solar masses), incorporating dust dynamics and gas tracer particles to track thermodynamic histories. The main findings show that magnetic fields and turbulence drive highly anisotropic, streamer-fed accretion that delivers material with angular momentum deficits, sustaining disk eccentricity around ~0.1; vertical accretion also generates strong turbulence, producing an effective turbulent viscosity near 0.1 and driving rapid disk spreading. These results have implications for early planetesimal formation and Solar System cosmochemistry by linking magnetized collapse to disk kinematics and isotopic delivery, while recognizing limitations such as inner-disk resolution and missing physical processes like jets and Hall effects.

Abstract

The formation and early evolution of protoplanetary disks are governed by a wide variety of physical processes during a gravitational collapse. Observations have begun probing disks in their earliest stages, and have favored the magnetically-regulated disk formation scenario. Disks are also expected to exhibit ellipsoidal morphologies in the early phases, an aspect that has been widely overlooked. We aim to describe the birth and evolution of the disk while accounting for the eccentric motions of fluid parcels. Using 3D radiative magnetohydrodynamic (MHD) simulations with ambipolar diffusion, we self-consistently model the collapse of isolated $1~\mathrm{M_\odot}$ and $3~\mathrm{M_\odot}$ cores to form a central protostar surrounded by a disk. We account for dust dynamics, and employ gas tracer particles to follow the thermodynamical history of fluid parcels. We find that magnetic fields and turbulence drive highly anisotropic accretion onto the disk via dense streamers. This streamer-fed accretion, occurring from the vertical and radial directions, drives vigorous internal turbulence that facilitates efficient angular momentum transport and rapid radial spreading. Crucially, the anisotropic inflow delivers material with an angular momentum deficit that continuously generates and sustains significant disk eccentricity ($e\sim 0.1$). Our results reveal ubiquitous eccentric kinematics in Class 0 disks, with direct implications for disk evolution, planetesimal formation, and the interpretation of cosmochemical signatures in Solar System meteorites.

Figures (21)

• Figure 1: Column density images in the $z$ (a, b, d, e) and $x$ (c, f) directions for runs R1 (first row) and R2 (second row), at both large scales (a, d) and small scales (b, c, e, f). The lime colored contours in panels (b,e) are a least-square fit of an ellipse enveloping the disk's surface. The associated eccentricity is shown in the top-right corner of each panels (b,e).
• Figure 2: Global evolution of the protoplanetary disk as a function of time, where $t=0$ represents the epoch of sink (i.e., protostellar) formation. The quantities shown are the protostellar mass (solid lines in panel a), disk mass (dotted lines in panel a), disk radius (solid lines in panel b), disk semi-major axis (dotted lines in panel b), and apparent disk eccentricity (c). The disk semi-major axis and apparent eccentricity are inferred from an elliptical fit. The blue (resp. red) curve corresponds to the 1 $\mathrm{M_{\odot}}$ (resp. 3 $\mathrm{M_{\odot}}$) run R1 (resp. R2). The shaded regions in panel (d) represent temporal fluctuations in the measurement, and the solid line is an average value.
• Figure 3: Hammer projections displaying the time and surface integrated radial mass flux on a sphere of $R_{\mathrm{shell}}=~30$ AU for runs R1 (left) and run R2 (right), displaying both the inflow (top colorbar) and outflow (bottom colorbar) of material throughout the simulation's duration post sink formation ($t_{\mathrm{f}}$), computed by integrating Eq. \ref{['eq:mdotsphere']} in time. The lime colored contour delimitates the transition from positive to negative values.
• Figure 4: Total inflow (solid lines) and outflow (dotted lines) of mass (panel a) and specific angular momentum (panel b) through a sphere of radius $R_{\mathrm{shell}}=~30$ AU around the sink particle as a function of time, where $t=0$ corresponds to the epoch of sink formation, for run R1 (blue) and R2 (red). This figure is complementary to Fig. \ref{['fig:shellacc']}.
• Figure 5: Total inflow of material through a cylinder of radius $R_{\mathrm{shell}}=~30$ AU and height $h=16$ AU throughout the simulation's duration post-sink formation for run R1 ($\approx 58$ kyr, first row) and R2 ($\approx 27$ kyr, second row), computed by integrating Eq. \ref{['eq:mdotcyl']} (first column) and Eq. \ref{['eq:mdotz']} (second and third columns) in time. The red circles in the second and third columns correspond to the minimum and maximum semi-major axis of the disk throughout each simulation's duration, and thus represent the locations where material has landed in the disk.