Early Stages of Protostellar Disk Evolution: A Link to the Initial Cloud Core

TL;DR

This work develops a self-similar, non-isothermal protodisk model in which disk self-gravity dominates and envelope-fed infall drives early evolution. By parameterizing GI-driven angular-momentum transport with a viscous analogue $\nu_{\rm GI}$ and including disk winds, the authors connect initial core states—encoded in $\alpha_0$—to disk structure, Toomre stability, and the angular-momentum budget during the first several thousand years after protostar formation, with a validity window of $\lesssim 2\times 10^{3}$ yr. They find that more unstable cores (lower $\alpha_0$) yield higher infall, larger GI-active disks with $Q<1$ over extended annuli and a rotation profile $v_{\phi} \propto r^{-0.2}$, while GI torques and winds transport angular momentum outward and reduce the net disk angular momentum. The framework aligns reasonably with early hydrodynamic simulations and clarifies how core thermodynamics and transport efficiency shape disk outcomes, while noting limitations from neglecting the central star, irradiation, and fragmentation. The results offer a physically motivated basis for interpreting the earliest stages of disk formation and the initial conditions for planet formation.

Abstract

We study the structure and evolution of the very early protostellar disk (``protodisk'') just after protostar formation, where disk self-gravity dominates and the stellar contribution is dynamically minor. The disk redistributes angular momentum outward through outflows and gravitational torques, thereby helping to resolve the angular momentum problem of star formation. We develop a self-similar model and carry out a parameter study that examines disk stability as a function of the key drivers of early evolution, notably the infall rate from the envelope and the strength of the gravitational torques. The mass infall rate onto the disk is estimated to be that from the collapse of a Bonnor-Ebert sphere. Our results indicate that protostellar disks that form from more unstable initial cores are more likely to be Toomre-unstable. We also find that the specific angular momentum of young protostellar disks lie in the range $10^{19}\text{--}10^{20}\,{\rm cm^2\,s^{-1}}$. We find distinct power-law profiles of physical quantities in the protodisk stage, including a rotation velocity profile that is shallower than the Keplerian profile that would be established at a later stage. As a rough validity window, our assumptions are most secure during the first $\lesssim 2\times 10^{3}$\,yr after protostar formation and may plausibly extend to $\sim(0.5\text{--}1)\times 10^{4}$\,yr under weak magnetic braking and strong infall.

Figures (10)

• Figure 1: The profiles of the physical variables at three epochs for $\alpha_0 = 0.5$, $\eta^{\prime}=10^{-2}$, $\gamma=1.1$ and a typical outflow emanating from the disk set at $(\Lambda_0,l,s)=(0.1, 1.5, 0.7)$. The panels show surface density, radial and tangential velocities, sound speed, and Toomre $Q$ profiles, illustrating both the radial and temporal evolution of the system.
• Figure 2: The profiles of the physical variables at $t=10^3~{\rm yr}$ for $\alpha_0 = 0.7,0.5,0.3$ with $\eta=10^{-2}$, $\gamma=1.1$ and a typical outflow emanating from the disk set at $(\Lambda_0,l,s)=(0.1, 1.5, 0.7)$.
• Figure 3: Same as Figure \ref{['alpha']} but with fixed $\alpha_0 = 0.5$ and $\eta^{\prime}=10^{-1},10^{-2},10^{-3},10^{-4}$.
• Figure 4: Same as Figure \ref{['alpha']} but with fixed $\alpha_0 = 0.5$ and different strength attributed to outflows, i.e., $\Lambda_0=0,0.1,0.2$.
• Figure 5: Same as Figure \ref{['alpha']} but with fixed $\alpha_0 = 0.5$ and $\gamma=1.0,1.05,1.1$.