Planetesimal Formation Across the Stellar Mass Spectrum and its Influence on Exoplanet-Inherited Volatile Budgets

Technical Summary: Planetesimal Formation Across the Stellar Mass Spectrum and its Influence on Exoplanet-Inherited Volatile Budgets

Problem Statement
Current models of planet formation often assume a uniform starting point ($t=0$) for protoplanetary discs, typically defined as the onset of dust evolution in a pre-formed Class II disc. However, the timing and mechanisms of planetesimal formation are sensitive to the thermal and dynamical history of the disc, which is dictated by the collapse of the parent molecular cloud. The authors investigate how planetesimal formation varies across the stellar mass spectrum, specifically examining the interplay between cloud collapse, viscous disc evolution, and the water snowline. A critical motivation is understanding the origin of the Carbonaceous/Non-Carbonaceous (CC/NC) heterogeneity observed in the Solar System and determining whether exoplanets, particularly those around low-mass M-dwarfs, inherit volatile-rich or volatile-poor compositions based on their formation epoch relative to the decay of radioactive Aluminium-26 ($^{26}\text{Al}$).

Methodology
The authors employ 1D simulations coupling a viscously evolving disc model with a molecular cloud collapse model (based on Shu 1977; Ulrich 1976). The framework integrates:

• Cloud Collapse: A singular isothermal sphere collapses at a constant rate until the cloud is depleted. Initial conditions vary by cloud mass ($M_{\text{cloud}}$) and rotation rate ($\Omega_{\text{cloud}}$), scaled to maintain observational trends in specific angular momentum ($J \propto R^{1.5}$).
• Dust and Ice Evolution: Dust growth follows a two-population algorithm (Birnstiel et al. 2012), excluding growth in the molecular cloud phase. Water ice transport includes sublimation and condensation (Ciesla & Cuzzi 2006).
• Planetesimal Formation: The model utilizes the streaming instability triggered by a "traffic jam" at the water snowline (due to differing fragmentation velocities of dry vs. wet dust) and the "cold-finger effect" (diffusion of water vapor across the snowline).
• Stellar Parameters: Simulations cover a range of stellar masses ($0.1 M_{\odot}$ to $1.4 M_{\odot}$) derived from cloud masses. Stellar luminosity and radius are fixed at 10 Myr evolutionary stages (Baraffe et al. 2015).
• Key Parameters: Viscous $\alpha_{\text{visc}} = 10^{-3}$ and turbulent $\alpha_{\text{turb}} = 10^{-5}$.

Key Results

1. Stellar Mass Dependence of Formation Timing:

   • Low-Mass M-Dwarfs ($0.1 M_{\odot}$): Planetesimal formation occurs exclusively during the Class II phase, approximately $< 500$ kyr after the onset of collapse. The infall phase does not produce planetesimals due to low pebble mass flux to the snowline.
   • Solar and Higher Mass Stars ($\ge 0.3 M_{\odot}$): Planetesimals form in two distinct reservoirs. "Reservoir I" forms during the cloud infall phase, and "Reservoir II" forms during the Class II phase, separated by a pause in formation when the snowline migrates outward due to viscous heating.
   • Timescales: Discs around low-mass stars evolve significantly faster. Pebble drift and dust depletion occur within $< 2$ Myr for $0.1 M_{\odot}$ systems, whereas higher mass systems retain dust reservoirs for $> 5$ Myr.

2. Chemical Heterogeneity and Volatile Budgets:

   • Solar-like Systems: The temporal separation between Reservoir I and II creates a chemical dichotomy. Reservoir I forms early ($t < \tau_{^{26}\text{Al}}$) and is heated by $^{26}\text{Al}$, leading to dehydration. Reservoir II forms later ($t > \tau_{^{26}\text{Al}}$) and remains volatile-rich (wet). This mirrors the proposed CC/NC dichotomy in the Solar System.
   • M-Dwarf Systems: Due to the rapid evolution and short infall phase, all planetesimals around $0.1 M_{\odot}$ stars form within the half-life of $^{26}\text{Al}$ ($\sim 700$ kyr). Consequently, if $^{26}\text{Al}$ is present, all resulting planetesimals undergo radiogenic heating and become dehydrated. There is no "wet" reservoir formed later.

3. Disc Evolution and $t=0$:

   • The choice of $t=0$ (cloud collapse onset vs. Class II disc start) significantly impacts the interpretation of disc ages. At a fixed time post-collapse (e.g., 2 Myr), a $0.1 M_{\odot}$ disc is in a much more advanced evolutionary stage (depleted of dust) compared to a $1.0 M_{\odot}$ disc.
   • The observed steep-than-linear relationship between mass accretion rate and stellar mass ($\dot{M}_{\text{acc}} \propto M_{\star}^2$) is reproduced by the simulations only when connecting discs at equivalent evolutionary stages rather than equal time snapshots.

4. Sensitivity to Cloud Rotation:

   • Increasing cloud rotation rates delays the onset of infall-phase planetesimal formation (Reservoir I) but increases the total mass of planetesimals formed in the Class II phase due to larger centrifugal radii and dust reservoirs.
   • Higher rotation rates generally produce narrower planetesimal belts (in fractional width), consistent with the upper limits of observed debris disc widths.

Significance and Claims
The paper argues that the variation in disc evolution across stellar masses makes it difficult to define a universal $t=0$ for all protoplanetary discs. The primary significance of the work lies in its implications for the volatile content of exoplanets:

• Volatile-Poor M-Dwarf Planets: The authors propose that rocky planets forming around low-mass M-dwarfs will likely be born volatile-poor. Because planetesimal formation is rapid and occurs entirely within the $^{26}\text{Al}$ heating window, the building blocks of these planets are dehydrated.
• JWST Observations: This mechanism offers a potential explanation for the lack of detected atmospheres on rocky worlds around M-dwarfs observed by the James Webb Space Telescope (JWST), suggesting these worlds may be inherently dry rather than having lost atmospheres via photoevaporation.
• Solar System Context: The model supports the hypothesis that the CC/NC heterogeneity in the Solar System arises from the temporal separation of planetesimal formation during the infall and Class II phases, driven by the specific thermal history of a solar-mass cloud collapse.

The authors conclude that while their 1D models successfully reproduce observational trends in accretion rates and planetesimal formation timing, the specific architectures of planetary systems remain highly sensitive to the initial conditions of the collapsing molecular cloud, particularly mass and angular momentum.