The CO snow line favours strong clumping by the streaming instability in protoplanetary discs with porous grains

TL;DR

Problem: can the streaming instability (SI) yield strong clumping in protoplanetary discs containing porous grains? Approach: apply the local clumping criterion $\varepsilon>\varepsilon_\mathrm{crit}$ from Lim2024 to porosity-evolution simulations across disc setups with and without the CO snow line. Key results: the CO snow line enables extended, early strong clumping up to $\sim80$ au, with inner clumps forming around $\sim20$ kyr and outer clumps around $\sim70$ kyr, yielding $M_{\mathrm{d},\varepsilon>\varepsilon_\mathrm{crit}} \gtrsim 28\,M_\oplus$ by 300 kyr; without it, clumping remains confined and delayed. Significance: highlights the CO snow line as a crucial factor promoting SI-driven planetesimal formation in porous-disc environments and motivates coupled, high-resolution simulations (e.g., GPU-accelerated Shamrock) to test SI with porosity evolution.

Abstract

Context: The radial drift and fragmentation of small dust grains in protoplanetary discs impedes their growth past centimetre sizes. Several mechanisms have been proposed to overcome these planet formation barriers, such as dust porosity or the streaming instability (SI), which is today regarded as the most promising mechanism to form planetesimals. Aims: Here, we examine whether the conditions for the SI to lead to strong clumping, the first step in planetesimal formation, are realised in protoplanetary discs containing porous grains. Methods: We used results from previous simulations of the evolution of porous grains subjected to growth, fragmentation, compaction and bouncing in protoplanetary discs. In the ensuing disc structures, we determined the regions where the dust-to-gas ratio exceeds the critical value for strong clumping found in simulations of the SI including external turbulence. Results: We find that the conditions for strong clumping are met within the first hundred thousand years in large regions of protoplanetary discs containing porous grains, provided that the CO snow line is taken into account. If the CO snow line is neglected, the conditions are met only very close to the inner disc edge early on, or over large areas well after 200,000 yr.

Figures (7)

• Figure 1: Positions of the SPH particles in the St-$\varepsilon$ plane, coloured by their radial distance to the star $r$, at $t=150,000$ yr in simulations without (left) and with (right) the CO snow line. The solid and dashed lines show the critical dust-to-gas ratios $\varepsilon_\mathrm{crit}$ from Lim2024 and $\varepsilon_\mathrm{LY21}$ from Li2021, respectively.
• Figure 2: Map of the dust-to-gas ratio $\varepsilon$ where it exceeds $\varepsilon_\mathrm{crit}$ in the meridian plane $(r,z)$ at $t=150,000$ yr in simulations without (left) and with the CO snow line, marked by the vertical dashed line (right). The extent of the gas disc is shown in light grey.
• Figure 3: Map of the Stokes number St in the meridian plane $(r,z)$, with the light grey background showing the extent of the gas disc in simulations without (left column) and with the CO snow line, marked by the vertical dashed line (right column). Time evolution is shown from top to bottom from $t=1$ to 200 kyr.
• Figure 4: Radial grain size distribution, with colour representing the filling factor $\phi$, in simulations without (left column) and with the CO snow line, marked by the vertical dashed line (right column). Time evolution is shown from top to bottom from $t=1$ to 200 kyr.
• Figure 5: Same as Fig. \ref{['Fig:r-z-St-evol']}, zoomed in on the disc interior to 90 au to show the late evolution at $t=200$, 250 and 300 kyr.