Bouncing Grains Keep Protoplanetary Disks Bright

TL;DR

This work addresses how protoplanetary disks remain millimeter-bright for several Myr, despite grain growth and radial drift. It argues that a bouncing barrier, capping grain growth at around $a_{\rm bounce} \approx 100\,\mu$m, suppresses drift and preserves optical thickness, thereby sustaining the observed size-luminosity relation and low spectral indices across regions from Lupus to Upper Scorpius. The authors combine multi-region disk data (including new USco measurements) with order-of-magnitude analytical estimates and DustPy simulations to contrast bouncing versus no-bouncing scenarios, finding that only bouncing can reproduce the long-lived, bright, compact disks. They also review observational evidence for small grains (e.g., mm polarization) and discuss theoretical caveats and the possible fate of disks after bounce, including how planetesimals might form without large grains. Overall, the bouncing barrier emerges as a robust, universal mechanism linking grain physics to disk observables and evolution, with implications for planetesimal formation and disk longevity.

Abstract

Proto-planetary disks display the so-called size-luminosity relation, where their mm-wavelength fluxes scale linearly with their emitting areas. This suggests that these disks are optically thick in mm-band, an interpretation further supported by their near-black-body spectral indexes. Such characteristics are seen not only among disks in very young star-forming regions like Lupus (1-3 Myrs), but, as we demonstrate here, also among disks in the much older Upper Scorpius region (5-11 Myrs). How can disks shine brightly for so long, when grain growth and subsequent radial drift should have quickly depleted their solid reservoir? Here, we suggest that the "bouncing barrier" provides the answer. Even colliding at very low speeds (below 1cm/s), grains already fail to stick to each other but instead bounce off in-elastically. This barrier stalls grain growth at a near-universal size of 100 micron. These small grains experience much reduced radial drift, and so are able to keep the disks bright for millions of years. They are also tightly coupled to gas, offering poor prospects for processes like streaming instability or pebble accretion. We speculate briefly on how planetesimals can arise in such a bath of 100-micron grains.

Figures (8)

• Figure 1: Disk fluxes versus disk sizes, compiled from literature (see text for references). The disk radii enclose 68 % of the total flux. All fluxes are at $0.88$mm and are calibrated to a distance of 140 pc. The orange line represents the SLR obtained by Andrews2018 for large disks in Lupus: $L_{\rm mm}=0.05 {\rm mJy} (R/au)^{2}$. Most disks appear to obey this trend ($L \propto R^2$), except for the USco disks. The Lupus sample (73 disks) have a median resolution of $0.04"$ ($\sim 6$AU); while the USco sample (21 disks) have a worse median resolution at $0.37"$ ($\sim 58$AU).
• Figure 2: Same as Fig. \ref{['fig:sizel observation']} but with disk fluxes scaled by the stellar luminosities. Our model radii for USco disks (detailed in text) are shown as solid blue circles. These are typically much smaller than the values from Hendler2020. The gray line is theory prediction for disks that remain optically thick throughout (at $3$mm) and are viewed at an inclination of $60^\circ$ (see Appendix \ref{['sec:modelcontinuum']}). The Lupus sample suggest that almost all disks are optically thick, with the exception of the largest ones. The same conclusion also holds for the USco disks, if we adopt our model radii. Colored contours are kernel density estimates of disks in Lupus and USco (using our model radii).
• Figure 3: Spectral indexes for disks from Lupus Tazzari2021 and USco (this work), plotted against the scaled disk fluxes. USco disks are dimmer than those in Lupus but have similarly low spectral indexes.
• Figure 4: The dependency of spectral index on the optical thickness at the disk outer edge, $\tau_{\rm 3mm}(r=R_d)$. The default dust population (thick black curve) have a maximum size of $a_\mathrm{max}=100 \, \mu m$ and a power-law exponent of $a_{\rm pow}=3.5$. Other solid curves show different values of $a_{\rm max}$, while the dashed group repeat with $a_{\rm pow} = 2$. To reproduce the observed distribution of $\alpha_{1-3}$ (right histogram), one either requires optically thick disks (with any $a_{\rm max}$), or optically thin disks with a dust population that is nearly mono-disperse (low $a_{\rm pow}$) and large ($> 1$mm).
• Figure 5: A cartoon illustrating the three regimes of collision outcomes, emulating those in Guttler2010Dominik2024. The regimes are separated by the bouncing and fragmentation thresholds (between two equal-sized grains), as in eqs. (\ref{['eq:v bounce']}) and (\ref{['eq:vfrag']}). The two lines represent relative encounter velocities, from turbulent stirring, $V_\alpha$ (assuming $\alpha=10^{-4}$, solid curve) and from differential radial drift, $\Delta V_{\rm drift}$ (between grains a factor of 2 in size, dashed curve). These values are evaluated for our default disk at $20$ au. In the presence of bouncing, grain growth is truncated at a small size, $a_{\rm bounce}\sim 100\mu$m, rather than the much larger $a_{\rm frag}$.