Grain-size measurements in protoplanetary disks indicate fragile pebbles and low turbulence

Context. Constraining the turbulence level and pebble size in protoplanetary disks is an essential initial step in understanding the aerodynamic properties of pebbles, which are crucial for planet formation. Recent laboratory experiments have revealed that destructive collisions of icy dust particles may occur at much lower velocities than previously believed. These low fragmentation velocities push down the maximum grain size in collisional growth models. Aims. Motivated by the smooth radial distribution of pebble sizes inferred from ALMA/VLA multi-wavelength continuum analysis, we propose a concise model to explain this feature and aim to constrain the turbulence level at the midplane of protoplanetary disks. Methods. Our approach is built on the assumption that the fragmentation threshold is the primary barrier limiting pebble growth within pressure maxima. Consequently, the grain size at the ring location can provide direct insights into the turbulent velocity governing pebble collisions and, by extension, the turbulence level at the disk midplane. We validate this method using the Dustpy code, which simulates dust transport and coagulation. Results. We applied our method to seven disks, namely TW Hya, IM Lup, GM Aur, AS 209, HL Tau, HD 163296, and MWC 480, for which grain sizes have been measured from multi-wavelength continuum analysis. A common feature emerges from our analysis, with an overall low turbulence coefficient of alpha similar to 10(-4) observed in five out of seven disks when assuming a fragmentation velocity upsilon(frag) = 1 m s(-1). A higher fragmentation velocity would imply a significantly larger turbulence coefficient than that suggested by current observational constraints. IM Lup stands out, with a relatively high coefficient of 10(-3). Notably, HL Tau exhibits an increasing trend in alpha with distance. This supports enhanced turbulence at its outer disk region, which is possibly associated with the infalling streamer onto this particular disk. Alternatively, if the turbulence were found to be low, this might indicate that grain sizes have not reached the growth barrier. Conclusions. We conclude that the current (sub)mm pebble size constrained in disks implies low levels of turbulence; it also implies fragile pebbles, which is consistent with recent laboratory measurements.