Coagulation-Fragmentation Equilibrium for Charged Dust: Abundance of Submicron Grains Increases Dramatically in Protoplanetary Disks

Dust coagulation in protoplanetary disks is not straightforward and is subject to several slowdown mechanisms, such as bouncing, fragmentation, and radial drift to the star. Furthermore, dust grains in UV-shielded disk regions are negatively charged due to collisions with the surrounding electrons and ions, which leads to their electrostatic repulsion. For typical disk conditions, the relative velocities between micron-sized grains are small, and their collisions are strongly affected by the repulsion. On the other hand, collisions between pebble-sized grains can be too energetic, leading to grain fragmentation. The aim of the present paper is to study the combined effect of the electrostatic and fragmentation barriers on dust evolution. We numerically solve the Smoluchowski coagulation-fragmentation equation for grains whose charging occurs under conditions typical for the inner disk regions, where thermal ionization operates. We find that dust fragmentation efficiently resupplies the population of small grains under the electrostatic barrier. As a result, the equilibrium abundance of submicron grains is enhanced by several orders of magnitude compared to the case of neutral dust. For some conditions with fragmentation velocities of & SIM;1 m s(-1), macroscopic grains are completely destroyed.