Role of translational noise in motility-induced phase separation of hard active particles

Self-propelled particles, like motile cells and artificial colloids, can spontaneously form macroscopic clusters. This phenomenon is called motility-induced phase separation (MIPS) and occurs even without attractive forces, provided that the self-propulsion direction fluctuates slowly. In addition to rotational noise, these particles may experience translational noise, not coupled to rotational noise, due to environmental fluctuations. We study the role of translational noise in the clustering of active Brownian hard disks. To tease apart the contribution of translational noise, we model excluded-volume interactions through a Monte-Carlo-like overlap rejection approach. We find that increasing translational diffusivity has a nonmonotonic effect on clustering. At low values, it makes clusters more compact and rounded (less filamentous), eventually promoting genuine MIPS. For sufficiently higher translational diffusivity, clusters evaporate. We develop a theory for the cluster mass distribution, and employ a hydrodynamic approach with parameters taken from the simulation, which explains the clustering phase diagram.