Polarization-Density Patterns of Active Particles in Motility Gradients

The co-localization of density modulations and particle polarization is a characteristic emergent feature of motile active matter in activity gradients. It can therefore play the role of a smoking gun for the mesoscale detection of intrinsic microscopic activity. We employ the active-Brownian-particle (ABP) model to derive precise analytical expressions for the density and polarization profiles of a single Janus-type swimmer in the vicinity of an abrupt activity step, including situations with an orientation-dependent propulsion speed. Our results agree well with measurement data for a hot microswimmer presented in the companion paper [1] and can serve as a template for more complex applications, e.g., to motility-induced phase separation or studies of physical boundaries. The essential physics behind our formal results is robustly captured and elucidated by a schematic two-species ``run-and-tumble'' model.