Interplay between timescales governs the residual activity of a harmonically bound active Brownian particle

Active microparticles in confining potentials manifest many complex dynamical phenomena as their activity competes with confinement. The steady-state position distributions of harmonically bound active Brownian particles exhibit a crossover from Boltzmann-like to bimodal, commonly referred to as passive and active regimes, respectively, with variations in activity and confinement strength. By studying optically trapped active Janus colloids, numerical simulations, and analytical calculations, we demonstrate that the underlying crossover is from activity-dominated bound dynamics to activity-depleted Brownian motion in a radially displaced harmonic well; and is solely governed by the ratio of the persistence time to the equilibration time in the harmonic potential, being independent of the propulsion speed.