  We find an exact series solution for the steady-state probability
distribution of a harmonically trapped active Brownian particle in two
dimensions, in the presence of translational diffusion. This series solution
allows us to efficiently explore the behavior of the system in different
parameter regimes. Identifying "active" and "passive" regimes, we predict a
surprising re-entrant active-to-passive transition with increasing trap
stiffness. Our numerical simulations validate this finding. We discuss various
interesting limiting cases wherein closed form expressions for the
distributions can be obtained.
