  We investigate the collective behavior of sterically interacting
self-propelled particles confined in a harmonic potential. Our theoretical and
numerical study unveils the emergence of distinctive collective polar
organizations, revealing how different levels of interparticle torques and
noise influence the system. The observed phases include the shear-banded
vortex, where the system self organizes in two concentric bands rotating in
opposite directions around the potential center; the uniform vortex, where the
two bands merge into a close packed configurations rotating uniformly as a
quasi-rigid body; and the orbiting polar state, characterized by parallel
orientation vectors and the cluster revolving around the potential center,
without rotation, as a rigid body. Intriguingly, at lower filling fractions,
the vortex and polar phases merge into a single phase where the trapped cluster
breaks into smaller polarized clusters, each one orbiting the potential center
as a rigid body.
