  We investigate how the competing presence of a nonuniform motility landscape
and an external confining field affects the properties of active particles. We
employ the active Ornstein-Uhlenbeck particle (AOUP) model with a periodic swim
velocity profile to derive analytical approximations for the steady-state
probability distribution of position and velocity, encompassing both the
Unified Colored Noise Approximation and the theory of potential-free active
particles with spatially dependent swim velocity recently developed. We test
the theory by confining an active particle in a harmonic trap, which gives rise
to interesting properties, such as a transition from a unimodal to a bimodal
(and, eventually multimodal) spatial density, induced by decreasing the spatial
period of the self propulsion. Correspondingly, the velocity distribution shows
pronounced deviations from the Gaussian shape, even displaying a bimodal
profile in the high-motility regions. Our results can be confirmed by
real-space experiments on active colloidal Janus particles in external fields.
