  We develop a dynamic mean-field theory for polar active particles that
interact through a self-generated field, in particular one generated through
emitting a chemical signal. While being a form of chemotactic response, it is
different from conventional chemotaxis in that particles discontinuously change
their motility when the local concentration surpasses a threshold. The
resulting coupled equations for density and polarization are linear and can be
solved analytically for simple geometries, yielding inhomogeneous density
profiles. Specifically, here we consider a planar and circular interface. Our
theory thus explains the observed coexistence of dense aggregates with an
active gas. There are, however, differences to the more conventional picture of
liquid-gas coexistence based on a free energy, most notably the absence of a
critical point. We corroborate our analytical predictions by numerical
simulations of active particles under confinement and interacting through
volume exclusion. Excellent quantitative agreement is reached through an
effective translational diffusion coefficient. We finally show that an
additional response to the chemical gradient direction is sufficient to induce
vortex clusters. Our results pave the way to engineer motility responses in
order to achieve aggregation and collective behavior even at unfavorable
conditions.
