  Thermally or chemically active colloids generate thermodynamic gradients in
the solution in which they are immersed and thereby induce hydrodynamic flows
that affect their dynamical evolution. Here we study a mean-field model for the
many-body dynamics of a monolayer of active particles located at a fluid-fluid
interface. In this case, the activity of the particles creates long-ranged
Marangoni flows due to the response of the interface, which compete with the
direct interaction between the particles. For the most interesting case of a
$r^{-3}$ soft repulsion that models the electrostatic or magnetic interparticle
forces, we show that an "onion-like" density distribution will develop within
the monolayer. For a sufficiently large average density, two-dimensional phase
transitions (freezing from liquid to hexatic, and melting from solid to
hexatic) should be observable in a radially stratified structure. Furthermore,
the analysis allows us to conclude that, while the activity may be too weak to
allow direct detection of such induced Marangoni flows, it is relevant as a
collective effect in the emergence of the experimentally observable spatial
structure of phase coexistences noted above. Finally, the relevance of these
results for potential experimental realizations is critically discussed.
