  Ordered phases emerged in active suspensions of polar swimmers are under
long-wavelength hydrodynamic mediated instabilities. In this letter, we show
that chemical molecules dissolved in aqueous suspensions, as an unavoidable
part of most wet active systems, can mediate long-range interactions and
subsequently stabilize the ordered phases. Chemoattractant in living
suspensions and dissolved molecules producing phoretic forces in synthesized
Janus suspensions are reminiscent of such molecules. Communication between
swimmers through the gradients of such chemicals generated by individual
swimmers, is the foundation of this stabilization mechanism. To classify the
stable states of such active systems, we investigate the detailed phase
diagrams for two classes of systems with momentum conserving and non-conserving
dynamics. Our linear stability analysis shows how the stabilization mechanism
can work for swimmers with different dynamical properties, e.g., pushers or
pullers and with various static characteristics, e.g., spherical, oblate or
prolate geometries.
