  We consider a hydrodynamic model of swarming behavior derived from the
kinetic description of a particle system combining a noisy Cucker-Smale
consensus force and self-propulsion. In the large self-propulsion force limit,
we provide evidence of a phase transition from disordered to ordered motion
which manifests itself as a change of type of the limit model (from hyperbolic
to diffusive) at the crossing of a critical noise intensity. In the hyperbolic
regime, the resulting model, referred to as the `Self-Organized Hydrodynamics
(SOH)', consists of a system of compressible Euler equations with a speed
constraint. We show that the range of SOH models obtained by this limit is
restricted. To waive this restriction, we compute the Navier-Stokes diffusive
corrections to the hydrodynamic model. Adding these diffusive corrections, the
limit of a large propulsion force yields unrestricted SOH models and offers an
alternative to the derivation of the SOH using kinetic models with speed
constraints.
