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chemotaxis, may be needed to obtain a polar state. Non- physical or external mechanisms of this type are embod- ied in Bertin et al in an alignment rule, but are absent in the work by Baskaran and Marchetti that aimed at identifying the role of purely physical interactions in con- trolling the large scale behavior of self-propelled systems. The goal of the present paper is to study the stability of the homogeneous polar state. For this reason we have added phenomenologically the term proportional to a$_{4}$ to the equations derived in [23]. Both a$_{2}$ and a$_{4}$ will then treated as phenomenological parameters. 

The density satisfies a conservation law, with a flux controlled by two terms: ρv$_{0}$ P describing convection along the mean self-propulsion velocity, v$_{0}$ P , and a dif- 

fusive current − D ∇ ρ that drives the system to a ho- mogeneous state. The anisotropy of the diffusion coeffi- cient relative to the direction of mean motion is neglected here for simplicity. The various terms in Eq. (2) (other than the one proportional to a$_{4}$ ) are obtained from the microscopic hard rod model and have a simple physi- cal interpretation. The polarization field P plays a dual role in self-propelled systems. On one hand, it represents the vector order parameter associated with the sponta- neous breaking of rotational symmetry in the polarized state. Its dynamics is then in the class of that of equi- librium polar liquid crystals and X-Y spin systems. On the other hand, v$_{0}$ P is also the mean velocity of the flock with which particles are convected. The interplay be- 

