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in these systems that distinguishes them from conven- tional liquid crystalline systems is the dual role of the polarization field as i) a physical velocity that leads to mass convection and hence couples orientational fluctu- ation to density fluctuations and ii) an order parameter associated with a spontaneously broken continuous sym- metry. This duality leads to the remarkable phenomenon of long range ordering identified in [16]. Here we show that this same physics destabilizes the homogeneous or- dered state above a critical value of self propulsion speed and allows the nonlinear equations to admit a propagat- ing front solution that yields the striped phase identified numerically. Further, the coupling of orientational fluc- tuations to density fluctuations gives rise to anomalous fluctuations even in the regime where the ordered state is stable and leads to nontrivial coarsening dynamics that is different from the dynamics of both the equilibrium 2D X-Y model and that of active nematics. 

The two phases observed here, namely the striped phase and the fluctuating flocking phase, have been iden- tified earlier in the context of numerical studies of the Vicsek model. Our work identifies the origin of these phenomena in the model independent framework of the dynamics of conserved quantities and broken symmetry variable. It has been shown in different systems of this class that pattern formation phenomena might be cru- cially related to biological functionality [42, 43]. This work would facilitate the application of theoretical tools, 

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such as the amplitude equations and pattern selection analysis that are well developed in the context of chem- ical reacting systems to collections of self propelled par- ticles. 

