$v_0\to 0$ the model reduces to a system of identical oscillators in a static network governed by a Kuramoto dynamics with a tendency towards phase synchronization or, equivalently, to the XY model on the 2D geometric network generated by the position of each particle, connected which each other as soon as they are distant of $r<R_{\theta}$. In this static limit, it is well known that the Mermin-Wagner theorem forbids the development of long-range order in 2D. The role of mobility in this context has been investigated recently [@Uriu2013; @Grossmann2015; @AlbertPRX]. For a network which evolves in time as the result of the self-propelled motion of its nodes, the 2D XY universality class is preserved as soon as the ’internal’ state of the XY-spin attached to each node is decoupled to its dynamics in real space [@AlbertPRX]. Hence, a mobile system cannot sustain long range order if the density field and the polarization field are decoupled. However, once the 2D spin (or oscillator phase) dictates the direction of self-propulsion, i.e. the density field is advected by the polarization field, the situation changes qualitatively: the system can then sustain long-range polar order as predicted by the Toner-Tu phase and featuring giant density 