  Recently, an Enskog-type kinetic theory for Vicsek-type models for
self-propelled particles has been proposed [T. Ihle, Phys. Rev. E 83, 030901
(2011)]. This theory is based on an exact equation for a Markov chain in phase
space and is not limited to small density. Previously, the hydrodynamic
equations were derived from this theory and its transport coefficients were
given in terms of infinite series. Here, I show that the transport coefficients
take a simple form in the large density limit. This allows me to analytically
evaluate the well-known density instability of the polarly ordered phase near
the flocking threshold at moderate and large densities. The growth rate of a
longitudinal perturbation is calculated and several scaling regimes, including
three different power laws, are identified. It is shown that at large
densities, the restabilization of the ordered phase at smaller noise is
analytically accessible within the range of validity of the hydrodynamic
theory. Analytical predictions for the width of the unstable band, the maximum
growth rate and for the wave number below which the instability occurs are
given. In particular, the system size below which spatial perturbations of the
homogeneous ordered state are stable is predicted to scale with $\sqrt{M}$
where $M$ is the average number of collision partners. The typical time scale
until the instability becomes visible is calculated and is proportional to M.
