  A striking feature of the collective behavior of spherical microswimmers is
that for sufficiently strong self-propulsion they phase-separate into a dense
cluster coexisting with a low-density dis- ordered surrounding. Extending our
previous work, we use the squirmer as a model swimmer and the particle-based
simulation method of multi-particle collision dynamics to explore the influence
of hydrodynamics on their phase behavior in a quasi-two-dimensional geometry.
The coarsening dynamics towards the phase-separated state is diffusive in an
intermediate time regime followed by a final ballistic compactification of the
dense cluster. We determine the binodal lines in a phase diagram of P\'eclet
number versus density. Interestingly, the gas binodals are shifted to smaller
densities for increasing mean density or dense-cluster size, which we explain
using a recently introduced pressure balance [S. C. Takatori et al., Phys. Rev.
Lett. 113, 028103 (2014)] extended by a hydrodynamic contribution. Furthermore,
we find that for pushers and pullers the binodal line is shifted to larger
P\'eclet numbers compared to neutral squirmers. Finally, when lowering the
P\'eclet number, the dense phase transforms from a hexagonal "solid" to a
disordered "fluid" state.
