  Previous particle-based computer simulations have revealed a significantly
more pronounced tendency of spontaneous global polar ordering in puller
(contractile) microswimmer suspensions than in pusher (extensile) suspensions.
We here evaluate a microscopic statistical theory to investigate the emergence
of such order through a linear instability of the disordered state. For this
purpose, input concerning the orientation-dependent pair-distribution function
is needed, and we discuss corresponding approaches, particularly a heuristic
variant of the Percus test-particle method applied to active systems. Our
theory identifies an inherent evolution of polar order in planar systems of
puller microswimmers, if mutual alignment due to hydrodynamic interactions
overcomes the thermal dealignment by rotational diffusion. In the theory, the
cause of orientational ordering can be traced back to the actively induced
hydrodynamic rotation--translation coupling between the swimmers. Conversely,
disordered pusher suspensions remain linearly stable against homogeneous polar
orientational ordering. We expect that our results can be confirmed in
experiments on (semi-)dilute active microswimmer suspensions, based, for
instance, on biological pusher- and puller-type swimmers.
