  Flocking behavior is observed in biological systems from the cellular to
super-organismal length scales, and the mechanisms and purposes of this
behavior are objects of intense interest. In this paper, we study the
collective dynamics of bovine sperm cells in a viscoelastic fluid. These cells
appear not to spontaneously flock, but transition into a long-lived flocking
phase after being exposed to a transient ordering pulse of fluid flow.
Surprisingly, this induced flocking phase has many qualitative similarities
with the spontaneous polar flocking phases predicted by Toner-Tu theory, such
as anisotropic giant number fluctuations and non-trivial transverse density
correlations, despite the induced nature of the phase and the clearly important
role of momentum conservation between the swimmers and the surrounding fluid in
these experiments. We also find self-organized global vortex state of the sperm
cells, and map out an experimental phase diagram of states of collective motion
as a function of cell density and motility statistics. We compare our
experiments with a parameter-matched computational model of persistently
turning active particles, and find that the experimental order-disorder phase
boundary as a function of cell density and persistence time can be
approximately predicted from measures of single-cell properties. Our results
may have implications for the evaluation of sample fertility by studying the
collective phase behavior of dense groups of swimming sperm.
