Collective phases of motile sperm*

Sperm are self-propelled particles that interact with each other to move collectively in viscoelastic fluid. Here, we report that a transient pulse of ordering fluid flow was able to generate a long-lived flocking phase. Surprisingly, this induced flocking phase exhibits anisotropic giant number fluctuations and possesses transverse density fluctuation correlations consistent with the Toner-Tu theory of the polar fluid phase, 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. In addition, we also find a self-organized global vortex phase of the sperm from the same experiments. To help us understand the organization behind different phases, we modeled sperm as persistently turning active particles, and found that the numerical polar-disorder phase boundary as a function of cell density and persistence time that is predictive of the experiments, although the model does not reproduce the vortex state. Our results may have implications for the evaluation of sample fertility by studying the collective phase behavior of dense groups of motile sperm.