Pseudo-giant number fluctuations and nematic order in microswimmer suspensions

Abstract: Giant number fluctuations (GNFs), whereby the standard deviation $\Delta N$ in the local number of particles $\langle N \rangle$ grows faster than $\sqrt{\langle N \rangle}$, are a hallmark property of dry active matter systems with orientational order, such as a collection of granular particles on a vibrated plate. This contrasts with momentum-conserving ("wet") active matter systems, such as suspensions of swimming bacteria, where no theoretical prediction of GNFs exist, although numerous experimental observations of such enhanced fluctuations have been reported. In this Letter, we numerically confirm the emergence of super-Gaussian number fluctuations in a 3-dimensional suspension of pusher microswimmers undergoing a transition to collective motion. These fluctuations emerge sharply above the transition, but only for sufficiently large values of the bacterial persistence length $\ell_p = v_s / \lambda$, where $v_s$ is the bacterial swimming speed and $\lambda$ the tumbling rate. Crucially, these "pseudo-GNFs" differ from true GNFs, as they only occur on length scales shorter than the typical size $\xi$ of nematic patches in the collective motion state, which is in turn proportional to the single-swimmer persistence length $\ell_p$. Our results thus suggest that observations of enhanced density fluctuations in biological active matter systems actually represent transient effects that decay away beyond mesoscopic length scales, and raises the question to what extent "true" GNFs with universal properties can exist in the presence of fluid flows.