Opacity dependence of elliptic flow in kinetic theory

The observation of large azimuthal anisotropies $v_n$ in the particle spectra of proton-proton (pp) and proton-nucleus (pA) collisions challenges fluid dynamic interpretations of $v_n$, as it remains unclear how small collision systems can hydrodynamize and to what extent hydrodynamization is needed to build up $v_n$. Here, we study in a simple kinetic theory how the same physics that leads to hydrodynamization in large systems represents itself in small systems. We observe that one third to one half of the elliptic flow signal seen in fully hydrodynamized systems can be built up in collisions that extend over only one mean free path $l_{\rm mfp}$ and that do not hydrodynamize. This is qualitatively in line with observing a sizeable $v_2$ in $pp$ collisions for which other characteristics of soft multi-particle production seem well-described in a free-streaming picture. We further expose a significant system size dependence in the accuracy of hybrid approaches that match kinetic theory to viscous fluid dynamics. The implications of these findings for a reliable extraction of shear viscosity are discussed.