Elliptic flow fluctuations in heavy ion collisions at RHIC and the perfect fluid hypothesis

We analyse the recently measured $v_2$ fluctuation in the context of establishing the degree of fluidity of the matter produced in heavy ion collisions. We argue that flow observables within systems with a non-negligible mean free path should acquire a "dynamical" fluctuation, due to the random nature of each collision between the system's degrees of freedom. Because of this, $v_2$ fluctuations can be used to estimate the Knudsen number of the system produced at RHIC. To illustrate this quantitatively, we apply the UrQMD model, with scaled cross sections, to show that collisions at RHIC have a Knudsen number at least one order of magnitude above the expected value for an interacting hadron gas. Furthermore, we argue that the Knudsen number is also bound from above by the $v_2$ fluctuation data, because too large a Knudsen number would break the observed scaling of $v_2$ fluctuations due to the onset of turbulent flow. We propose, therefore that $v_2$ fluctuation measurements, together with an understanding of the turbulent regime for relativistic hydrodynamics, will provide an upper as well as a lower limit for the Knudsen number.