Effects of flow fluctuations and partial thermalization on $v_4$

The second and fourth Fourier harmonic of the azimuthal distribution of particles, $v_2$ and $v_4$, have been measured in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). The harmonic $v_4$ is mainly induced from $v_2$ as a higher-order effect. However, the ratio $v_4/(v_2)^2$ is significantly larger than predicted by hydrodynamics. Effects of partial thermalization are estimated on the basis of a transport calculation, and are shown to increase $v_4/(v_2)^2$ by a small amount. We argue that the large value of $v_4/(v_2)^2$ seen experimentally is mostly due to elliptic flow fluctations. However, the standard model of eccentricity fluctuations is unable to explain the large magnitude of $v_4/(v_2)^2$ in central collisions.