Saturation of Elliptic Flow and the Transport Opacity of the Gluon Plasma at RHIC

Differential elliptic flow and particle spectra are calculated taking into account the finite transport opacity of the gluon plasma produced in Au+Au at Ecm ~ 130 A GeV at RHIC. Covariant numerical solutions of the ultrarelativistic Boltzmann equation are obtained using the MPC parton cascade technique. For typical pQCD (~3 mb) elastic cross sections, extreme initial gluon densities, dN/deta ~ 15000, are required to reproduce the elliptic flow saturation pattern reported by STAR. However, we show that the solutions depend mainly on the transport opacity, $\chi=\int dz \sigma_t\rho_g$, and thus the data can also be reproduced with dN/deta ~ 1000, but with extreme elastic parton cross sections, \~45 mb. We demonstrate that the spectra and elliptic flow are dominated by numerical artifacts unless parton subdivisions ~100-1000 are applied to retain Lorentz covariance for RHIC initial conditions.