Near-zone Navier-Stokes analysis of heavy quark jet quenching in an N=4 super-Yang-Mills plasma

The near zone energy-momentum tensor of a supersonic heavy quark jet moving through a strongly coupled N=4 super Yang-Mills (SYM) plasma is analyzed in terms of first-order Navier-Stokes hydrodynamics. It is shown that the hydrodynamic description of the near quark region worsens with increasing quark velocities. For realistic quark velocities, v=0.99, the nonhydrodynamic region is located at a narrow band surrounding the quark with a width of approximately 3/πT in the direction parallel to the quark's motion and with a length of roughly 10/πT in the perpendicular direction. Our results can be interpreted as an indication of the presence of coherent Yang-Mills fields where deviation from hydrodynamics is at its maximum. In the region where hydrodynamics does provide a good description of the system's dynamics, the flow velocity is so small that all the nonlinear terms can be dropped. Our results, which are compatible with the thermalization timescales extracted from elliptic flow measurements, suggest that if anti-de-Sitter/conformal field theory (AdS/CFT) provides a good description of the BNL Relativistic Heavy Ion Collider system, the bulk of the quenched jet energy has more than enough time to locally thermalize and become encoded in the collective flow. The resulting flow pattern close to the quark, however, is shown to be considerably different from the superposition of Mach cones and diffusion wakes observed at large distances.