  The agreement of elliptic flow data at RHIC at central rapidity with the
hydrodynamic model has led to the conclusion of very rapid thermalization. This
conclusion is based on the intuitive argument that hydrodynamics, which assumes
instantaneous local thermalization, produces the largest possible elliptic flow
values and that the data seem to saturate this limit. We here investigate the
question whether incompletely thermalized viscous systems may actually produce
more elliptic flow than ideal hydrodynamics. Motivated by the extremely fast
primordial longitudinal expansion of the reaction zone, we investigate a toy
model which exhibits thermalization only in the transverse directions but
undergoes collisionless free-streaming expansion in the longitudinal direction.
For collisions at RHIC energies, elliptic flow results from the model are
compared with those from hydrodynamics. With the final particle yield and
$\kt$-distribution fixed, the transversally thermalized model is shown not to
be able to produce the measured amount of elliptic flow. This investigation
provides further support for very rapid local kinetic equilibration at RHIC. It
also yields interesting novel results for the elliptic flow of massless
particles such as direct photons.
