  We use Brownian Dynamics computer simulations of a moderately dense colloidal
system undergoing steady shear flow to investigate the uniqueness of the
so-called effective temperature. We compare effective temperatures calculated
from the fluctuation-dissipation ratios and from the linear response to a
static, long wavelength, external perturbation along two directions: the shear
gradient direction and the vorticity direction. At high shear rates, when the
system is strongly anisotropic, the fluctuation-dissipation ratio derived
effective temperatures are approximately wave-vector independent, but the
temperatures along the gradient direction are somewhat higher than those along
the vorticity direction. The temperatures derived from the static linear
response show the same dependence on the direction as those derived from the
fluctuation-dissipation ratio. However, the former and the latter temperatures
are different. Our results suggest that the presently used formulae for
effective temperatures may not be applicable for strongly anisotropic, driven
systems.
