  We measure the distribution of velocities for prograde and retrograde
satellite galaxies using a combination of published data and new observations
for 78 satellites of 63 extremely isolated disc galaxies (169 satellites
total). We find that the velocity distribution is non-Gaussian (>99.9%
confidence), but that it can be described as the sum of two Gaussians, one of
which is broad (sigma = 176 \pm 15 km/s), has a mean prograde velocity of 86
\pm 30 km/s, and contains ~55% of the satellites, while the other is slightly
retrograde with a mean velocity of -21 \pm 22 km/s and sigma = 74 \pm 18 km/s
and contains ~45% of the satellites. Both of these components are present over
all projected radii and found in the sample regardless of cuts on primary
inclination or satellite disc angle. The double-Gaussian shape, however,
becomes more pronounced among satellites of more luminous primaries. We remove
the potential dependence of satellite velocity on primary luminosity using the
Tully-Fisher relation and still find the velocity distribution to be asymmetric
and even more significantly non-Gaussian. The asymmetric velocity distribution
demonstrates a connection between the inner, visible disc galaxy and the
kinematics of the outer, dark halo. The reach of this connection, extending
even beyond the virial radii, suggests that it is imprinted by the satellite
infall pattern and large-scale effects, rather than by higher-level dynamical
processes in the formation of the central galaxy or late-term evolution of the
satellites.
