  In our recent report, observational evidence supports that the rotational
direction of a galaxy tends to be coherent with the average motion of its
nearby neighbors within 1 Mpc. We extend the investigation to neighbors at
farther distances, in order to examine if such dynamical coherence is found
even in large scales. The Calar Alto Legacy Integral Field Area (CALIFA) survey
data and the NASA-Sloan Atlas (NSA) catalog are used. From the composite map of
velocity distribution of 'neighbor' galaxies within 15 Mpc from the CALIFA
galaxies, the composite radial profiles of the luminosity-weighted mean
velocity of neighbors are derived. These profiles show unexpectedly strong
evidence of the dynamical coherence between the rotation of the CALIFA galaxies
and the average line-of-sight motion of their neighbors within several Mpc
distances. Such a signal is particularly strong when the neighbors are limited
to red ones: the luminosity-weighted mean velocity at 1 < D <= 6 Mpc is as
large as 30.6+/-10.9 km/s (2.8-sigma significance to random spin-axis
uncertainty) for central rotation (R <= Re). In the comparison of several
subsamples, the dynamical coherence tends to be marginally stronger for the
diffuse or kinematically-well-aligned CALIFA galaxies. For this mysterious
coherence in large scales, we cautiously suggest a scenario that it results
from a possible relationship between the long-term motion of a large-scale
structure and the rotations of galaxies in it.
