  At the epoch of decoupling, cosmic baryons had supersonic velocities relative
to the dark matter that were coherent on large scales. These velocities
subsequently slow the growth of small-scale structure and, via feedback
processes, can influence the formation of larger galaxies. We examine the
effect of streaming velocities on the galaxy correlation function, including
all leading-order contributions for the first time. We find that the impact on
the BAO peak is dramatically enhanced (by a factor of ~5) over the results of
previous investigations, with the primary new effect due to advection: if a
galaxy retains memory of the primordial streaming velocity, it does so at its
Lagrangian, rather than Eulerian, position. Since correlations in the streaming
velocity change rapidly at the BAO scale, this advection term can cause a
significant shift in the observed BAO position. If streaming velocities impact
tracer density at the 1% level, compared to the linear bias, the recovered BAO
scale is shifted by approximately 0.5%. This new effect, which is required to
preserve Galilean invariance, greatly increases the importance of including
streaming velocities in the analysis of upcoming BAO measurements and opens a
new window to the astrophysics of galaxy formation.
