Streaming Velocities and the Baryon Acoustic Oscillation Scale

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 baryon acoustic oscillation (BAO) peak is dramatically enhanced (by a factor of $\sim 5$) 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.

Figure 1

(Top panel) All contributions to the correlation function from streaming velocities up to $O({\delta }_{\mathrm{lin}}^4)$ are shown at $z=1.2$, with $b_1=b_2=b_s=1$, and $b_v=0.01$. The new advection term (the black solid line) is the dominant effect. (Bottom panel) The ELG correlation function is shown for fiducial bias values ($b_1=1.5$, $b_2=0.25$, $b_s=-0.14$) at $z=1.2$ with different values of $b_v$. Dashed (dot-dashed) indicates positive (negative) $b_v$. For reference, the thin solid (grey) line shows the linear theory prediction.

Figure 2

The shift in BAO position due to streaming velocities is shown as a function of $b_v/b_1$. Thick (thin) lines show the shift with (without) the advection term. The solid black lines include the one-loop SPT correction to the dark matter power spectrum ($b_2=b_s=0$), while the solid grey line also includes fiducial $b_2$ and $b_s$ values for the ELG sample. (Inset) Detailed behavior for a small $b_v$.