Measuring cosmic velocities with 21 cm intensity mapping and galaxy redshift survey cross-correlation dipoles

We investigate the feasibility of measuring the effects of peculiar velocities in large-scale structure using the dipole of the redshift-space cross-correlation function. We combine number counts of galaxies with brightness-temperature fluctuations from 21 cm intensity mapping, demonstrating that the dipole may be measured at modest significance ($\lesssim 2\sigma$) by combining the upcoming radio survey Canadian Hydrogen Intensity Mapping Experiment with the future redshift surveys of Dark Energy Spectroscopic Instrument (DESI) and Euclid. More significant measurements ($\lesssim 10\sigma$) will be possible by combining intensity maps from the Square Kilometre Array (SKA) with these of DESI or Euclid, and an even higher significance measurement ($\lesssim 100\sigma$) may be made by combining observables completely internally to the SKA. We account for effects such as contamination by wide-angle terms, interferometer noise and beams in the intensity maps, nonlinear enhancements to the power spectrum, stacking multiple populations, sensitivity to the magnification slope, and the possibility that number counts and intensity maps probe the same tracers. We also derive a new expression for the covariance matrix of multitracer redshift-space correlation function estimators with arbitrary orientation weights, which may be useful for upcoming surveys aiming at measuring redshift-space clustering with multiple tracers.

Figure 1

Cross-correlation dipole between CHIME 21 cm intensity emission and Euclid ELGs as a function of the pair separation $d$. The signal is plotted at (from bottom to top) $z=1.0$ (blue solid curve), $z=1.2$ (red solid curve), and $z=1.4$ (green solid curve). We also plot the wide-angle terms at (from top to bottom) $z=1.0$ (blue dashed curve), $z=1.2$ (red dashed curve), and $z=1.4$ (green dashed curve). The black dashed line indicates zero cross-correlation. The minimum and maximum values of $d$ shown for these curves are the those used in the $S/N$ calculations at each redshift.

Figure 2

Contributions to the variance of the cross-correlation dipole between CHIME (left panel) and SKA (right panel) with Euclid ELGs at $z=1.2$. Plotted are the contributions from cosmic variance $\times$ cosmic variance (blue lower solid curve), cosmic variance $\times$ Poisson (red upper dashed curve), cosmic variance $\times$ interferometer noise (black upper solid curve), Poisson $\times$ interferometer noise (magenta upper dot-dashed curve in left panel, lower dot-dashed curve in right panel), Poisson $\times$ Poisson (green lower dot-dashed curve in left panel, upper dot-dashed curve in right panel), and the extra variance incurred by removing the wide-angle term (yellow lower dashed curve). The pixel size is $L_p=9.9\mathrm{Mpc}/h$ for CHIME and $L_p=1.3\mathrm{Mpc}/h$ for SKA.

Figure 3

Absolute value of the correlation matrix for the cross-correlation dipole between CHIME (left panel) and SKA (right panel) with Euclid ELGs at $z=1.2$.

Figure 4

Forecast $S/N$ values for correlations between CHIME and single-population galaxy surveys. Shown are values for correlations between CHIME and Euclid ELGs (blue circles), DESI combined ELGs and LRGs (green squares), eBOSS ELGs (red crosses), eBOSS LRGs (magenta plus signs), eBOSS QSOs (yellow down-pointing triangles), and SKA (black upward-pointing triangle). The horizontal black dashed line indicates a $S/N$ of unity.

Figure 5

Forecast $S/N$ values for correlations between SKA and single-population galaxy surveys. Shown are values for correlations between SKA and Euclid ELGs (blue circles), DESI combined ELGs and LRGs (green squares), eBOSS ELGs (red crosses), eBOSS LRGs (magenta plus signs), eBOSS QSOs (yellow down-pointing triangles), BOSS (cyan diamonds), SKA assuming distinct tracers (black upward-pointing triangles), and SKA assuming common tracers (black stars). The horizontal black dashed line indicates a $S/N$ of unity.

Figure 6

Forecast $S/N$ values for correlations between SKA and CHIME with multiple-population galaxy surveys, assuming the weights of Eq. (22) are applied. Shown are values for correlations between CHIME and DESI (blue circles), CHIME and eBOSS (red squares), SKA and DESI (black diamonds), SKA and eBOSS (green crosses), and SKA and BOSS (magenta plus signs). The horizontal black dashed line indicates a $S/N$ of unity.

Figure 7

Pairwise $S/N$ for DESI with CHIME and SKA. Shown are values for correlations between DESI ELGs and LRGs (red squares), CHIME and DESI ELGs (green dashed line, plus signs), SKA and DESI ELGs (green solid line, crosses), CHIME and DESI LRGs (blue dashed line, diamonds), SKA and DESI LRGs (blue solid line, circles). The horizontal black dashed line indicates a $S/N$ of unity.

Figure 8

Effect of varying the flux count slope on the forecast $S/N$ for the SKA 21 cm and SKA galaxy survey cross-correlation dipole, assuming common tracers, as a function of redshift. We vary the flux slope $s(m_{*},z)$ by $\pm 20\%$ at each redshift (red dot-dashed line and blue dashed line, respectively).