A faster, cleaner way to find directional patterns around galaxies

Directional stacking — averaging a field around sources while aligning each patch along a preferred axis like a galaxy's shape or local tidal force — is a standard tool for detecting subtle cosmological signals. This work shows that all such measurements are exactly equivalent to cross-power spectra between the target field and the E/B modes of the orienting spin field, weighted by galaxy density. The power spectrum formulation handles finite resolution, data visualization, and combination with other probes more naturally than pixel-space stacks. A secondary finding warns that signals built from density-derived velocities or tidal forces may largely recycle information already in the simpler galaxy–field cross-spectrum.