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We show that the fast moving component of the "bullet cluster" (1E0657-56)can induce potentially resolvable redshift differences between multiply-lensedimages of background galaxies. The moving cluster effect can be expressed asthe scalar product of the lensing deflection angle with the tangential velocityof the mass components, and it is maximal for clusters colliding in the planeof the sky with velocities boosted by their mutual gravity. The bullet clusteris likely to be the best candidate for the first measurement of this effect dueto the large collision velocity and because the lensing deflection and thecluster fields can be calculated in advance. We derive the deflection fieldusing multiply-lensed background galaxies detected with the Hubble SpaceTelescope. The velocity field is modeled using self-consistentN-body/hydrodynamical simulations constrained by the observed X-ray andgravitational lensing features of this system. We predict that thetriply-lensed images of systems "G" and "H" straddling the critical curve ofthe bullet component will show the largest frequency shifts up to ~0.5 km/sec.This is within the range of the Atacama Large Millimeter/sub-millimeter Array(ALMA) for molecular emission, and is near the resolution limit of the newgeneration high-throughput optical-IR spectrographs. A detection of this effectmeasures the tangential motion of the subclusters directly, thereby clarifyingthe tension with LCDM, which is inferred from gas motion less directly. Thismethod may be extended to smaller redshift differences using the Ly-alphaforest towards QSOs lensed by more typical clusters of galaxies. Moregenerally, the tangential component of the peculiar velocities of clustersderived by our method complements the radial component determined by thekinematic SZ effect, providing a full 3-dimensional description of velocities.

Tangential Velocity of the Dark Matter in the Bullet Cluster from Precise Lensed Image Redshifts