  An observer that is moving towards a high-density region sees, on average, a
higher matter density and more foreground-emitting sources ahead than behind
themself. Consequently, the average abundance and luminosity of objects
producing cosmological signals around an in-falling dark matter halo is larger
in the direction of the halo's motion. In this Letter, we demonstrate this
effect from simulated cosmological maps of the thermal Sunyaev Zel'dovich
effect and the cosmic infrared background. We find that, for a wide range of
halo masses and redshifts, oriented stacked profiles of these foregrounds show
significant, potentially detectable gradients aligned with the transverse
velocity of halos. The signal depends on the halo's mass and redshift, as well
as the physical properties of the cosmic web surrounding the halos. We show
that this signal is sufficiently prominent to be detected in future Cosmic
Microwave Background experiments, therefore offering a new window into the
study of cosmological structures. We argue that the dipolar morphological
structure of this signal, its orientation, as well as its overall large
amplitude, constitute a challenge for the detection of the transverse velocity
through the study of the moving lens effect for stacked halos.
