A Simple Scaling Relationship for the Dark Matter Surface Density Enclosed within Symmetrical Detector Fields of View

We show that the dark matter surface density enclosed within any field of view (FoV) that is symmetrically oriented about the center of a dark matter halo is linearly proportional to the angular extent of the FoV. We verify our result numerically, and discuss its implications for assessing the strength of the dark matter constraints that can be imposed by a given target galaxy.