Dark Matter Astrometry: Accuracy of sub-halo positions for the measurement of self-interaction cross sections

Direct evidence for the existence of dark matter and measurements of its interaction cross-section have been provided by the physical offset between dark matter and intra- cluster gas in merging systems like the Bullet Cluster. Although a smaller signal, this effect is more abundant in minor mergers where infalling substructure dark matter and gas are segregated. In such low-mass systems the gravitational lensing signal comes primarily from weak lensing. A fundamental step in determining such an offset in sub- structure is the ability to accurately measure the positions of dark matter sub-peaks. Using simulated Hubble Space Telescope observations, we make a first assessment of the precision and accuracy with which we can measure infalling groups using weak gravitational lensing. We demonstrate that using an existing and well-used mass re- construction algorithm can measure the positions of 1.5x1013 M substructures that have parent halos ten times more massive with a bias of less than 0.3 . In this regime, our analysis suggests the precision is sufficient to detect (at 3 {\sigma} statistical significance) the expected mean offset between dark matter and baryonic gas in infalling groups from a sample of 50 massive clusters.