Dark matter astrometry: accuracy of subhalo positions for the measurement of self-interaction cross-sections

Direct evidence for the existence of dark matter and measurements of its interaction crosssection have been provided by the physical offset between dark matter and intracluster 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 substructure is the ability to accurately measure the positions of dark matter subpeaks. 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 reconstruction algorithm can measure the positions of 1.5 10 13 M substructures that have parent haloes 10 times more massive with a bias of less than 0.3 arcsec. In this regime, our analysis suggests the precision is sufficient to detect (at 3 statistical significance) the expected mean offset between dark matter and baryonic gas in infalling groups from a sample of 50 massive clusters.