Measuring dark matter substructure with galaxy-galaxy flexion statistics

It is of great interest to measure the properties of substructures in dark matter haloes at galactic and cluster scales. Here we suggest a method to constrain substructure properties using the variance of weak gravitational flexion in a galaxy–galaxy lensing context; this is a statistical method, requiring many foreground–background pairs of galaxies. We show the effectiveness of flexion variance in measuring substructures in N-body simulations of dark matter haloes, and present the expected galaxy–galaxy lensing signals. We show the insensitivity of the method to the overall galaxy halo mass, and predict the method's signal-to-noise ratio for a space-based all-sky survey, showing that the presence of substructure down to 109 M⊙ haloes can be reliably detected.