Examples of the determination of the optimal search radius for cross-correlation of X-ray source lists with GC catalogs for two galaxies – M 31 (solid lines) and NGC 4278 (dashed lines). Upper panel: the number of true matches (N_true, computed as the difference between the number of total matches N_total the number of expected random matches N_r) as a function of the search radius R. Lower panel: the ratio of the number of random matches to the number of total matches. The dash-dotted line is the 5% level. The vertical lines in the upper panel show our choice of the search radii for these two galaxies.