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 (Ntrue, computed as the difference between the number of total matches Ntotal the number of expected random matches Nr) 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.
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