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Weighted correlation functions are an increasingly important tool forunderstanding how galaxy properties depend on their separation from each other.We use a mock galaxy sample drawn from the Millenium simulation, assigningweights using a simple prescription to illustrate and explore how well aweighted correlation function recovers the true radial dependence of the inputweights. We find that the use of a weighted correlation function results in adilution of the magnitude of any radial dependence of properties and a smearingout of that radial dependence in radius, compared to the input behavior. Wepresent a quantitative discussion of the dilution in the magnitude of radialdependence in properties in the special case of a constant enhancement at r <rc. In this particular case where there was a SFR enhancement at small radius r< rc = 35 kpc, the matching of one member of an enhanced pair with anon-enhanced galaxy in the same group gives an artificial enhancement out tolarge radius ~ 200 kpc. We compare this with observations of SFR enhancementfrom the SDSS (Li et al. 2008; MNRAS, 385, 1903) finding very similar behavior- a significant enhancement at radii < 40 kpc and a weak enhancement out tomore than 150 kpc. While we explore a particular case in this Letter, it iseasy to see that the phenomenon is general, and precision analyses of weightedcorrelation functions will need to account carefully for this effect usingsimulated mock catalogs.

Systematic errors in weighted 2-point correlation functions: An application to interaction-induced star formation