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The age matching model has recently been shown to predict correctly theluminosity L and g-r color of galaxies residing within dark matter halos. Thecentral tenet of the model is intuitive: older halos tend to host galaxies witholder stellar populations. In this paper, we demonstrate that age matching alsocorrectly predicts the g-r color trends exhibited in a wide variety ofstatistics of the galaxy distribution for stellar mass M* threshold samples. Inparticular, we present new measurements of the galaxy two-point correlationfunction and the galaxy-galaxy lensing signal as a function of M* and g-r colorfrom the Sloan Digital Sky Survey, and show that age matching exhibitsremarkable agreement with these and other statistics of low-redshift galaxies.In so doing, we also demonstrate good agreement between the galaxy-galaxylensing observed by SDSS and the signal predicted by abundance matching, a newsuccess of this model. We describe how age matching is a specific example of alarger class of Conditional Abundance Matching models (CAM), a theoreticalframework we introduce here for the first time. CAM provides a generalformalism to study correlations at fixed mass between any galaxy property andany halo property. The striking success of our simple implementation of CAMprovides compelling evidence that this technique has the potential to describethe same set of data as alternative models, but with a dramatic reduction inthe required number of parameters. CAM achieves this reduction by exploitingthe capability of contemporary N-body simulations to determine dark matter haloproperties other than mass alone, which distinguishes our model fromconventional approaches to the galaxy-halo connection.

The Dark Side of Galaxy Color: evidence from new SDSS measurements of galaxy clustering and lensing