Kate Storey-Fisher (NYU) (with some consulting by me and others) has been trying to model the selection function (in the form of an accurate random catalog) for the ESA Gaia DR3 quasar sample (or a cleaned-up version of it). We currently believe that the selection function should depend most on the Gaia scan history, the local stellar crowding, and the interstellar dust. We are finding that scan history is a very subtle (maybe ignorable) effect, and that dust is big. But when we apply the dust correction, the random-catalog features don't look quite like the features in the real data. Today KSF showed (anti-) correlations between the observed quasar density and the stellar density on the sky. Will correcting for this fix our issues? I sure hope so.
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