birthday paradox for stellar births

Yesterday at Milky Way group meeting, Adrian Price-Whelan brought up the possibility that the halo might be made up of many disrupted globular clusters. Sarah Martell (UNSW) showed up today and said more along these lines, based on chemical arguments. That got me thinking about the birthday paradox: If you have 30 people in the room, you are more than likely to have two that share the same birthday. The implication of this paradox for the Galaxy is the following:

Imagine that the Milky Way halo (or even better, bulge) is made up of 1000 disrupted stellar clusters that fell in. If we look at even 100-ish stars, we would expect to find pairs of stars with identical abundances, with very good confidence. And this confidence can be kept high even if there is a smooth background of stars that doesn't participate in the cluster origin, and even if there are multiple populations in the original clusters. As long as we can show that pairs of stars are not co-eval (chemically), we can rule out all of these hypotheses with far less data than we already have, in hand. Awesome! I wrote code to check this, but am far from having a real-data test.

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