Research returned to my life briefly today when I got a chance to catch up with Price-Whelan. He modified his stream-fitting likelihood function to have the stars in the tidal streams depart their progenitor near the classcial Lagrange points, instead of just anywhere near the tidal radius. This change was not complicated to implement (here's to good code), makes his model more realistic, and (it turns out) improves the constraints he gets on the gravitational potential, both in precision and accuracy. So it is all-win.
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