In the past few days, journalists have been playing the usual "X could be aliens" game. This time, X is repeating FRBs from a galaxy 1.5 billion light years away. (Or is it 1.5 billion years ago? The proper/conformal time distinction isn't clear in pop sci.) I couldn't find the galaxy's name anywhere, but then I suppose a galaxy that distant might not have been named, even if it's now of some interest. Still, the claim of "repeated" bursts (regardless of their cause) made me wonder: what is our tightest empirical upper bound on how far apart the detected bursts' sources are?
I'm prepared to believe we can see 1.5 billion light years away, clearly enough to pin two events to the same 100,000-light-year wide galaxy, with no others within 2 million light years of it (these are plausible example numbers based on comparing the Milky way to Andromeda). They're small fractions of 1.5 billion light years, but not so small we couldn't resolve an image that clearly. On the other hand, I sincerely doubt we can prove any two bursts that distant are from the same star. I presume what's notable about repeat FRBs is they're so close together in time we expect the source to be common, but I'm curious as to how tightly observations constrain that.