Stars can be ejected to the outskirts of a globular cluster, where the time required for dynamical friction to return them to the core is a significant fraction of the age of the universe. Both binary and single stars can attain high velocities in three-body (or binary-binary) interactions, and perhaps by asymmetric mass-loss during a tidal encounter. Here we show how the binary pulsar 2127+11C in M15 and perhaps 1744--24A in Terzan 5 must have formed in this way. Ejection of systems like PSR~2127+11C is probable if the core of M15 is composed of heavy degenerate stars, and has had density $\gtorder 10^7\,\rm pc^{-3}$ for $\gtorder 10^8\,\rm y$. This is consistent with previous dynamical estimates. We show that a natural combination of factors conspires to enable us to see PSR~2127+11C. A binary of longer period could not have received an impulse large enough to escape the core. A binary of shorter period would have been ejected from the cluster and/or collapsed through decay of its orbit by gravitational radiation.
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