The orbital eccentricities of binary millisecond pulsars in globular clusters

Low-mass binary millisecond pulsars (LMBPs) are born with very small orbital eccentricities, typically of order eᵢ~10⁻⁶--10⁻³. In globular clusters, however, higher eccentricities ef eᵢ can be induced by dynamical interactions with passing stars. Here we show that the cross section for this process is much larger than previously estimated. This is because, even for initially circular binaries, the induced eccentricity ef for an encounter with pericenter separation rₚ beyond a few times the binary semi-major axis a declines only as a power-law, ef∝(rₚ/a)^ -5/2, and { not\/} as an exponential. We find that { all\/} currently known in clusters were probably affected by interactions, with their current eccentricities typically an order of magnitude or more greater than at birth.