The Orbital Eccentricities of Binary Millisecond Pulsars in Globular Clusters

Abstract

Low-mass binary millisecond pulsars 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. Using both analytical perturbation calculations and numerical integrations, we have shown (Heggie & Rasio 1996) 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 pericentre 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 low-mass binary millisecond pulsars in globular clusters must have been affected by interactions, with their current eccentricities being at least an order of magnitude larger than at birth (Rasio & Heggie 1995).