The origin of isolated millisecond pulsars in globular clusters

A significant fraction of millisecond pulsars (MSPs) in globular clusters (GCs) are observed as isolated objects, despite the widely accepted scenario in which MSPs are formed through recycling in compact binary systems. The origin of these isolated objects therefore remains an open problem. In this Letter, we propose a physically motivated encounter rate per binary, $\Lambda \propto n a/(\sigma a_H)$, incorporating the local stellar density $n$, velocity dispersion $\sigma$, binary separation $a$, and the Heggie--Hills ionization radius $a_H$. Combined with companion ablation by the MSP, this rate successfully predicts the observed fraction of isolated MSPs in GCs, that is $\mathcal{F}_i \propto\Lambda \propto a_H^{-1}$, establishing dynamical ionization as the primary channel for producing isolated MSPs. We quantitatively test this model against a null hypothesis in which $\mathcal{F}_i$ is independent of $a_H$, and find that the ionization-driven model is 220 times more likely than the null hypothesis. Our framework naturally explains the observed overabundance of isolated MSPs in $\omega$ Centauri and establishes binary ionization as the primary mechanism responsible for the production of isolated MSPs in GCs.