Pulsars and Millisecond Pulsars II: Deep diving into the Evolutionary Mechanisms

This study investigates the evolutionary spin behaviors, both spin-down and spin-up, of canonical pulsars and millisecond pulsars (MSPs) in the unique dynamical environments of globular clusters, with a particular focus on identifying distinct evolutionary channels that can be modeled using direct N body simulations (via NBODY6++GPU). Leveraging observational data from the ATNF Pulsar Catalogue, we compile a sample of 80 pulsars divided into four populations: normal and millisecond pulsars in both the Galactic field and globular clusters. Through detailed analysis of pulsar spin periods (P) and their derivatives (P˙), along with derived quantities such as surface magnetic field strength (B), rotational energy loss rate (E˙), and characteristic age (τc), we construct a comprehensive P–P˙ diagram that captures the physical and evolutionary diversity of these sources. This visualization not only delineates the classical separation between young, high-B, high-P˙ pulsars and recycled MSPs, but also reveals population-dependent patterns shaped by environmental influences such as stellar encounters, binary exchanges, and accretion-induced spin-up mechanisms. We identify seven distinct evolutionary scenarios that describe the spin evolution of pulsars in globular clusters, including tidal spin-up, exchange interactions, accretion from low-mass companions, magnetic field decay, and triple system evolution. Each scenario outlines a possible formation channel for observed pulsar properties and is suitable for forward modeling using direct N-body methods coupled with binary stellar evolution recipes. By integrating pulsar observational data with astrophysical modeling requirements, this work lays the foundation for self-consistent simulation frameworks aimed at reproducing observed pulsar populations in dense stellar systems. The results have implications for neutron star retention, recycling pathways, and the long-term dynamical evolution of stellar clusters harboring MSPs