The Conversion Efficiency of Gamma-ray Pulsars

High-energy gamma-ray pulsars are important sources for studying particle acceleration and pulsar geometry. The third Fermi Large Area Telescope catalog of gamma-ray pulsars (3PC) detected about 300 gamma-ray pulsars, which enlarges the number and diversity of pulsar population. Among geometry models of pulsar magnetosphere, Outer Gap (OG) model has been considered to describe emissions characteristic of gamma-ray pulsars. This research adopts OG model to study the theoretical conversion efficiency, and compares it with observational conversion efficiency. The study finds that the two are highly consistent, and the OG model is applicable to both young pulsars and millisecond pulsars, verifying its universality. Furthermore, this study further reveals the scaling relationships between the conversion efficiency and the fundamental parameters of pulsars. The \eta_\rmth of young pulsars and millisecond pulsars have the relationships \lg \eta_\rmth = -6.79 + (1.04\pm0.05)\times \lg \tau_\rmc and \lg \eta_\rmth = -9.56 + (0.84\pm0.06)\times \lg \tau_\rmc with the characteristic age \tau_\rmc, respectively. The study also shows that \eta_\rmth is correlated with \dotE. For the luminosities L_\gamma, \rmth of Fermi pulsars predicted by the OG model, that of young pulsars is concentrated around or below 10^34\ \rmerg\cdot\mathrms^-1 , while that of millisecond pulsars is concentrated around or below 10^33\ \rmerg\cdot\mathrms^-1 , hence they each show a stripe-like distribution in the \eta_\rmth - \dotE plot. We discuss their fractional size distributions of outer gap and possible explanations for extremely high or low \eta_\rmth values.