Gamma-Ray Millisecond Pulsars: Off-pulse Emission Characteristics, Phase-Resolved Pseudo-Luminosity--Cutoff Energy Correlation, and High-energy Pulsed Emission

Abstract

We investigate the $\gamma$-ray emission from 38 millisecond pulsars using 15 years of Fermi-LAT Pass 8 data in the 0.3--500 GeV range. Off-pulse intervals defined objectively with the Bayesian Blocks algorithm reveal significant off-pulse emission from 15 sources. Ten exhibit clear spectral cutoffs indicative of magnetospheric origin, while the remaining five show no compelling evidence for non-magnetospheric origins, as their off-pulse emission is spatially unresolved and inconsistent with hadronic, inverse Compton, or intrabinary contributions, implying a likely magnetospheric origin. We perform phase-resolved spectral fits for these 15 sources. In 11 of them, the cutoff energy $E_{\rm cut}$ varies markedly with rotation phase and correlates positively with the phase-resolved photon counts. Defining a phase-resolved pseudo-luminosity, these 11 pulsars follow a linear relation between $\log_{10}L$ and $\log_{10}E_{\rm cut}$, with slope $\alpha = 2.31^{+0.22}_{-0.25}$, consistent with curvature-radiation predictions from the equatorial current sheet ($\alpha \approx 2.29$). The same relation appears in the bright pulsar J0614$-$3329, implying the same emission mechanism across all rotational phases. We detect pulsed emission above 10 GeV from 19 sources, and a significant fraction of these also exhibit robust off-pulse emission. The coexistence of robust off-pulse flux and pulsed emission extending to high energies challenges standard outer-gap models. While other frameworks can also produce off-pulse flux, the phase-resolved $L$--$E_{\rm cut}$ correlation could provide a key diagnostic, and our measured slope may provide new evidence supporting the equatorial current sheet scenario as an important $\gamma$-ray emission mechanism in millisecond pulsars.