Gamma-Ray Millisecond Pulsars: Off-pulse Emission Characteristics, Phase-resolved Pseudoluminosity–Cutoff Energy Correlation, and High-energy Pulsed Emission

Abstract We investigate the γ -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 nonmagnetospheric 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 cut varies markedly with rotation phase and correlates positively with the phase-resolved photon counts. Defining a phase-resolved pseudoluminosity, these 11 pulsars follow a linear relation between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>log</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> <mml:mi>L</mml:mi> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>log</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">cut</mml:mi> </mml:mrow> </mml:msub> </mml:math> , with slope <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2.3</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.25</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.22</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , consistent with curvature radiation predictions from the equatorial current sheet ( α ≈ 2.29). The same relation appears in the bright pulsar J0614−3329, implying the existence of 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 cut correlation could provide a key diagnostic, and our measured slope may provide new evidence supporting the equatorial current sheet scenario as an important γ -ray emission mechanism in millisecond pulsars.