A Comprehensive Interpretation of Fermi-LAT Pulsars: Fundamental-Plane Death Border, Visibility Thresholds, and GeV-TeV Unification

Abstract

We present a framework that links equatorial-current-sheet (ECS) physics to catalog-level, phase-averaged gamma-ray pulsar properties. Guided by analytic scalings and particle-in-cell (PIC) simulations, we show that the pulsar ``Fundamental Plane'' (relating gamma-ray luminosity, spectral cutoff energy, spin-down power $\dot{\cal{E}}$, and surface magnetic field) is bounded by two regimes: a radiation-reaction-limited branch and a potential-drop-limited branch. Their intersection defines a transition in $\dot{\cal{E}}$ that maps to a gamma-ray visibility threshold on the $P-\dot{P}$ diagram, above which detectability is set by distance and beaming, and below which both cutoff energy and efficiency decline rapidly. Placing ATNF pulsars and McGill magnetars onto these planes reproduces the observed Fermi occupancy, with millisecond pulsars (MSPs) on the observable side, young pulsars (YPs) straddling the threshold, and magnetars clustering at or just below it. At higher $\dot{\cal{E}}$, both MSPs and YPs depart from the maximal radiation-reaction-limited envelope at similar cutoff energies, suggesting that enhanced pair creation screens the accelerating electric field in the ECS. We interpret this behavior with a compactness-based criterion for optically thin $\gamma\gamma$ pair feedback in or near the ECS and briefly note an extension to $\gamma\gamma\rightarrow\mu^\pm$ that could yield pulsed multi-TeV neutrinos in the most energetic systems. The framework predicts a MeV-bright, GeV-faint corridor below Fermi sensitivity, a target for next-generation MeV missions. Finally, motivated by the recent HESSII detection of pulsed multi-TeV emission from Vela, we use PIC particle distributions with a seed-photon model to reproduce a multi-TeV inverse-Compton component alongside the GeV curvature emission, supporting a unified ECS-based GeV-TeV origin.