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

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 $γγ$ pair feedback in or near the ECS and briefly note an extension to $γγ\rightarrowμ^\pm$ 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.

💡 Research Summary

This paper develops a unified physical framework that connects the electrodynamics of the equatorial current sheet (ECS) in pulsar magnetospheres to the catalog‑level, phase‑averaged gamma‑ray observables measured by the Fermi Large Area Telescope (LAT). Guided by analytic scalings and three‑dimensional particle‑in‑cell (PIC) simulations, the authors show that the previously identified “Fundamental Plane” (FP) – a multi‑parameter correlation among gamma‑ray luminosity (Lγ), spectral cutoff energy (εc), spin‑down power (Ė), and surface magnetic field (B⋆) – is bounded by two distinct physical regimes.

In the radiation‑reaction‑limited (RRL) branch, particle acceleration in the ECS is balanced by curvature‑radiation losses. Assuming a curvature radius proportional to the light‑cylinder radius (Rc≈ηRL·RLC) and an accelerating electric field Eacc≈ηBLC·BLC, the authors derive εc∝γ^3/Rc and a scaling Lγ∝εc^1.39 B⋆^0.12 Ė^0.39. In the potential‑drop‑limited (PDL) branch, the available rotational voltage ΔV≈ΩΦRLC caps the acceleration, leading to εc∝ΔV ηBLC BLC and a scaling Lγ∝εc^1.18 B⋆^0.17 Ė^0.41. The two envelopes intersect at a characteristic spin‑down power Ėtrans≈10^34.5 erg s⁻¹. This intersection defines a “gamma‑ray death border” that maps onto a visibility threshold on the P–Ṗ diagram: above the threshold, detectability is governed by distance and beaming; below it, both εc and the gamma‑ray efficiency ηγ=Lγ/Ė drop sharply.

The authors confront these analytic expectations with PIC results. By extracting particle distributions and radiation from global simulations, they confirm the FP scalings and quantify degeneracies among the dimensionless factors (ηBLC, ηRL, etc.). Both young pulsars (YPs) and millisecond pulsars (MSPs) follow the same FP branches, but MSPs lie predominantly above the death border, while YPs straddle it.

Population analysis places ATNF catalog pulsars and McGill magnetars onto the FP. MSPs cluster on the observable side, YPs occupy the transition region, and magnetars sit at or just below the border. This arrangement predicts a substantial, yet undetected, population of MeV‑bright, GeV‑faint pulsars that lie below the current Fermi sensitivity—a “MeV corridor” that future MeV missions (e.g., AMEGO, e‑ASTROGAM) could uncover.

At higher Ė, the observed cutoff energies flatten relative to the RRL envelope, indicating that the accelerating electric field is being screened. The paper introduces a compactness‑based criterion for optically thin γγ→e± pair creation in or near the ECS. When the compactness exceeds a critical value, copious pair production reduces Eacc, moving sources from the RRL to the PDL branch. This mechanism naturally explains the observed deviation and suggests that the most energetic systems may also permit γγ→μ±, opening a speculative channel for pulsed multi‑TeV neutrino emission.

The authors extend the framework to the TeV regime by coupling PIC‑derived particle spectra with a simple seed‑photon field to calculate inverse‑Compton (IC) emission. Applying this to the Vela pulsar reproduces both the GeV curvature‑radiation component and the newly detected multi‑TeV pulsed emission reported by H.E.S.S. II, demonstrating that a single ECS‑resident particle population can generate a unified GeV–TeV spectrum.

In summary, the paper establishes: (1) the FP is physically bounded by radiation‑reaction and voltage limits; (2) the intersection of these limits defines a gamma‑ray death border that explains the observed occupancy of pulsars in FP space and on the P–Ṗ diagram; (3) a sizable MeV‑bright, GeV‑faint pulsar population is predicted, motivating next‑generation MeV observatories; (4) pair‑creation feedback regulates the high‑Ė behavior, and (5) the same ECS physics can account for both GeV curvature radiation and TeV IC emission, offering a coherent picture of pulsar high‑energy phenomenology and suggesting new avenues such as pulsed TeV neutrinos.