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

TL;DR

This work presents a unified ECS-based framework linking magnetospheric structure to gamma-ray pulsar populations through the Fundamental Plane. It identifies two operative regimes—radiation-reaction-limited (RRLmax) and potential-drop-limited (PDL)—bounded by a transition spin-down power $\dot{\mathcal{E}}_{TR}$ that maps to a gamma-ray visibility line on the $P$-$\\dot P$ diagram, explaining observed occupancy of MSPs, young pulsars, and magnetars. PIC simulations validate the FP scalings, reveal degeneracies among microphysical parameters, and show a pair-screening transition that causes deviations from the maximal-RRL envelope at high $\\dot{\mathcal{E}}$, consistent with compactness-driven $\\gamma\\gamma$ pair feedback. The framework also unifies GeV curvature and TeV IC emission within the ECS, predicts a MeV-bright, GeV-faint pulsar corridor, and motivates MeV missions and population-synthesis studies to further test the model and its implications for high-energy neutrinos and multi-wavelength pulsar phenomenology.

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 $γγ$ 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.

Figures (11)

• Figure 1: Projected FP of Fermi-detected gamma-ray pulsars. Light-blue filled circles: MSPs; light-red filled circles: YPs, compiled from 2022ApJ...934...65K. Dark-blue and dark-red triangles show, for the same objects, the locations obtained by adopting the theoretical maximum cutoff energies $\epsilon_{\rm c}$ from Eqs. \ref{['eq:ecut RRX']} and \ref{['eq:ecut max']} with $\eta_{B_{\rm LC}}=\eta_{R_{\rm LC}}=\eta_{\rm pc}=1$, $r_{\star}=10^6$ cm, and $\eta_{\alpha}=3/2$. Gray curves indicate loci of the death lines, i.e., maximum $\epsilon_{\rm c}$ along RRL and potential-drop limited regimes, for constant surface field $B_\star=10^{8},\,10^{9},\,10^{12},\,10^{13}$ G values. The "knees" along the curves mark the transition from the maximum RRL to the potential-drop-limited branch (see Eqs. \ref{['eq:transition spin-down B']} and \ref{['eq:transition spin-down P']}). Throughout this and all subsequent FP projections, $\epsilon_{\rm c}$, $\dot{\mathcal{E}}$, and $B_\star$ are expressed in MeV, ${\rm erg\,s^{-1}}$, and G, respectively. Note: For the adopted scaling factors, the theoretical (triangle) locations are effectively deterministic and depend mainly on the measured $\dot{\mathcal{E}}$ and $B_\star$. By contrast, the catalog-based cutoff proxy values used for the circles inherit the spectral-fit uncertainties and parameter covariances. Individual cutoff error bars are omitted for clarity; for the vast majority of sources, the quoted cutoff uncertainties are $\lesssim 0.3$ dex (often substantially smaller).
• Figure 2: Projected FP for the Fermi-LAT pulsars as in Fig. \ref{['fig:projectedFP Fermi pulsars and maximum ecut']}. Each panel overlays families of death lines obtained by varying the indicated scaling factor. Left-hand column: $B_\star=10^{8}$ G (MSP branch). Right-hand column: $B_\star=10^{12}$ G (YP branch). The color scale indicates increasing values of the varied parameter. Except for the varied factor, all other scalings are fixed to unity, with $r_\star=10^6$ cm and $\eta_\alpha=3/2$.
• Figure 3: Left-hand panel: Degeneracy curves showing $\eta_{B_{\rm LC}}$ (orange) and $\eta_{\rm pc}$ (blue) as functions of $\eta_{R_{\rm LC}}$ that reproduce the same death-line envelope as the reference choice $(\eta_{R_{\rm LC}},\,\eta_{B_{\rm LC}},\,\eta_{\rm pc})=(1,1,0.2)$, which matches well the trends in the observed pulsars and the PIC simulations (see Fig. \ref{['fig:FP projected Fermi PIC Theory - moving average trend']} below). Right-hand panel: The corresponding reference-case envelope is shown by the cyan curves for $\eta_\alpha=3/2$, $r_\star=10^6$ cm, and the indicated $B_\star$ values. The orange and blue point distributions in the left-hand panel map onto the black bands in the right-hand panel, illustrating the range of $(\eta_{R_{\rm LC}},\,\eta_{B_{\rm LC}},\,\eta_{\rm pc})$ combinations that are observationally degenerate around the reference solution.
• Figure 4: Behavior of gamma-ray emission across the transition from the RRL to the potential-limited regime. Each panel shows two representative curves: one for YPs ($B_\star = 10^{12}$ G, red) and one for MSPs ($B_\star = 10^{8}$ G, blue). Left-hand panel: gamma-ray efficiency $\eta_{\rm eff}$ as a function of $\dot{\mathcal{E}}$. Middle panel: $\eta_{\rm eff}$ versus $\epsilon_{\rm c}$ (identical for YPs and MSPs). Right-hand panel: total gamma-ray luminosity $L_\gamma$ as a function of $\epsilon_{\rm c}$.
• Figure 5: Left-hand panel: Projection of the FP showing Fermi-detected pulsars (gray: MSPs; black: YPs) together with the corresponding PIC model results (orange: MSPs; blue: YPs); for the PIC points, the color gradation encodes $L_\gamma$ (lighter shades indicate lower $L_\gamma$, sarker shades higher $L_\gamma$). Square symbols denote PIC models located within the observed FP region (compatible), while triangles indicate models without observed counterparts (non-compatible; see also 2023ApJ...954..204K). The magenta and green dashed death lines correspond to those shown as solid lines in Fig. \ref{['fig:projectedFP Fermi pulsars and maximum ecut degeneracies']} for YPs ($B_\star=10^{12}$ G) and MSPs ($B_\star=10^{8}$ G), respectively. The orange and blue solid lines show the theoretical death lines computed using the specific $B_\star$ and $\dot{\mathcal{E}}$ values of the PIC models. These models extend slightly below the observed range in $B_\star$ and $\dot{\mathcal{E}}$ while capturing the behavior of both emission regimes, indicating scaling factors consistent with those adopted in Fig. \ref{['fig:projectedFP Fermi pulsars and maximum ecut degeneracies']}. Right-hand panel: Same FP projection including the Fermi pulsars and the death lines from the left-hand panel, now overlaid with the moving-average trends for the Fermi MSPs (purple) and YPs (cyan). The smoothed trends reveal that at lower $\dot{\mathcal{E}}^{5/12} B_\star^{1/6}$ values the data follow the RRL branch, while at higher values they deviate from the maximal RRL regime—consistent with enhanced screening of $E_{\rm acc}$ and an implicit dependence of $\eta_{B_{\rm LC}}$ on $\dot{\mathcal{E}}$.