The Fundamental Plane Relation for Gamma-Ray Pulsars Implied by 4FGL

Abstract

We explore the validity of the recently reported fundamental plane (FP) relation of gamma-ray pulsars using 190 pulsars included in the latest 4FGL-DR3 catalog. This sample number is more than twice as large as that of the original study. The FP relation incorporates 4 parameters, i.e., the spin-down power, $\dot{\mathcal{E}}$, the surface magnetic field, $B_{\star }$, the total gamma-ray luminosity, $L_{\gamma }$, and a spectral cutoff energy, ${\epsilon }_{\mathrm{cut}}$. The derivation of ${\epsilon }_{\mathrm{cut}}$ is the most intriguing one because ${\epsilon }_{\mathrm{cut}}$ depends on the proper interpretation of the available phase-averaged spectra. We construct synthetic phase-averaged spectra, guided by the few existing phase-resolved ones, to find that the best fit cutoff energy, ${\epsilon }_{c1}$, corresponding to a purely exponential cutoff (plus a power law) spectral form, is the parameter that optimally probes the maximum cutoff energy of the emission that originates from the core of the dissipative region, i.e., the equatorial current sheet. Computing this parameter for the 190 4FGL pulsars, we find that the resulting FP relation, i.e. the gamma-ray luminosity in terms of the other observables, reads $L_{\gamma }=10^{14.3\pm 1.3}({\epsilon }_{c1}/\mathrm{MeV}{)}^{1.39\pm 0.17}(B_{\star }/\mathrm{G}{)}^{0.12\pm 0.03}(\dot{\mathcal{E}}/\mathrm{erg}{\mathrm{s}}^{-1}{)}^{0.39\pm 0.05}\mathrm{erg}{\mathrm{s}}^{-1}$; this is in good agreement with both the empirical relation reported by Kalapotharakos et al. (2019) and the theoretically predicted relation for curvature radiation. Finally, we revisit the radiation reaction limited condition, to find it is a sufficient but not necessary condition for the theoretical derivation of the FP relation. However, the assumption of the radiation reaction limited acceleration reveals the underlying accelerating electric field component and its scaling with $\dot{\mathcal{E}}$.

arXiv comment20 pages, 14 figures, 3 tables, minor revisions and a typo correction in the most important equation of the paper, accepted for publication in ApJ

References in corpus (34)

• The ATNF Pulsar Catalogue
• Fermi Large Area Telescope Fourth Source Catalog
• A New Electron Density Model for Estimation of Pulsar and FRB Distances
• Time-dependent force-free pulsar magnetospheres: axisymmetric and oblique rotators
• The Second Fermi Large Area Telescope Catalog of Gamma-ray Pulsars
• Incremental Fermi Large Area Telescope Fourth Source Catalog
• The Fermi Galactic Center GeV Excess and Implications for Dark Matter
• Strong support for the millisecond pulsar origin of the Galactic center GeV excess
• Modeling of Gamma-Ray Pulsar Light Curves with Force-Free Magnetic Field
• The Consistency of Fermi-LAT Observations of the Galactic Center with a Millisecond Pulsar Population in the Central Stellar Cluster
• Modeling high-energy pulsar lightcurves from first principles
• Ab-Initio Pulsar Magnetosphere: Particle acceleration in Oblique Rotators and High-energy Emission Modeling
• Three-dimensional numerical simulations of the pulsar magentoshere: Preliminary results
• Time-Dependent 3D Magnetohydrodynamic Pulsar Magnetospheres: Oblique Rotators
• Disrupted Globular Clusters Can Explain the Galactic Center Gamma Ray Excess
• Gamma-Ray Emission in Dissipative Pulsar Magnetospheres: From Theory to Fermi Observations
• 3D Kinetic Pulsar Magnetosphere Models: Connecting to Gamma-Ray Observations
• The Vela Pulsar: Results from the First Year of Fermi LAT Observations
• The pulsar force-free magnetosphere linked to its striped wind: time-dependent pseudo-spectral simulations
• The very-high energy emission from pulsars: a case for inverse Compton scattering
• Fermi LAT observations of the Geminga pulsar
• The Gamma-Ray Luminosity Function of Millisecond Pulsars and Implications for the GeV Excess
• The pulsar synchrotron in 3D: curvature radiation
• Fermi Gamma-Ray Pulsars: Understanding the High-Energy Emission from Dissipative Magnetospheres
• Millisecond Pulsars from Accretion Induced Collapse as the Origin of the Galactic Centre Gamma-ray Excess Signal
• Order parameters for the high-energy spectra of pulsars
• A Fundamental Plane for Gamma-Ray Pulsars
• Population syntheses of millisecond pulsars from the Galactic Disk and Bulge
• Multi-TeV Emission From the Vela Pulsar
• Comparing the Galactic Bulge and Galactic Disk Millisecond Pulsars
• Fermi Large Area Telescope Observations of Gamma-ray Pulsars PSR J1057-5226, J1709-4429, and J1952+3252
• Very-High-Energy Emission From Pulsars
• Synchro-curvature modelling of the multi-frequency non-thermal emission of pulsars
• The Galactic bulge millisecond pulsars shining in X rays: A gamma-ray perspective

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