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

Abstract We explore the validity of recently reported fundamental plane (FP) relation γ -ray pulsars using 190 included in latest 4FGL-DR3 catalog. This sample number is more than twice as large that original study. The FP incorporates four parameters, i.e., spin-down power,  ̇ , surface magnetic field, B ⋆ total luminosity, L and a spectral cutoff energy, ϵ cut . derivation most intriguing one because depends on proper interpretation available phase-averaged spectra. construct synthetic spectra, guided by few existing phase-resolved ones, to find best-fit c1 corresponding purely exponential (plus power-law) form, parameter optimally probes maximum energy emission originates from core dissipative region, equatorial current sheet. Computing this for 4FGL pulsars, we resulting relation, luminosity terms other observables, reads ${L}_{\gamma }={10}^{14.3\pm 1.3}{({\epsilon }_{{\rm{c}}1}/\mathrm{MeV})}^{1.39\pm 0.17}$?> L γ = 10 14.3 ± 1.3 ( ϵ mathvariant="normal">c 1 stretchy="true">/ MeV stretchy="false">) 1.39 0.17 ${({B}_{\star }/{\rm{G}})}^{0.12\pm 0.03}{(\dot{{ }}/\mathrm{erg}\,{{\rm{s}}}^{-1})}^{0.39\pm 0.05}\,\mathrm{erg}\,{{\rm{s}}}^{-1};$?> B ⋆ mathvariant="normal">G 0.12 0.03 erg mathvariant="normal">s − 0.39 0.05 width="0.50em" ; good agreement with both empirical Kalapotharakos et al. theoretically predicted curvature radiation. Finally, revisit radiation reaction limited condition, it sufficient but not necessary condition theoretical relation. However, assumption acceleration reveals underlying accelerating electric field component its scaling