2019ApJ...883L...4K

We show that the γ-ray pulsar observables, i.e., their total γ-ray luminosity, L_γ, spectral cutoff energy, ε_cut, stellar surface magnetic field, B_*, and spin-down power {dot}E , obey a relation of the form L_γ=f(ε_cut,B_*,{dot}E ), which represents a 3D plane in their 4D logspace. Fitting the data of 88 pulsars of the second Fermi pulsar catalog, we show this relation to be L_γ∝ε_cut^1.18±0.24^B*_^0.17±0.05^{dot}E ^0.41±0.08^, a pulsar fundamental plane (FP). We show that the observed FP is remarkably close to the theoretical relation L_γ∝ε_cut^4/3B_*^1/6{dot}E ^5/12 obtained assuming that the pulsar γ-ray emission is due to curvature radiation by particles accelerated at the pulsar equatorial current sheet just outside the light cylinder. Interestingly, the FP seems incompatible with emission by synchrotron radiation. The corresponding scatter about the FP is ∼0.35 dex and can only partly be explained by the observational errors while the rest is probably due to the variation of the inclination and observer angles. We predict also that ε_cut∝{dot}E ^7/16 toward low {dot}E for both young and millisecond pulsars implying that the observed death line of γ-ray pulsars is due to ε_cut dropping below the Fermi band. Our results provide a comprehensive interpretation of the observations of γ-ray pulsars, setting requirements for successful theoretical modeling.