Energetic requirements of the gamma-ray emission from pulsars: A nonparametric analysis of the data in the Fermi-LAT 12-Year Catalog

TL;DR

This study challenges the traditional inverse-square law assumption for gamma-ray pulsar fluxes, showing they follow a D^{-3/2} dependence, which aligns with a transient radiation process and results in comparable luminosities to radio pulsars.

Contribution

It provides a nonparametric analysis of Fermi-LAT data, revealing a different flux-distance dependence and reconciling gamma-ray pulsar luminosities with those of radio pulsars.

Findings

Gamma-ray fluxes follow a D^{-3/2} dependence, not D^{-2}

Luminosities of gamma-ray pulsars are similar to radio pulsars after correction

Supports a transient radiation process consistent with energy conservation

Abstract

The prevalent view that the radio-loud gamma-ray pulsars have gamma-ray luminosities that exceed their radio luminosities by several orders of magnitude is based on the assumption that the decay with distance of their gamma-ray fluxes obeys the inverse-square law as does that of their radio fluxes. The results presented here, of testing the hypothesis of independence of luminosities and distances of gamma-ray pulsars by means of the Efron-Petrosian statistic, do not uphold this assumption however: they imply that the observational data in the Fermi-LAT 12-Year Catalog are consistent with the dependence $S\propto D^{-3/2}$ of the flux densities $S$ of the gamma-ray pulsars on their distances $D$ at substantially higher levels of significance than they are with the dependence $S\propto D^{-2}$. These results, which were theoretically predicted in Ardavan (2021, MNRAS, 507, 4530), are not incompatible with the requirements of the conservation of energy because the radiation process by which the superluminally moving current sheet in the magnetosphere of a neutron star has been shown to generate the slowly decaying gamma-ray pulses is intrinsically transient: the difference in the fluxes of power across any two spheres centred on the star is balanced by the change with time of the energy contained inside the shell bounded by those spheres. Once the over-estimation of their values is rectified, the luminosities of gamma-ray pulsars turn out to have the same range of values as do the luminosities of radio pulsars. This conclusion agrees with that reached earlier on the basis of the smaller data set in the Second Fermi-LAT Catalog of Gamma-ray Pulsars.