  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.
