THE LUMINOSITY OF AN EXTERNALLY TRIGGERED DISCHARGE IN THE DEAD PULSAR MAGNETOSPHERE AND THE CURRENT CLOSURE PROBLEM

An externally triggered transient discharge in the dead pulsar magnetosphere was proposed as a possible origin of the gamma-ray bursts (GRBs) by Ruderman & Cheng. We prove that the luminosity of the transient discharge is at most that of the magnetic dipole radiation. The result is derived from the fact that the energy source is the rotation of the neutron star: the size of the discharge-current loop must be smaller than a certain value in order that the inverse electromotive force due to the sudden increase of the current be less than the applied voltage of the star's dynamo, while the size of the same current loop must be larger than the light cylinder radius because the angular momentum must be lost at the energy loss rate divided by the angular velocity of the star. It is proved that a pair plasma outflow (wind) carries angular momentum efficiently so as to compensate for the deficient loss of angular momentum caused by energy release near the stellar surface. It is found, however, that the discharge current never closes well within the light cylinder even if the discharge is followed by the pair plasma wind. Energy release near the star is possible only through field-aligned acceleration. The expected recurrence time of the GRBs does not rule out the hypothesis for the dead pulsar origin of GRBs in the galactic disc.