Physical conditions in the reconnection layer in pulsar magnetospheres

Abstract

The magnetosphere of a rotating pulsar naturally develops a current sheet (CS) beyond the light cylinder (LC). Magnetic reconnection in this CS inevitably dissipates a nontrivial fraction of the pulsar spin-down power within a few LC radii. We develop a basic physical picture of reconnection in this environment and discuss its implications for the observed pulsed gamma-ray emission. We argue that reconnection proceeds in the plasmoid-dominated regime, via a hierarchical chain of multiple secondary islands/flux ropes. The inter-plasmoid reconnection layers are subject to strong synchrotron cooling, leading to significant plasma compression. Using the conditions of pressure balance across these current layers, the balance between the heating by magnetic energy dissipation and synchrotron cooling, and Ampere’s law, we obtain simple estimates for key parameters of the layers - temperature, density, and layer thickness. In the comoving frame of the relativistic pulsar wind just outside of the equatorial CS, these basic parameters are uniquely determined by the strength of the reconnecting upstream magnetic field. For the case of the Crab pulsar, we find them to be of order 10 GeV, 1013 cm-3, and 10 cm, respectively. After accounting for the bulk Doppler boosting due to the pulsar wind, the synchrotron and inverse-Compton emission from the reconnecting CS can explain the observed pulsed high-energy (GeV) and very high energy (∼100 GeV) radiation, respectively. Also, we suggest that the rapid relative motions of the secondary plasmoids in the hierarchical chain may contribute to the production of the pulsar radio emission.