Is the light cylinder the site of emission in pulsars?

Abstract

There is no agreement in reports on the oblique-rotator model of pulsars^1–9 as to the site of emission within the pulsar magnetosphere. It is generally assumed, however, that the plasma-electromagnetic fields constituting the magnetosphere obey the quasistatic constraint ∂f/∂t = -ω₀∂f/∂φ, where ω₀ is the angular frequency of rotation of the central neutron star, t the time, and the cylindrical coordinates (r, φ, z) refer to an inertial frame whose z-axis is coincident with the axis of rotation of the star. Accordingly, the pulsar emission is attributed to a source whose distribution has a rigidly rotating pattern; though, of course, none of the charged particles which constitute the source and provide the medium for the propagation of the pattern associated with the source, are themselves constrained to be co-rotating. Here, the spectral distribution of the power emitted by such a rotating pattern is calculated and it is shown that electromagnetic radiation of frequency to ω ≫ ω₀, the observed radiation from pulsars, is produced predominantly by the electric currents at the light cylinder r = c/ω₀ of the magnetosphere. This is a model-independent result; it is valid irrespective of the type of emission mechanism and applies to all previously proposed models of the magnetosphere which are quasistatic and in which the radial length scale of the plasma distribution is of the order of c/ω₀.