Large‐Amplitude, Pair‐creating Oscillations in Pulsar and Black Hole Magnetospheres

Abstract

A time-dependent model for pair creation in a pulsar magnetosphere is developed in which the parallel electric field oscillates with large amplitude. Electrons and positrons are accelerated periodically, and the amplitude of the oscillations is assumed to be large enough to cause creation of upgoing and downgoing pairs at different phases of the oscillation. With a charge-starved initial condition, we find that the oscillations result in bursts of pair creation in which the pair density rises exponentially with time. The pair density saturates at N AE ' E 2 0 /(8 m e c 2 À thr ), where E 0 is the parallel electric field in the charge-starved initial state and À thr is the Lorentz factor for effective pair creation. The frequency of oscillations following the pair creation burst is given roughly by ! osc ¼ eE 0 /(8m e cÀ thr ). A positive feedback keeps the system stable, such that the average pair creation rate balances the loss rate due to pairs escaping the magnetosphere.

Radio emission physics in the Crab pulsar

“…Unsteady pair creation in an unshielded gap has also been suggested as the source of oscillating E fields (e.g. Levinson et al 2005;Timokhin & Arons 2013). These models are still being developed, and the time signature of the unshielded E field is not yet clear.…”

A model for double notches and bifurcated components in radio profiles of pulsars and magnetars

“…There are at least two basic reasons for which the elementary emission beam can have the hollow cone shape: 1) Electrons may be accelerated along their velocity u a and the radio emission observed in the pedestal can be due to this acceleration (Melrose 1978;Kunzl et al 1998;Schopper et al 2002;Levinson et al 2005). In this case the opening angle of the elementary beam 2θ R ∼ 1/γ, where γ ∼ 10 is the Lorentz factor of the electrons.…”

“…Melrose 1978;Schopper et al 2002;Levinson et al 2005) the ambient electric field and plasma density within emission region(s) in pulsar magnetosphere tend to oscillate with a frequency ν wgl that can result either from global magnetospheric electrodynamics (e.g. Sturrock 1971;Levinson et al 2005) or can be locally excited by streams of energetic electrons penetrating the ambient plasma (e.g. Schopper et al 2002).…”

Plasma processes in pulsar magnetospheres

“…One new feature in such an acceptable model should be large-amplitude electric oscillations (LAEWs). As argued by Sturrock (1971) and confirmed by numerical calculations (Levinson et al 2005, Beloborodov & Thompson 2007, when the displacement current is included, the magnetosphere is unstable to the development of LAEWs. Models for wave dispersion Pulsar magnetospheres 209 and pulsar radio emission are affected substantially by LAEWs.…”