Wave modes in the magnetospheres of pulsars and magnetars

Abstract

We study the wave propagation modes in the relativistic streaming pair plasma of the magnetospheres of pulsars and magnetars, focusing on the effect of vacuum polarization. We show that the combined plasma and vacuum polarization effects give rise to a vacuum resonance, where ‘avoided mode crossing’ occurs between the extraordinary mode and the (superluminous) ordinary mode. When a photon propagates from the vacuum‐polarization‐dominated region at small radii to the plasma‐dominated region at large radii, its polarization state may undergo significant change across the vacuum resonance. We map out the parameter regimes (e.g. field strength, plasma density and Lorentz factor) under which the vacuum resonance occurs and examine how wave propagation is affected by the resonance. Some possible applications of our results are discussed, including high‐frequency radio emission from pulsars and possibly magnetars, and optical/infrared emission from neutron star surfaces and inner magnetospheres.

Nonlinear QED effects in X-ray emission of pulsars

“…While the QED interactions below the threshold energy of the electron-positron pair production do not modify the light amplitude in the different directions, here the vacuum rotation is a result of the spatial and temporal variations of the magnetic field. In contrast to some of the previous studies [14,15,18,19] in which the resonance effect between the plasma and QED in a very specific region (resonance region) dictates several polarization characteristics of the X-ray radiation, namely (i) the conversion of photon modes following by 90 3 Circular polarization of the X-ray emission from the polar cap Stokes parameters are additive and each photon is characterized by its own set of Stokes parameters which are defined with respect to a given frame. Therefore a polarimeter will collect a large number of seed photons to measure the polarization properties of a given source.…”

“…radio waves), this plasma is birefringent giving rise to similar effects to vacuum polarization effects, but at sufficiently high frequency (e.g. X-rays) the plasma only negligibly affects the radiation as it travels through the magnetosphere [12][13][14][15][16][17]. It is worth mentioning that the combined plasma and vacuum polarization effects lead to a "vacuum resonance", where the contribution to the dielectric tensors of the plasma and of the vacuum compensate each other [14].…”

Polarization changes of pulsars due to wave propagation through magnetospheres

“…The dielectric tensor ε in the x ′ y ′ z ′ frame (with in the x ′ z ′ plane and ; see Fig. 1) can be written as (see equations 2.11–2.13 and 2.19 of Wang & Lai 2007) where with Here the subscript ‘s’ specifies different species (‘e’ is for electron and ‘p’ for positron) and β s , γ s and f s (γ s ) are the velocity (divided by c ), Lorentz factor and its distribution function, respectively. The dimensionless parameters u s and v s are Here N s is the number density of particles, N = N p + N e , and ω c and ω pl are the cyclotron and plasma frequencies, respectively, which are given by where the magnetic field B 12 = B /(10 12 G), the pulsar spin period P 1s = P /(1 s) and the dimensionless density η= N / N GJ is measured in units of the Goldreich–Julian density, N GJ =Ω B /(2π ec ) ≃ 7.0 × 10 10 B 12 P 1s cm −3 .…”

The Faraday rotation in the pulsar magnetosphere

“…In any magnetized medium, when the natural modes are circularly polarized and the mode evolution is adiabatic, the Faraday rotation effect should rotate the linear polarization PA (φ PA ) by Here Δ k =Δ n ω/ c is the wavenumber difference of the two circularly polarized natural modes, d r is the unit distance in photon ray 1 . In our previous papers (Wang & Lai 2007; Wang, Lai & Han 2010, hereafter WLH10), we have already derived the dielectric tensor and wave modes in the pulsar magnetospheres composed of streaming, relativistic plasmas of various compositions and Lorentz factors. With the dielectric tensor, we can solve the Maxwell equation and obtain two eigenmodes, to be labelled as the plus ‘+’ mode and minus ‘−’ mode, and corresponding refractive indices n ± .…”