A linearly polarised radio wave of wavelength from a distant quasar crosses a…

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Waves in plasmas · Waves in plasmas

Plasma Physics, Ch Cold magnetised plasma waves: the dielectric tensor, cutoffs, resonances and the CMA diagram

Problem

A linearly polarised radio wave of wavelength

\lambda = 0.50\,\mathrm{m}

from a distant quasar crosses a foreground galactic halo cloud, modelled as uniform over a path length

l = 500\,\mathrm{pc}

(

1\,\mathrm{pc}=3.086\times10^{16}\,\mathrm{m}

), with electron density

n_e = 3.0\times10^{4}\,\mathrm{m^{-3}}

and a line-of-sight field component

B_\parallel = 1.0\times10^{-10}\,\mathrm{T}

along the direction of propagation. The wave frequency is far above every plasma and gyrofrequency of the cloud. ((a)) Writing the linearly polarised wave as an equal superposition of R and L circularly polarised waves, and expanding the exact

R

and

L

(electrons only, since the ion terms are smaller by

m_e/m_i

) to first order in

X=\omega_{pe}^2/\omega^2\ll1

and

Y=|\Omega_e|/\omega\ll1

, show that

n_L-n_R \approx XY

and hence that the plane of polarisation turns by

\Delta\chi = \frac{\omega l}{2c}(n_L-n_R) = 2.63\times10^{-13}\,n_eB_\parallel l\,\lambda^2

with

n_e

\mathrm{m^{-3}}

B_\parallel

\mathrm{T}

l

\mathrm{m}

and

\lambda

\mathrm{m}

, giving

\Delta\chi

in radians. ((b)) Use this result to calculate the rotation measure and the Faraday rotation angle for the stated cloud.

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