A radio pulsar is observed with dispersion measure and rotation measure .

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 radio pulsar is observed with dispersion measure DM=30 pc cm−3\mathrm{DM} = 30\,\mathrm{pc\,cm^{-3}} and rotation measure RM=−60 rad m−2\mathrm{RM} = -60\,\mathrm{rad\,m^{-2}}. ((a)) Estimate the density-weighted mean line-of-sight magnetic field ⟨B∥⟩\langle B_\parallel\rangle towards the pulsar, in microgauss, and state whether it points towards or away from the observer. ((b)) Along a different, denser patch of the same line of sight the plasma has ion density ni=5.0×106 m−3n_i = 5.0\times10^{6}\,\mathrm{m^{-3}} (protons, singly charged) and field strength B0=1.0×10−8 TB_0 = 1.0\times10^{-8}\,\mathrm{T}. For a wave with ω≪Ωi\omega \ll \Omega_i there, compute the Alfven speed vAv_A, the Stix function S=1+c2/vA2S = 1 + c^2/v_A^2, and the refractive index n=c/vAn = c/v_A. Then, using the polarisation-drift current density of a single ion, Jp=(ρ/B02) dE⊥/dt\mathbf{J}_p = (\rho/B_0^2)\,\mathrm{d}\mathbf{E}_\perp/\mathrm{d}t with ρ=nimi\rho = n_im_i, show that the dielectric response it implies, S−1=ρ/(ϵ0B02)S - 1 = \rho/(\epsilon_0B_0^2), agrees with the value found from vAv_A.

Browse the problem library