A radio pulsar emits regular pulses at 1-s intervals, which propagate to Earth through the ionized interstellar plasma with electron density n_e ≈ 3 × 10⁴ m⁻³. The pulses observed at f = 100MHz are believed to be emitted at the same time as those observed at much higher frequency, but they arrive with a delay of 100ms.
(a) Explain briefly why pulses travel at the group velocity instead of the phase velocity, and show that the expected time delay of the f = 100-MHz pulses relative to the high-frequency pulses is given by

where the integral is along the waves’ propagation path. Hence compute the distance to the pulsar.

(b) Now suppose that the pulses are linearly polarized and that their propagation is accurately described by the quasi-longitudinal approximation. Show that the plane of polarization will be Faraday rotated through an angle

where (B_‖) = ∫n_eB · dx/∫n_edx. The plane of polarization of the pulses emitted at 100 MHz is believed to be the same as the emission plane for higher frequencies, but when the pulses arrive at Earth, the 100-MHz polarization plane is observed to be rotated through 3 radians relative to that at high frequencies. Calculate the mean parallel component of the interstellar magnetic field.

Transcribed Image Text:

Δt = ρό 8π?me€o_f2c Snea nedx, (21.69)