A dynamic spectrum (frequency-time plot) of a newly detected pulsar shows a single…

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Plasma Physics · Waves in plasmas

Modes, Packets and Media, Ch Transmission lines and electromagnetic waves in matter, plasmas and guides

Problem

A dynamic spectrum (frequency-time plot) of a newly detected pulsar shows a single bright pulse tracing a curved diagonal band. Reading two points off the band: the pulse arrives at

t=50\,\mathrm{ms}

1.4\,\mathrm{GHz}

, and at

t=300\,\mathrm{ms}

(on the same time axis) at

0.7\,\mathrm{GHz}

. ((a)) Translate the two readings into the dispersion measure of the path, using

\Delta t = 4.149\,\mathrm{ms}\times\mathrm{DM}\times(f_{\rm lo}^{-2}-f_{\rm hi}^{-2})

, where

f_{\rm lo}

and

f_{\rm hi}

are the lower and higher frequencies, with

\mathrm{DM}

\mathrm{pc\,cm^{-3}}

and frequencies in

\mathrm{GHz}

. ((b)) An independent distance estimate places the pulsar at

1.3\,\mathrm{kpc}

. Infer the mean electron density along the line of sight.

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