The space between the stars responds
Imagine sending a short radio pulse through a very thin fog of electric charges. Its electric field pushes the electrons back and forth. Their motion produces another electric field, which combines with the arriving wave. The result is a pulse whose envelope travels a little more slowly than light in a vacuum.
An envelope is the broad rise and fall containing many rapid oscillations. It carries the flash that the telescope times. The individual crests and the envelope have different speeds in this medium. Following a crest would give the wrong arrival time.
At lower radio frequencies the electrons have more time to respond during each cycle. The extra delay grows rapidly toward the low end of the band. Double a frequency and its excess delay relative to infinitely high frequency falls by a factor of four. This frequency dependence is called dispersion.
Reading: Condon & Ransom, Essential Radio Astronomy, Appendix D
A tiny effect accumulates over a long path
Interstellar gas is extremely sparse, but a pulse may cross a great deal of it. Astronomers describe the accumulated electrons by the dispersion measure, usually shortened to DM. Picture a tube extending from the telescope to the source: DM counts the free electrons along that tube, with a conventional astronomical unit.
For a DM of one hundred, a pulse at four hundred megahertz arrives about 1.94 seconds after the same pulse at eight hundred megahertz. A telescope can resolve this difference even when the flash itself lasts only a few milliseconds. Measuring a delay between frequencies also removes the unknown time when the source emitted the flash.
The first public CHIME/FRB catalog contains intensity pictures of these flashes. In such a picture, called a dynamic spectrum, one axis is time and the other is frequency. A curved streak marks successive arrivals. A processed picture may already have the expected sweep removed; its axis labels and processing history tell you which picture you are looking at.
Reading: Condon & Ransom, Essential Radio Astronomy, Chapter 6 · CHIME/FRB first catalog data and waterfall documentation
Why a pulse can keep a tail
A perfectly smooth electron fog delays a narrow pulse without turning every frequency channel into a long echo. Real density fluctuations also bend the waves. Several paths then connect a source to the telescope. The straightest route arrives first, and longer routes add later light.
Those delayed contributions can make a sharp pulse trail off slowly. This is scattering. In a simple thin-screen model the tail decays exponentially, and it becomes longer at lower frequencies. A measured tail also depends on the original pulse shape and the instrument’s time resolution. Estimating the propagation contribution therefore requires a model of the emitted pulse and the instrument.
Reading: Geyer & Karastergiou (2016), revisiting pulsar scattering · Condon & Ransom, Essential Radio Astronomy, Chapter 6
The wave can turn as well as arrive late
A linearly polarized wave has an electric field that oscillates along one direction. A magnetic field along the path makes that direction rotate during propagation. This is Faraday rotation. The angle changes faster at long wavelengths.
Timing counts electrons without caring which way the magnetic field points. Faraday rotation adds a sign: reversing the field reverses the slope of polarization angle against wavelength squared. Together, these measurements can reveal the electron-weighted magnetic field along the path.
The telescope must actually record polarization to do this. A picture containing intensity alone shows when the flash was bright, but it has lost the information about the electric-field direction. The course therefore uses measured CHIME intensity for timing and a separate synthetic polarization experiment for rotation.
Reading: Condon & Ransom, Essential Radio Astronomy, Appendix D · Brentjens & de Bruyn (2005), Faraday Rotation Measure Synthesis, arXiv v2