# Just how fast is a Fast Radio Burst thought to be?

According to Wikipedia;s Fast Radio Bursts; Frequencies and dispersion are recorded they

The component frequencies of each burst are delayed by different amounts of time depending on the wavelength. This delay is described by a value referred to as a dispersion measure (DM). This results in a received signal that sweeps rapidly down in frequency, as longer wavelengths are delayed more.

The time between the arrival of the pulse at two different frequencies can be used to generate a kind of measure of distance, based on a dispersion constant. The measure does not have units of length, but of integrated electron density over the path from source to observer.

Using some fancy Fourier tricks one could first undo the $$1/\nu^2$$ delay and then try to reconstruct what the original pulse might have looked like before dispersion.

Has this been done? If so, how fast (narrow in time) might the original disturbance be? A millisecond? Less?

• The delay of peak with respect to wavelength is a well known characteristics studied a lot in pulsars. You might want to check those out. – Kornpob Bhirombhakdi Feb 6 '19 at 14:16
• @KornpobBhirombhakdi Thanks, that part is really just background. I'm asking about the FRBs and how short their pulse might be with the dispersion effects artificially removed. – uhoh Feb 6 '19 at 14:56
• Thinking about your question a bit more... One part is not clear to me: normally, dedispersion of signals with an unknown dispersion measure (aka "pulsar search") is done by just selecting an arbitrary DM, using a filterbank to divide the signal into frequency bands, applying the dedispersion calculation to the individual bands, folding the result and seeing whether that resulted in a nice pulse profile. Are you asking whether the "fancy Fourier tricks" you mention could reduce the computational complexity of that and do everything in just one step? – jstarek Feb 11 '19 at 15:30
• @jstarek some radiotelescopes may record the complete digitized baseband signal itself so that it can be processed later. (e.g. like these guys with suitcases full of hard drives) Yes, I'm wondering if one could just take the FT of the whole half-second recording, apply a frequency-dependent phase shift, then FT it back to time domain to straighten out the burst. I am not sure if that needs, or can benefit from a separate question & answer? – uhoh Feb 11 '19 at 15:38

The publication describing the original detection of the first known FRB (Lorimer, D. R., Bailes, M., McLaughlin, M. A., Narkevic, D. J. & Crawford, F.: A Bright Millisecond Radio Burst of Extragalactic Origin. arXiv:0709.4301) has a plot of the measurement that makes the effects of dispersion on this particular FRB nicely visible. Take a look at Fig. 2 in the paper.

The actual signal is less than 10 ms, while dispersion delays the signal by around 200 ms over the 200 MHz frequency range between 1.3 and 1.5 GHz (note that this relationship is nonlinear).

Your idea about algorithmically removing the effects of dispersion on the signal is regularly done in practice, search for "dedispersion". At our (hobbyist) observatory, we are using D. Lorimer's own sigproc package to do this, and it seems to be in widespread use amongst professional observers as well. The basic idea is to simulate a classical filterbank arrangement and shift each filter channel according to the DM.

From Lorimer et al. (cited above):

Figure 2: Frequency evolution and integrated pulse shape of the radio burst. The survey data, collected on 2001 August 24, are shown here as a two-dimensional ‘waterfall plot’ of intensity as a function of radio frequency versus time. The dispersion is clearly seen as a quadratic sweep across the frequency band, with broadening towards lower frequencies. From a measurement of the pulse delay across the receiver band using standard pulsar timing techniques, we determine the DM to be 375±1 cm−3 pc. The two white lines separated by 15 ms that bound the pulse show the expected behavior for the cold-plasma dispersion law assuming a DM of 375 cm−3 pc. The horizontal line at ∼ 1.34 GHz is an artifact in the data caused by a malfunctioning frequency channel. This plot is for one of the offset beams in which the digitizers were not saturated. By splitting the data into four frequency sub-bands we have measured both the half-power pulse width and flux density spectrum over the observing bandwidth. Accounting for pulse broadening due to known instrumental effects, we determine a frequency scaling relationship for the observed width W = 4.6 ms (f/1.4 GHz)−4.8±0.4 , where f is the observing frequency. A power-law fit to the mean flux densities obtained in each sub-band yields a spectral index of −4 ± 1. Inset: the total-power signal after a dispersive delay correction assuming a DM of 375 cm−3 pc and a reference frequency of 1.5165 GHz. The time axis on the inner figure also spans the range 0–500 ms.

• Hey this is a great answer, thank you very much! It's great when someone ends up being a hobbyist/expert and can address a question from an authoritative point of view! By the way we've been discussing a different radiotelescope here Gee, I think I have seen Astropeiler Stockert in some recent tweets somewhere as well. – uhoh Feb 11 '19 at 15:22
• I've added the plot itself, I think being able to see the narrow peak really makes the answer complete. – uhoh Feb 11 '19 at 15:33
• Great, thanks for the edit, I forgot about the not-only-linking-principle. Good to hear that Dwingeloo also made it onto this site, they are good friends of our team. – jstarek Feb 11 '19 at 15:51

Astronomer Emily Petroff (informative website) studies FRB time structure and has recently commented on the rapidly increasing number and diversity of observations of FRBs in twitter.

These show that in addition to the overall widths several milliseconds for the dispersion "corrected" (or compensated) spectral histograms, there is finer structure at order 100 microseconds and possibly below!

When you correct for this DM and extract the intrinsic pulse, we see that some FRBs have structure in the pulse, but some don't