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Pulsars and Transients

We are getting our hands dirty on KAT-7 in order to start preparing for the pulsar and transient science projects planned for MeerKAT. The emphasis at this stage is on the commissioning of the KAT-7 beamformer (coherent summation of the signals from the seven dishes), to develop some tools and skills in pulsar and transient search to better understand our system and RFI (radio frequency interference) environment, and to support the science projects in the longer term. Pulsars are well studied objects with a natural on-and-off nature which is excellent for developing techniques relating to transient signals. Pulsars are indeed amazing objects: highly magnetized, spinning neutron stars that emit electromagnetic radiation which flashes like a lighthouse as the beam points towards your telescope. Pulsars are formed through supernovae explosions, are constrained by physics to be about 20 km in diameter and are incredibly dense with a mass about 1.4 times the mass of our sun. Some of them spin faster than 500 times per sec(!) and new and interesting systems are still being discovered, some of which provide some of our most stringent tests of Einstein's general relativity. Would recommend taking a glance at the pulsar page on wikipedia.

Vela Pulsar

As captured by the KAT-7 telescope in beamformer mode, here's the broadband signal from the Vela pulsar, one of the strongest pulsars around, which spins about 11 times per second. Each frequency channel is 0.39 MHz wide and channel 512 corresponds to 1822 MHz. The curved vertical lines are the signal from the pulsar in this time-frequency plot. The lower frequency signals (labelled with the larger channel numbers in our case) arrive later than the higher frequency signals hence the curves. This is called "dispersion" and results from the interaction of the pulsar signal with the electron content in space through which the signals travel.

(Click on all plots to enlarge)

The plots below show the time series data for this short observation of about 9 secs as measured by the telescopes. The "raw" signal is shown in the top plot and is comprised of background noise plus the Vela dispersed pulse spikes showing on the top. The background noise is produced as a combination of electronic noise from within the system (which we try to reduce by careful design and cooling our first stage electronics to about -200 deg C on KAT-7) and noise from other sources in the universe (and the area around the telescope - even the ground produces radio noise). Just for fun, we can convert this to an audio signal (remembering that radio telescopes actually measure electromagnetic/light waves at low frequency rather than sound which does not propagate through the vacuum of space). The dispersed raw time series signal as per the plot sounds like this. Note that one can clearly hear the background noise, but not the pulsar signal. It sounds a bit like what you get when you don't have a good enough aerial on your car radio.

The so-called "de-dispersed" time series signal is shown in the lower plot above. This is what you get once you have corrected for the dispersion i.e. effectively straightened the curves in the time-frequency plot. Clearly the Vela pulses are now much stronger relative to the noise (the base part) of the signal. This can also be appreciated by listening to the de-dispersed signal and comparing with the dispersed raw signal as discussed previously for the upper plot. Note now that the pulsar pulses can be clearly heard due to the major increase in the signal-to-noise ratio brought about by the de-dispersion operation. How cool is that!

Now, as pulsars are incredibly heavy and compact spinning objects, they also make for great clocks in some cases since the pulse arrival times are so predictable (pulsars rival atomic clocks in accuracy). We can use this regular arrival time of the pulses in order to increase our signal-to-noise further by "folding" the time series at the pulsar spin period. This gives us the folded profiles below for his approx. 9 sec duration dataset (click on image to enlarge).

In the plots above, we show the folded profile repeated a second time (to make it easier to see things if the peak should lie near the edge of the profile). Pulse "phase" in the plots is a number between 0 and 1 for one rotation of the pulsar. Note that the plots are identical comparing phase 0-1 and what we have labelled here as "1-2" since we have just duplicated the results. If the integrated folded profile as per the top left plot above, the profile after de-dispersion and folding using the full observation time (all subintervals) and all frequencies (all subbands), is duplicated many times and converted to an audio signal at the correct timing, the following sound for the Vela folded profile as observed by KAT-7 is produced. Note how even less background noise is now audible with the pulsar sounding loud and clear. Better and better!


All good. Now what if we are looking for new pulsars or transient events and don't know the dispersion measure (DM) (for transients or pulsars) or period (if it is a pulsar)? One way to start is to see what happens to our Vela signal above when we get the DM or period wrong.

Here is the de-dispersed time series again, but this time sweeping over a range of dispersion measures (using 5 pulse periods worth of data per DM):

Note how the pulse profile peaks for a DM somewhere between 60-75. The audio waveform for the above de-dispersed time series plot sweeping over DM values sounds like this. Note how the pulses sound strongest and clearest close to the correct DM of around 68 cm^-3.pc. As we move away from the correct DM, the signal becomes harder to detect relative to the noise (and remembering that Vela is a very strong pulsar!).

Another way to look at this is to create a single-pulse search plot (using the reduced chi-squared statistic as applied to a time bin of 0.05 secs of data for each DM in this case - google chi-squared goodness of fit, if interested). This creates the pretty picture below. Note that most of the energy/red colour occurs in a horizontal line spread around DM=68 (as one would expect for Vela) and that one can see the on-and-off nature of the Vela pulses. Such single-pulse plots are of course also useful for detecting non-periodic signals if strong enough to appear above the noise or perhaps can even be helpful in showing up periodicity.

We can also sweep across a range of folding periods and see what happens:

Viewed as a time series gives you the plots above (the lower plot is using less of the dataset than the top plot). The top plot shows how the pulse profile (shape) quickly degrades when you get the folding period wrong. The audio version of the period sweep folded pulse profile output sounds like this (where the distinct jumps are where we switch period - we have arbitrarily created 11 pulse periods worth of sound file per folding period). Closest to correct folding period occurs at about 12 secs into the audio file.

Another way to see what is happening when changing folding periods is to produce an image of folded profile versus period. This is shown below. Note how the folded profile loses its shape away from the correct folding period and makes for a pretty "butterfly" picture (who says science is dull!):

We can also search across both a range of DMs and periods and plot this, where the bright part of the plot shows one the correct DM and period as per below:

Weaker Pulsars - PSR J0742-2822

Vela is nice and strong and so makes for a good visible test case. What happens when the pulsar is much weaker as most of them are? Here are some results from KAT-7 observing a pulsar known as PSR J0742-2822 which is a lot weaker than Vela and spins 6 times per sec.

The time-freq plot in this case shows no sign of the pulsar, in comparison to the case of Vela above where we saw vertical curved streaks:

And neither do the time series plots for the raw and de-dispersed signals (the little spike around 31 secs is some kind of impulsive terrestrial / satellite interference):

As before, we can "listen" to these (raw signal and de-dispersed signal), but all one can hear is noise in this case.

Likewise, the pulsar is too weak to show up in the single pulse plot (though the interference with a DM around zero shows up around 31 secs):

However, putting one's computer to work and searching over DM and period space shows up an encouraging hotspot (note greater sensitivity to getting the period correct than the DM):

Folding using the correct DM and period gives the following profile and the J0742-2822 pulsar signal emerges from the background noise at last. Note that the signal is much weaker than the Vela signal and only appears above the noise in the two top plots (the integrated profile plot and individual subinterval plots and in the second row plot on the left (summing over subbbands - frequency channels). Just to remind you of our terminology as used throughout, the full observation is divided into smaller time slices called "subintervals" and frequency bands called "subbbands".

Listening to the J0742-2822 pulsar (the repeated folded profile from the top left plot above) sounds like this.

Well, that's all for now. Hope this has been interesting. Listening to the signals, while probably not the most sensitive way to search for new pulsars and transients, is fun, adds a nice dimension, and can help bring home the mind-boggling nature of what one is actually observing. Just think, a city sized object, spinning at incredible rates and not falling apart in the process! Jodrell Bank also has a nice page of pulsar sounds (listen to the fast ones, especially and think about what you are hearing - incredible!)

Credits: It takes many people to build and operate a radio telescope such as the KAT-7. Thanks to the SKA SA team and to Simon Ratcliffe and Neil Young, in particular, for providing the raw datasets. Thanks to Ewan Barr for producing the sigpyproc software (available on github) which formed a foundation for the software developed to perform this analysis. As will be evident, many of the plots are inspired by similar offerings in the PRESTO pulsar software. -- Jasper

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Jasper Horrell,
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