For more on this particular black widow pulsar, see:
https://en.wikipedia.org/wiki/PSR_J1311%E2%80%933430
About 41 black widow pulsars have been found: these are pulsars with a companion less than 1/10 the mass of our Sun. A smaller number of redback pulsars have been found: these have a companion with mass between 1/10 and 7/10 that of our Sun. If the companion's mass is even bigger, we get a 'huntsman'.
The Square Kilometer Array is a huge radio telescope array planned in Australia and South Africa. It should help us many more of these exotic binary stars. That will help us understand if redbacks turn into black widows as the companion gradually loses mass.
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