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LOL!! What I described was a fairly entry-level standard scenario. Obviously there are countless variations on that theme of deductive reasoning and the Math that accompanies it.<quoted text>You're making this up aren't you? Lol. J/k. That little star must have quite a wobble up with a planet of that density orbiting it that fast and so close. It's really mind boggling. Is that why they call it a neutron star?
I do not see where the parent star was called a 'Neutron Star', although that need not be ruled out. It was described as a 'Pulsar' which means that it is a star that has passed the more conventional part of its life cycle and has collapsed to a smaller diameter of spectacular density and spins much faster than before.
If it is interacting gravitationally with an orbiting companion and plundering it of material, that material gets superheated as it is shredded to Plasma on its way into the star and emits radiation at Radio and X-Ray wavelengths.
Some of that radiation gets jetted off the star at its poles and sweeps space like a searchlight beam as the star wobbles (appearing to pulse ... hence its name).
In this case it seems that is what Astronomers have observed and realized that the tug of something in orbit was causing those polar jets to waver.
Through steps of deductive reasoning comparable to what I described earlier they were able to arrive at the conclusions they've published.
There are not one but multiple ways they can assemble such calculations, and often use those alternative modes to double-check their findings.