Pulsars are intrinsically cool.
Take a massive star. Let it cook for a few millions years. Then the core collapses, and the outer layers explode outward in a supernova. The inner part, the core, can become a black hole, or the almost-equally-bizarre neutron star, an object maybe 10 kilometers across, but packing the mass of an entire star.
The gravity of a neutron star is billions of times the Earth's, and the magnetic field is even stronger. Not only that, but that sucker can spin: conservation of angular momentum means that it can spin dozens of times per second. The combination of the rapid spin and magnetic field means it sends out radiation like a lighthouse, two beams of radiation and matter that sweep around in a circle several times per second. When the beams sweep over the Earth, we see a little blip, a pulse, and that's why these are called pulsars.
If the pulsar is in a close orbit with another, more normal star, its gravity can draw material off the star. This adds energy to the spin of the pulsar, speeding it up. Some, called millisecond pulsars, rotate hundreds of times per second. We're pretty sure this idea is correct, because almost* every time we see a millisecond pulsar we see a companion star. Not only that, but the pulsar has to be so close to the companion star that its orbit is almost a perfect circle; the rules of gravity and tides ensure that.
But we've run into a problem: a millisecond pulsar has been found that has a wide, elliptical orbit. Worse, the companion star is the wrong kind.
The pulsar is dubbed J1903+0327, and it sits about 21,000 light years away, a fair chunk of distance. It's orbiting a rather Sun-like star, and the orbit is odd: it's too big, and too elliptical. All other millisecond pulsars have circular, small orbits.
The pulsar itself is more massive than usual for its type, too, which may be a clue to its origin... though astronomers really don't know.
So what's going on? Maybe we're missing something... like a third star.
One idea is that there is another neutron star involved, one that isn't pulsating so we don't see it, and the two neutron stars (one pulsing, one not) orbit each other. That would make more sense to me. How would a system like this be created?
In this case, a few million years ago, it looked like this: we actually had three stars; two massive, and one not so massive. The two massive ones orbit each other close together, with the lighter one farther out. One of the big stars explodes as a supernova, leaving behind a pulsar. It draws material from the other massive star, speeds up its spin, and the orbit becomes a very tight circle. That first one is our millisecond pulsar.
Then, some time later, the second massive star explodes. The neutron star formed is a weak pulsar at best for some reason or another (it happens; not every neutron star is a pulsar). When the star exploded, it lost quite a bit of mass, and so its gravity decreased. When that happens, the orbits of the two stars becomes elliptical, a natural consequence of the mass loss. So now we have two neutron stars, one pulsing rapidly, the other one not, on an elliptical orbit. The third star doesn't play a big role, except that it's bright in visible light and it's easy to see from Earth. The other neutron star is much fainter, and hard to see.
So now, today, when we point our telescopes at the system, we see a normal star apparently orbiting a millisecond pulsar, which doesn't make sense. But that's because we don't see the second neutron star.
Is this the correct scenario? Beats me. It's a guess, but a good one. Still and all, I love it when a good astronomical theory is tested by some individual weird object. It means there are more factors in play, and that means more fun.*In the original version of this post, I left off the word "almost", but Ethan in the comments corrected me.