Neutron stars are observed in nature by the fact that they rotate: it makes them a source of radio emission, and makes them observable as pulsars. Most have rotation periods of a second or so, a few rotate much faster. Such a neutron star is the end products of a series of transformations taking place in the interior of an (initially normal) star. The last step in this process is a supernova explosion. Since all stars rotate, the rotation of pulsars is not usually considered a big surprise: it could just be leftover from the initial rotation of the star in which it was born.
In a recent paper in Nature Spruit and Phinney present calculations showing that the origin of pulsar spin is probably more interesting. First, they show that it is rather unlikely that much of the initial rotation of the progenitor star can remain in a pulsar; perhaps enough to explain rotation periods of 100 seconds but not 1 second. The reason is that these progenitors, like almost all stars, go through a giant phase in which their envelopes are very extended (as large as the earth's orbit around the Sun). During this phase, the star rotates very slowly, once in 10 to 100 years. It is also in this phase that the supernova explosion takes place. In this event the core of the star, about 1.7 solar masses worth of iron, collapses into a sphere of neutrons, pressed onto each other by gravity. The radius of this sphere is some 10km, its mass 1.4 solar masses. In the process, the mass difference of 0.3 is converted into energy (by E=mc2), and carried off as a burst of neutrinos lasting about a second. Though the core spins up during the collapse process (like the well-known ballerina who increases her spin by drawing her arms in), the resulting spin is not enough to explain pulsars, if the pre-explosion core rotated at the same rate as the giant envelope.
We cannot look into the interior of most stars, so it is hard to know if their cores may perhaps rotate more rapidly than their envelopes, so that more rapidly rotating pulsars might form. After all, stars are not solid objects; many forms of differential rotation are possible in principle. A significant development in recent years, however throws doubt on this differential rotation hypothesis. Through the technique of helioseismology (measuring the oscillation frequencies of the Sun), the rotation of the core of the Sun has now been measured with remarkably precision, and the answer is: it rotates almost uniformly, at the average rate seen at the surface. This proves that a very effective mechanism is at work that keeps a star like the Sun rotating as a whole. If this mechanism works in the Sun, why should it not operate in a pre-supernova giant as well? In fact, the agent that is responsible for this strong coupling is probably known: a magnetic field. Fields much smaller than can be measured on stars are already sufficient to keep a star in a state of roughly uniform rotation.
Against this background, Spruit and Phinney have calculated the effect of the sudden burst of neutrinos emitted in the supernova, and find that it nicely explains rotation periods of 0.01 to 1 second. The neutrinos emitted in the supernova collapse, carrying 0.3 solar masses in energy, exert an enormous push on the neutron star. Most of this push is spherically symmetric and has no lasting effect, but a small part of it (a per cent or so) is asymmetric. This asymmetric part acts on the neutron star like the cue on a billiard ball: it kicks the star, so that it starts moving. That this effect is at work has been inferred previously from the fact that pulsars move through the galaxy with speeds of about 300 km/s, much faster than normal stars. Spruit and Phinney have taken this effect to its logical conclusion: if neutrinos are emitted asymmetrically, the star will in general start spinning, just like a billiard ball spins if one does not hit it dead center.
This suggestion has further consequences, however. Most giants do not go through a supernova explosion. They do not become neutron stars but expose their cores as white dwarfs, by shedding their envelope in a much more gently way. The rotation periods of white dwarfs are known less well than for neutron stars but, where known, they are about one day. This again is much faster than one would expect for something coming out of a giant rotating with a period of more than 10 years. In a separate paper, Spruit (Astronomy and Astrophysics, in press), shows that in this case an effect analogous to that operating in neutron stars can explain the spin: small asuymmetries in the way in which the giant sheds its envelope leaves a bit of spin on the remaining core. This shedding is, in fact, known to be asymmetric, as the beautiful images obtained with the Hubble Space Telescope (http://oposite.stsci.edu/pubinfo/pr/97/pn) and high resolution millimeter-wave interferometry have demonstrated. The degrees of asymmetry observed are sufficient to explain the observed periods of rotating white dwarfs.
Through this new explanation, the rotation of pulsars and white dwarfs has become a much more interesting phenomenon. Rather than being just a remnant of something well known, it now turns out to be intimately related to the processes that give birth to pulsars and white dwarfs, opening a new way of testing theories for these processes.