Do all neutron stars spin?
I know that some of them are pulsars and pulsars spin very fast, but do all of the neutron stars spin? I would think that they would because of conservation of momentum, but I'm really just not sure.
@Shufflepants: Is it? I suppose even an artificial satellite that had been deliberately made not to spin w.r.t. (say) the Earth or the solar system would still then be spinning along with the galaxy or whatever.
@LightnessRacesinOrbit You can't fix a satellite to not spin wrt the Earth. That's just not physically possible. The only thing you can do is go into the reference frame of the spinning satellite and then claim it isn't spinning (as you are for the Earth). But that requires you saying the rest of the Universe is spinning instead.
@zephyr: Why is it not physically possible? Depending on your reference frame: (a) Tidal locking exists. The moon (notwithstanding a little libration) does just that, no? (b) Just fire up some thrusters in the other direction until the spinning stops. .... But yeah I'm starting to see (as shown in my prior comment) that you're probably always spinning w.r.t. _something_. Is that what Shufflepants meant?
@LightnessRacesinOrbit Yes it is tidally locked, but it's still spinning. You'd have to go into a rotating frame yourself to claim its "not spinning", but like you say, it'd still be spinning in some other frame. That's all I really meant is that you can never claim something is not spinning.
And mostly I was just talking about the fact that it is absurdly unlikely that anything would just happen to have exactly zero angular momentum. If you look at it accounting for the heisenberg uncertainty principle, if something somehow actually wasn't spinning, you'd never be able to prove it. You'd only ever be able to say it's spinning slower than some delta x. And if you found such an object that was spinning more slowly than we can possibly measure, it would be quite the discovery. Everything is spinning, it's just a matter of how fast.
I think it is absolutely safe to say that all neutron stars spin.
Conservation of angular momentum ensures that as they collapse from a massive stellar core the size (roughly) of the Earth, to something with a 10km radius, their angular velocity increases roughly as the square of the decrease in their radius (i.e. a factor of $\sim 4\times 10^5$. Thus, even if the stellar core had the slightest spin to begin with, then the neutron star will be spinning very fast indeed.
Young pulsars appears to be born with rotation periods that vary from about 0.01 s to perhaps a second or so. They then lose angular momentum as they get older.
The difficulty in answering your question without any equivocation is that once neutron stars spin down to periods of longer than 1-10 seconds or so (depending on the pulsar magnetic field strength - see picture below from Wang et al. 2011) then the pulsar mechanism switches off and the neutron star, to all intents and purposes, becomes invisible (the so-called "pulsar deathline", Zhang 2003) .
It is expected that the spin down will continue, even after the pulsar has switched off, but the spin down rate itself depends on the rotation speed, so the neutron star will never come to a halt, even after tens of billions of years.
Interesting! More information (or a reference) for the pulsar mechanism switching off?