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My understanding is that a pulsar is a neutron star whose magnetic poles don't coincide with the rotational poles and whose magnetic poles sweep through Earth (allowing us to hear radio noise).

If we keep hearing pulsars, the polar offset must be very stable.

Why is such an alignment offset so stable?

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The magnetic field of a star is not entirely a result of the global spin of the star. The global spin is part of it, but there are other mechanisms as well. Within the star, there are convection zones, meridional flow, etc.

http://solarscience.msfc.nasa.gov/dynamo.shtml

All these flows generate their own field components. The overall field is simply the sum of all little fields. Its general orientation might be close to the global spin, if the strongest components are aligned to it, but there are many smaller components with different orientations. Therefore, the total field of the star can be somewhat slanted.

And then the star collapses into a neutron star, and its field is compressed. The collapse itself may be slightly asymmetrical, and may further deviate the magnetic field axis.

As a result of all of the above, it's by no means unusual that the magnetic field of the neutron star is not aligned with the spin.

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The polar offset is not stable. Most researchers now thing that the angle between the rotation axis and the magnetic field axis decreases with time. This is thanks to the same torquing mechanism which is slowing the pulsar down. The timescale on which this occurs is similar to the timescales on which pulsars lengthen their rotation periods to the point of switching off.

I guess if you mean stable on timescales of years, then yes they are stable. But over hundreds of thousands of years, they are not.

References:

Young et al. 2010

Philippov et al. 2014

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