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So in studying the topic of neutron stars I've encountered one particular detail that I've found no good explanation for. Most resources I have found say that the strong magnetic fields of neutron stars are due to conservation of magnetic flux during the supernova that created it, i.e., the supernova core is magnetized and through conservation of magnetic flux, the resulting neutron star is also magnetized (although to a much higher degree due to its smaller radius). I haven't been able to find any explanation on why the magnetic flux would be conserved, and would appreciate any input to help me understand this.

Thanks in advance!

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An easy argument goes like this: Picture the magnetic flux far from the star, going through some area there. The supernova event and collapse happens very fast. Hence, it is very reasonable to approximate the magnetic flux that goes through that area far from the star as being constant throughout that fast collapse. And voilà, this implies that the magnetic flux gets tightly compressed.

A more thorough treatment would consider Alfvén's theorem, which states that under typical conditions encountered in astrophysics, magnetic flux is frozen in with the matter, and thus both have to move together. Hence, as the star collapses, it drags the magnetic field in with it as well.

(That said, the way you phrased your question, I am now pondering whether there is an associated Noether symmetry... hmmmm... :) )

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  • $\begingroup$ Thanks for the explanation! I'll be properly covering magnetohydrodynamics in my astrophysical plasmas course in a few weeks' time so hopefully I'll understand the proper mathematical treatment of it soon enough. I'm guessing Alfvén's theorem applies here since the cores of neutron stars exhibit superconductivity? $\endgroup$ Oct 31, 2022 at 22:49
  • $\begingroup$ No, this has nothing to do with superconductivity at all. It's all about low density plasmas, in which the magnetic flux is frozen in... Alfven is just what Maxwells equations look like in the appropriate limit $\endgroup$
    – rfl
    Oct 31, 2022 at 23:55

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