What generates the intense magnetic field in a neutron star?
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It is not currently known. Right now the most popular theory (but far from a consensus) seems to be that the star somehow conserves its magnetic flux through the collapse process. (Speaking in ELI5 not-correct-but-close-enough generalities, magnetic flux is sort of like magnetic pressure across a given surface or boundary.) We will likely need to understand condensed matter physics better before we know for sure.
Neutron stars are weird because they exist in extreme conditions very close to those that would just give us a black hole instead. We can’t hope to reproduce such energy levels in a lab, so really it’s a matter of formulating a proper theory that we can then confirm with astronomical observation.
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