# Is the magnetic flux in a neuron star creation constant? Why?

• nicksbyman

#### nicksbyman

I did this problem on this British Physics Olympiad paper and it assumed that when a star bigger than the sun collapses under its own gravity to create a neuron star the magnetic flux stays constant.

Thanks

I did this problem on this British Physics Olympiad paper and it assumed that when a star bigger than the sun collapses under its own gravity to create a neuron star the magnetic flux stays constant.

Thanks

magnetic flux over what? A closed surface? Then yes, magnetic flux is always 0 over a closed surface since there is no magnetic monopole.

magnetic flux over what? A closed surface? Then yes, magnetic flux is always 0 over a closed surface since there is no magnetic monopole.

I don't think the magnetic flux is 0. Here is the whole question: As the core of the star collapses to form a neutron star (sorry not neuron, neutron), the electrical conductivity becomes very high. In this case the star's magnetic field lines become frozen to the material of the star and collapse down with the star, increasing the flux density. The neutron star will thus have a very strong magnetic field. If we take the flux = BR^2, with B being the magnetic field strength whose initial value is 10^-2 T, then determine the final magnetic field strength after the collapse. I would need to give you information from the other two problems for you to solve this, but I just want to understand why they assumed the change in flux (I don't know what you mean by "over") to be 0).

I did this problem on this British Physics Olympiad paper and it assumed that when a star bigger than the sun collapses under its own gravity to create a neuron star the magnetic flux stays constant.

Thanks

Hmm. It was a problem, so it doesn't necessarily reflect reality.

What I understand is this. When stars of a certain range of size go supernova they implode. The result is an exploding gas cloud and a neutron star. Magnetic flux is unaffected by the explosion, and the flux is divided between the gas cloud and the neutron star. The flux that the star has increases with 1/r^2, so if the radius decreases by a factor of a million then the flux density near the star increases by a factor of a trillion. So the amount of flux stays the same, but is very concentrated in the vicinity of the star. The flux travels mostly through empty space, which doesn't dissipate it, and the star is very conductive so going through the star hardly dissipates the flux at all, so this all can go on for a very long time.

So why does the flux have anything to do with the star at all? Why doesn't it just stay in the same diffuse configuration it had before? This is because flux going through very conductive material strongly tends to continue to do that, so as the star contracts the flux is concentrated. It's like a corset.

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By the way, some newly created and very hot neutron stars become dynamos and most of their rotational energy is transformed into a magnetic field. This field is limited to about 10^15 gauss because any stronger than that and the energy will condense into electron-positron pairs that annihilate into gamma rays which carry away the energy.

As the core of the star collapses to form a neutron star (sorry not neuron, neutron), the electrical conductivity becomes very high.

The electrical conductivity was already quite high before the collapse of the star. A star is composed of plasma which is conductive enough to tend to "freeze" the lines of flux. The conductivity becomes even higher after the star has cooled, but the magnetic field has already contracted before this.