# I Why do neutron stars have such powerful magnetic fields?

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1. Nov 13, 2017

### Gevorg

The sources I've looked at claim the magnetic field is present because there are still some electrons in the neutron star.
Here is how I understand their reasoning: a star's radius significantly decreases when it collapses into a neutron star, ultimately decreasing its moment of inertia. In order to conserve angular momentum, it obtains a tremendous angular velocity. Thus the magnetic field is generated due to the high tangential velocity of the electrons.

Still, I am not convinced that the residual amount of surviving electrons is entirely responsible for the insanely powerful magnetic field. Although they lack charge, is there some other property of neutrons that allows them to contribute to the magnetic field? Could it have something to do with their dipole moments?

Thank you

2. Nov 13, 2017

I have little expertise in this area, but neutrons do have spin 1/2. The nuclear magneton $\mu_N$ is about 1/1800 of the Bohr magneton, so that the magnetic field from a single neutron would be much smaller than that from a single electron spin. If the neutron density is high enough, and the neutron spins become aligned, the magnetic fields that are generated could be quite large. A very interesting question. I will need to google it and/or study the additional responses. $\\$ Editing: A google of the topic suggests the strong magnetic fields are caused by protons and electrons, (the neutron star also contains protons and electrons), that are in motion in the interior of the neutron star. The moving charged particles apparently generate most of the magnetic field. The vast majority of the magnetic field of a neutron star apparently doesn't originate from the spin of the neutron.

Last edited: Nov 13, 2017
3. Nov 13, 2017

### phyzguy

The material in stars is relatively conductive. In a conductive fluid, the magnetic field lines are more or less "frozen in" to the fluid. This is known as Alfven's theorem. Since the units of magnetic field are a flux density (Webers per m^2 for example), as the radius of the star decreases, the magnetic field increase as 1/R^2. So if a star like the sun with a radius of ~ 1 million km collapses to a neutron star with a radius of 10 km, the magnetic field is increased by a factor of (10^5)^2 = 10^10. So the sun's magnetic field of 1 Gauss would increase to 10^10 Gauss. On top of this, many stars have much higher magnetic fields to begin with, and start with much larger radii. So it is fairly easy to get magnetic fields of 10^12 to 10^14 Gauss, or even higher.

4. Nov 14, 2017

### Gevorg

Thank you for the reply phyzguy. What I still don't understand is what continues to generate the magnetic field when a majority of the electrons and protons are squeezed into neutrons.

5. Nov 14, 2017

In the google, approximately 10% of the particles are still bare protons and electrons. Apparently they keep the neutron star conductive and allow for the processes that @phyzguy described.

6. Nov 14, 2017

### Gevorg

7. Nov 14, 2017

Electric fields would cause these particles to move in opposite directions. In many plasmas, the electrons move much faster than the protons because of the heavier proton mass. Perhaps most of the magnetic field is due to electron motion.

8. Nov 14, 2017

### phyzguy

Neutron star matter has very high electrical conductivity. I don't know all of the details, but not all of the matter is neutrons, and there are still a significant number of protons and electrons. And the density is so high that even a small fraction of the component particles being charged leads to a very high conductivity. This is an old paper, but they state:

"THE time for the magnetic field of a neutron star to decay by ohmic dissipation plays an important part in theories of pulsars1–3. The decay time for the lowest mode in a spherical star of radius R and of constant electrical conductivity σ is given by4,5 Previous estimates3 of σ(≈6×10^22s−1) lead to values of τD ≈ 4 × 10^6 yr for R = 10 km. This time is relatively short on the evolutionary time scale of pulsars. We show below that σ is at least six orders of magnitude greater than the estimate quoted above. Consequently τD is greater than the age of the universe, and flux decay in neutron stars is therefore completely negligible."