<p>There are, in general, two classes of explanations for neutron star magnetic fields: fossilized magnetic fields and active magnetic fields (see <a href="http://dspace.rri.res.in/bitstream/2289/3315/20/Chapter%203.pdf" rel="noreferrer">here</a> for an early overview on some of the internal battery models).</p>

<p>The "fossilized" field theory - which is well-accepted, as far as I know - states that neutron star magnetic fields are leftovers from the magnetic fields of the progenitor stars. This seems plausible, and some (e.g. <a href="https://arxiv.org/abs/0711.3650" rel="noreferrer">Spruit (2008)</a>) have suggested that the supernova that formed the neutron stars may have endowed them with exceptionally strong fields during core collapse, leaving behind magnetars. This is what zephyr means by "frozen in": the magnetic fields remains the same after the star becomes a neutron star.</p>

<p>The "active" theories - and I'm using "active" as a non-technical term - posit that neutron stars continue to generate magnetic fields. This makes it possible for the magnetic fields to grow in strength, which can explain why magnetars have exceptionally strong fields; fossilized fields may not be sufficient to explain this in all cases. There have been several suggestions over the years for changes in magnetic fields, some of which are no longer accepted but some of which are still possible:</p>

<ul>
<li><p><strong>The battery model.</strong> This was originally proposed as a mechanism for generating magnetic fields in normal stars. It holds that electrons inside a star drift outward slightly relative to the ions, due to different effects from the gravitational field and any centrifugal force. The resulting pressures cause the electrons to move in ways similar to a battery, which generates a magnetic field.</p>

<p>As zephyr mentioned, the important equation is
$$-\frac{\partial\mathbf{B}}{\partial t}=\nabla\times\mathbf{E}$$
In the battery model, $\nabla\times\mathbf{E}$ turns out to be non-zero, meaning that the magnetic field can, in fact, change, thanks to thermal effects.  I believe, however, that the battery model has been ruled out for neutron stars. Taking degeneracy pressure into account does, in fact, lead to a vanishing $\nabla\times\mathbf{E}$, and therefore there is no time-varying field.</p></li>
<li><strong>The thermoelectric mechanism.</strong> This is actually a variation on the pure battery model, and is applicable only in the neutron star's crust. If there is a non-zero radial heat gradient <em>and</em> a small magnetic field, electrons will create a small pressure gradient, which in turn causes an opposing thermoelectric field to arise - which leads to a non-zero $\nabla
\times\mathbf{E}$! The precise equation is
$$\frac{\partial\mathbf{B}}{\partial t}=\overbrace{\nabla\times\left(\mathbf{V}\times\mathbf{B}\right)}^{\text{Field convection term}}-\overbrace{\nabla Q_0\times\nabla T}^{\text{Battery term}}-\overbrace{\nabla\times\left[\frac{\nabla\times\mathbf{B}}{4\pi\sigma_0}\right]}^{\text{Ohmic decay term}}$$
The thermoelectric model is much better than the traditional battery model, and does allow for the magnetic field to grow.</li>
<li><strong>Accretion from a companion.</strong> This is a slightly newer idea, which has gained traction after observations of binary systems (see a discussion by <a href="http://adsabs.harvard.edu/full/1999ptgr.conf..235B" rel="noreferrer">Bhattacharya (1999)</a>). Matter from a companion star follows the neutron star's pre-existing magnetic field lines. Pressure causes the matter to "drag" the field lines along the neutron star's surface until <a href="https://en.wikipedia.org/wiki/Magnetic_reconnection" rel="noreferrer">magnetic reconnection</a> occurs, "screening" the field underneath the accreted matter. This actually weakens the field, making it decay over time - which does match observations of some neutron stars. However, instabilities make it a difficult possibility.</li>
</ul>

CC BY-SA 3.0
2017-03-07T18:56:40.167Z
Great answer! You definitely added a lot more information than mine did.
zephyr
CC BY-SA 3.0
2017-03-08T02:58:34.920Z
Also, why is a magnetar's magnetic field stronger than a normal neutron star?
Phoenix91
CC BY-SA 3.0
2017-03-08T19:15:12.327Z
@zephyr Thanks. I took part of it from an older answer I had written on Physics.
HDE 226868
CC BY-SA 3.0
2017-03-08T19:15:34.667Z
@Phoenix91 A magnetar is pretty much just, by definition, a neutron star with a  very strong magnetic field.
HDE 226868
CC BY-SA 3.0
2017-03-07T17:05:36.100Z
2017-03-07T17:05:36.100Z
HDE 226868
<p>Magnetars (and neutron stars in general) don't need a dynamo to create their magnetic fields. Their magnetic fields are "frozen in" at the time of their formation. To really see why this is, you have to understand a lot about electromagnetism, but I can boil it down to the basics. Keep in mind that neutron stars are highly mysterious objects and we don't have a huge amount of good, observational evidence behind our theories since they're so hard to find and observe.</p>

<p>Neutron stars (and magnetars) are superconductors (or at least <a href="http://physicsworld.com/cws/article/news/2011/mar/02/neutron-star-has-superfluid-core" rel="nofollow noreferrer">most theory and objective evidence suggests that is the case</a>). What this means is that there is literally no resistance to the motion of electric charges moving throughout the star. To point out, even if the entire star was all neutrons (which <a href="https://astronomy.stackexchange.com/questions/20304/magnetars-and-the-dynamo-effect#comment33689_20304">zibadawa timmy points out is not the case</a>) you'd still have charges since neutrons themselves are composed of charged particles. In any case, since there's no resistance, there cannot exist any electric fields inside the star. Any field which arose would induce a force on the charged particles which would be able to immediately move to cancel said field out. All electric fields destroy themselves immediately in a superconductor.</p>

<p>If we venture into electromagnetic theory equations, you'll find the very useful equation:</p>

<p>$$\nabla \times \textbf{E} = -\frac{\partial \textbf{B}}{\partial t}$$</p>

<p>Without getting into the details of this equation, the general idea behind it is that electric fields result in time varying magnetic fields and vice versa. But we just said above that our neutron star was superconducting and thus has no electric fields. This means the left hand side of that equation is zero. The right side represents the change in magnetic field over time, but we know that has to be zero now so we're forced to conclude <strong>magnetic fields in neutron stars (and magnetars) cannot change. They're frozen in at the point of creation (when the star becomes superconducting).</strong></p>

<p>We can venture one step further and say that the magnetic fields of neutron stars and magnetars is so strong simply because of magnetic flux conservation. That is, you have a huge star of a few solar masses which has a massive field in its own right. That star then collapses into a neutron star but in the process, the magnetic field flux through its surface has to stay conserved. Magnetic field flux is a function of both the field strength and the radius of the star. Since the radius is decreasing so immensely, <strong>the magnetic field strength has to increase in proportion to the radius decrease (squared)</strong> to compensate and keep the overall flux the same, at which point that magnetic field is locked into place due to the superconducting nature of the star.</p>

CC BY-SA 3.0
2017-03-08T02:58:56.567Z
Why is a magnetar's magnetic field stronger than a normal neutron star?
Phoenix91
CC BY-SA 3.0
2017-03-08T17:21:39.347Z
@Phoenix91 I believe that is an active area of research.  So we're not quite sure.  It's possible that most neutron stars are born as magnetars, and then through some sort of magnetic breaking mechanism and neutrino emissions the neutron star loses energy (which could cause it to settle into a new, less magnetic state once it hits a certain threshold) and magnetic field strength.  A lot of this depends on knowing the equation of state for a neutron star, and we're still at the guessing stage on that one.
zibadawa timmy
CC BY-SA 3.0
2017-03-08T17:26:10.897Z
@Phoenix91 I think it's a bit of a misinterpretation to think of magnetars and neutron stars as separate objects. I think that magnetars are just neutron stars with especially strong magnetic fields. That is, neutron stars form with naturally strong magnetic fields (by the process I mentioned above) and we consider the neutron stars with especially strong magnetic fields to be magnetars.
zephyr
CC BY-SA 3.0
2017-03-07T14:57:35.120Z
2017-03-07T16:20:32.920Z
2017-04-13T12:59:06.910Z
zephyr
<p>How do magnetars create/sustain such strong magnetic fields? If a dynamo effect did create a magnetar, then what creates the magnetic field? The dynamo effect requires an electrically conductive fluid, but magnetars are purely composed of neutrons. In Earth, the dynamo effect is supported with evidence, but how does it apply to magnetars?</p>

CC BY-SA 3.0
2017-03-07T02:07:08.353Z
"purely composed of neutrons" is false.  Neutron stars are not composed purely of neutrons.  They've got a lot more than normal, but they still have electrons and protons (at least until you get close enough to the core, because then we don't yet really know *what* there is).
zibadawa timmy
<neutron-star><magnetic-field>
Magnetars and the Dynamo Effect
Phoenix91
# Magnetars and the Dynamo Effect

(Asked by: username_0 on 2017-03-07)

How do magnetars create/sustain such strong magnetic fields? If a dynamo effect did create a magnetar, then what creates the magnetic field? The dynamo effect requires an electrically conductive fluid, but magnetars are purely composed of neutrons. In Earth, the dynamo effect is supported with evidence, but how does it apply to magnetars?

**Tags:** neutron-star, magnetic-field
> **Comments:**
> **username_1**: "purely composed of neutrons" is false.  Neutron stars are not composed purely of neutrons.  They've got a lot more than normal, but they still have electrons and protons (at least until you get close enough to the core, because then we don't yet really know *what* there is).  

---

## 2 answers

### Answer by username_2 on 2017-03-07. Score: 6

There are, in general, two classes of explanations for neutron star magnetic fields: fossilized magnetic fields and active magnetic fields (see [here](http://dspace.rri.res.in/bitstream/2289/3315/20/Chapter%203.pdf) for an early overview on some of the internal battery models).

The "fossilized" field theory - which is well-accepted, as far as I know - states that neutron star magnetic fields are leftovers from the magnetic fields of the progenitor stars. This seems plausible, and some (e.g. [Spruit (2008)](https://arxiv.org/abs/0711.3650)) have suggested that the supernova that formed the neutron stars may have endowed them with exceptionally strong fields during core collapse, leaving behind magnetars. This is what zephyr means by "frozen in": the magnetic fields remains the same after the star becomes a neutron star.

The "active" theories - and I'm using "active" as a non-technical term - posit that neutron stars continue to generate magnetic fields. This makes it possible for the magnetic fields to grow in strength, which can explain why magnetars have exceptionally strong fields; fossilized fields may not be sufficient to explain this in all cases. There have been several suggestions over the years for changes in magnetic fields, some of which are no longer accepted but some of which are still possible:

* **The battery model.** This was originally proposed as a mechanism for generating magnetic fields in normal stars. It holds that electrons inside a star drift outward slightly relative to the ions, due to different effects from the gravitational field and any centrifugal force. The resulting pressures cause the electrons to move in ways similar to a battery, which generates a magnetic field.

  As zephyr mentioned, the important equation is
  $$-\frac{\partial\mathbf{B}}{\partial t}=\nabla\times\mathbf{E}$$
  In the battery model, $\nabla\times\mathbf{E}$ turns out to be non-zero, meaning that the magnetic field can, in fact, change, thanks to thermal effects. I believe, however, that the battery model has been ruled out for neutron stars. Taking degeneracy pressure into account does, in fact, lead to a vanishing $\nabla\times\mathbf{E}$, and therefore there is no time-varying field.
* **The thermoelectric mechanism.** This is actually a variation on the pure battery model, and is applicable only in the neutron star's crust. If there is a non-zero radial heat gradient *and* a small magnetic field, electrons will create a small pressure gradient, which in turn causes an opposing thermoelectric field to arise - which leads to a non-zero $\nabla
  \times\mathbf{E}$! The precise equation is
  $$\frac{\partial\mathbf{B}}{\partial t}=\overbrace{\nabla\times\left(\mathbf{V}\times\mathbf{B}\right)}^{\text{Field convection term}}-\overbrace{\nabla Q\_0\times\nabla T}^{\text{Battery term}}-\overbrace{\nabla\times\left[\frac{\nabla\times\mathbf{B}}{4\pi\sigma\_0}\right]}^{\text{Ohmic decay term}}$$
  The thermoelectric model is much better than the traditional battery model, and does allow for the magnetic field to grow.
* **Accretion from a companion.** This is a slightly newer idea, which has gained traction after observations of binary systems (see a discussion by [Bhattacharya (1999)](http://adsabs.harvard.edu/full/1999ptgr.conf..235B)). Matter from a companion star follows the neutron star's pre-existing magnetic field lines. Pressure causes the matter to "drag" the field lines along the neutron star's surface until [magnetic reconnection](https://en.wikipedia.org/wiki/Magnetic_reconnection) occurs, "screening" the field underneath the accreted matter. This actually weakens the field, making it decay over time - which does match observations of some neutron stars. However, instabilities make it a difficult possibility.

> **Comments:**
> **username_3**: Great answer! You definitely added a lot more information than mine did.  
> **username_0**: Also, why is a magnetar's magnetic field stronger than a normal neutron star?  
> **username_2**: @zephyr Thanks. I took part of it from an older answer I had written on Physics.  
> **username_2**: @Phoenix91 A magnetar is pretty much just, by definition, a neutron star with a  very strong magnetic field.  

---

### Answer by username_3 on 2017-03-07. Score: 6

Magnetars (and neutron stars in general) don't need a dynamo to create their magnetic fields. Their magnetic fields are "frozen in" at the time of their formation. To really see why this is, you have to understand a lot about electromagnetism, but I can boil it down to the basics. Keep in mind that neutron stars are highly mysterious objects and we don't have a huge amount of good, observational evidence behind our theories since they're so hard to find and observe.

Neutron stars (and magnetars) are superconductors (or at least [most theory and objective evidence suggests that is the case](http://physicsworld.com/cws/article/news/2011/mar/02/neutron-star-has-superfluid-core)). What this means is that there is literally no resistance to the motion of electric charges moving throughout the star. To point out, even if the entire star was all neutrons (which [zibadawa timmy points out is not the case](https://astronomy.stackexchange.com/questions/20304/magnetars-and-the-dynamo-effect#comment33689_20304)) you'd still have charges since neutrons themselves are composed of charged particles. In any case, since there's no resistance, there cannot exist any electric fields inside the star. Any field which arose would induce a force on the charged particles which would be able to immediately move to cancel said field out. All electric fields destroy themselves immediately in a superconductor.

If we venture into electromagnetic theory equations, you'll find the very useful equation:

$$\nabla \times \textbf{E} = -\frac{\partial \textbf{B}}{\partial t}$$

Without getting into the details of this equation, the general idea behind it is that electric fields result in time varying magnetic fields and vice versa. But we just said above that our neutron star was superconducting and thus has no electric fields. This means the left hand side of that equation is zero. The right side represents the change in magnetic field over time, but we know that has to be zero now so we're forced to conclude **magnetic fields in neutron stars (and magnetars) cannot change. They're frozen in at the point of creation (when the star becomes superconducting).**

We can venture one step further and say that the magnetic fields of neutron stars and magnetars is so strong simply because of magnetic flux conservation. That is, you have a huge star of a few solar masses which has a massive field in its own right. That star then collapses into a neutron star but in the process, the magnetic field flux through its surface has to stay conserved. Magnetic field flux is a function of both the field strength and the radius of the star. Since the radius is decreasing so immensely, **the magnetic field strength has to increase in proportion to the radius decrease (squared)** to compensate and keep the overall flux the same, at which point that magnetic field is locked into place due to the superconducting nature of the star.

> **Comments:**
> **username_0**: Why is a magnetar's magnetic field stronger than a normal neutron star?  
> **username_1**: @Phoenix91 I believe that is an active area of research.  So we're not quite sure.  It's possible that most neutron stars are born as magnetars, and then through some sort of magnetic breaking mechanism and neutrino emissions the neutron star loses energy (which could cause it to settle into a new, less magnetic state once it hits a certain threshold) and magnetic field strength.  A lot of this depends on knowing the equation of state for a neutron star, and we're still at the guessing stage on that one.  
> **username_3**: @Phoenix91 I think it's a bit of a misinterpretation to think of magnetars and neutron stars as separate objects. I think that magnetars are just neutron stars with especially strong magnetic fields. That is, neutron stars form with naturally strong magnetic fields (by the process I mentioned above) and we consider the neutron stars with especially strong magnetic fields to be magnetars.  

---

