<p>Radiation carries a momentum <em>per unit volume</em> given by
$$ \vec{p} = \epsilon_0 \vec{E} \times \vec{B}$$</p>

<p>It therefore carries an angular momentum of
$$ \vec{L} = \vec{r}\times \vec{p} = \epsilon_0 \vec{r} \times (\vec{E}\times \vec{B})$$</p>

<p>For plane-polarised transverse electromagnetic waves propagating in the $\hat{r}$ direction, then $\vec{L}=0$. However, if the axis of a magnetic dipole is inclined to the rotation axis then the radiation is not a single pure transverse wave; the dipole moment is the sum of two oscillating magnetic dipole moments that are perpendicular and oscillate $\pi/2$ out of phase. These produce two transverse waves, with arbitrary amplitudes, perpendicular polarisations and a $\pi/2$ phase shift between them - a.k.a. <a href="https://en.wikipedia.org/wiki/Elliptical_polarization" rel="noreferrer">elliptically polarised light</a>. Elliptically polarised light carries <a href="https://en.wikipedia.org/wiki/Spin_angular_momentum_of_light" rel="noreferrer">angular momentum</a>.</p>

CC BY-SA 3.0
2016-12-23T12:02:15.640Z
Magnetic-dipole radiation is not spherically symmetric, then a neutron star can decelerate. But the main reason is elliptically polarised light carries angular momentum?
questionhang
CC BY-SA 3.0
2016-12-23T12:44:54.757Z
Indeed dipolar fields are not spherically symmetric but that does not necessarily carry away angular momentum. The elliptical polarisation induced by a rotating dipole moment is I think crucial.
ProfRob
CC BY-SA 3.0
2017-01-02T04:45:35.230Z
I am not sure if you are right...
questionhang
CC BY-SA 3.0
2017-01-02T08:00:39.093Z
About what @questionhang ?
ProfRob
CC BY-SA 3.0
2017-01-02T11:38:10.360Z
I am not sure the elliptical polarization is the main reason.
questionhang
CC BY-SA 3.0
2016-12-22T21:20:01.187Z
2016-12-22T21:20:01.187Z
ProfRob
<p>Is the ultimate reason that the neutron star loses angular momentum that the <a href="https://en.wikipedia.org/wiki/Magnetic_moment" rel="noreferrer">magnetic-dipole radiation</a> is not spherically symmetric and photons have momentum?</p>

<p>Just for the loss of angular momentum, particles emitted from the neutron star surface are not necessary, right?</p>

CC BY-SA 3.0
2016-12-22T19:26:23.963Z
I'm voting to close this question as off-topic because you haven't made the connection to astronomy clear. Better on Physics.
James K
<neutron-star>
How does a neutron star emitting magnetic-dipole radiation lose angular momentum?
questionhang
# How does a neutron star emitting magnetic-dipole radiation lose angular momentum?

(Asked by: username_0 on 2016-12-22)

Is the ultimate reason that the neutron star loses angular momentum that the [magnetic-dipole radiation](https://en.wikipedia.org/wiki/Magnetic_moment) is not spherically symmetric and photons have momentum?

Just for the loss of angular momentum, particles emitted from the neutron star surface are not necessary, right?

**Tags:** neutron-star
> **Comments:**
> **username_1**: I'm voting to close this question as off-topic because you haven't made the connection to astronomy clear. Better on Physics.  

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## 1 answers

### Answer by username_2 on 2016-12-22. Score: 9

Radiation carries a momentum *per unit volume* given by
$$ \vec{p} = \epsilon\_0 \vec{E} \times \vec{B}$$

It therefore carries an angular momentum of
$$ \vec{L} = \vec{r}\times \vec{p} = \epsilon\_0 \vec{r} \times (\vec{E}\times \vec{B})$$

For plane-polarised transverse electromagnetic waves propagating in the $\hat{r}$ direction, then $\vec{L}=0$. However, if the axis of a magnetic dipole is inclined to the rotation axis then the radiation is not a single pure transverse wave; the dipole moment is the sum of two oscillating magnetic dipole moments that are perpendicular and oscillate $\pi/2$ out of phase. These produce two transverse waves, with arbitrary amplitudes, perpendicular polarisations and a $\pi/2$ phase shift between them - a.k.a. [elliptically polarised light](https://en.wikipedia.org/wiki/Elliptical_polarization). Elliptically polarised light carries [angular momentum](https://en.wikipedia.org/wiki/Spin_angular_momentum_of_light).

> **Comments:**
> **username_0**: Magnetic-dipole radiation is not spherically symmetric, then a neutron star can decelerate. But the main reason is elliptically polarised light carries angular momentum?  
> **username_2**: Indeed dipolar fields are not spherically symmetric but that does not necessarily carry away angular momentum. The elliptical polarisation induced by a rotating dipole moment is I think crucial.  
> **username_0**: I am not sure if you are right...  
> **username_2**: About what @questionhang ?  
> **username_0**: I am not sure the elliptical polarization is the main reason.  

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