<p>What you describe would not appear as a <em>pulsar</em>. The usual model of a pulsar has non-aligned magnetic and rotation axes, in order to get a Doppler boosted and beamed cone of radiation to sweep across the direction of an observer at regular intervals.</p>
<p>The main radiation mechanisms are caused by particle acceleration from the neutron star surface along the magnetic field lines. Such particles can cause synchrotron or curvature radiation and this would occur even if the rotation and magnetic axes were aligned.</p>
<p>In the simple model proposed in the paper you reference, the magnetosphere is filled with plasma. Once you rotate the neutron star, this become inevitable because a large poloidal electric field (see equation 15 in the paper) drives a poloidal current (shown as <span class="math-container">$I$</span> in your diagram). The poloidal current generates a toroidal magnetic field (see equation 9 in the paper).</p>
<p>Since there is a poloidal electric field and a toroidal magnetic field (not shown in your diagram), there is a radial Poynting flux from their cross product, (<span class="math-container">${\bf E \times B}$</span>) and hence radiation losses (discussed in Appendix B of the paper).</p>

CC BY-SA 4.0
2024-05-29T19:51:43.510Z
2024-10-27T05:34:01.777Z
2024-10-27T05:34:01.777Z
ProfRob
<p>It seems that the model of an &quot;aligned&quot; rotator is a common model to describe most features of isolated pulsars:</p>
<blockquote>
<p>Since the first works on pulsar magnetospheres, a stationary force-
free magnetosphere of an aligned rotator has been considered as an
underlying model for the real pulsar magnetosphere for more than
30 years.</p>
</blockquote>
<p>(Quote and figure below are randomly somewhat randomly picked from <a href="https://ui.adsabs.harvard.edu/abs/2006MNRAS.368.1055T/abstract" rel="nofollow noreferrer">Timokhin, 2006</a>.)</p>
<p>My very basic question is now: Why a rotating dipole field in vacuum should produce any radiation (or current)?</p>
<p>The whole geometry seems to have cylindrical symmetry, as rotation and dipole axis are supposed to be aligned:</p>
<p><a href="https://i.sstatic.net/VCB7vket.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VCB7vket.png" alt="enter image description here" /></a></p>
<p>So spinning it around its symmetry axis should not change the B-field anywhere in space. And without a varying B-field, no current or radiation.</p>
<p>Obviously I am missing something here.</p>

CC BY-SA 4.0
2024-05-28T13:22:11.427Z
Although not an exact duplicate, the excellent answer in this question: https://astronomy.stackexchange.com/questions/98/what-causes-a-neutron-star-to-become-a-pulsar?rq=1 might answer yours; briefly, the dipole axis is normally not perfectly aligned with the spin axis.
antlersoft
<neutron-star><magnetic-field><pulsar>
Why does an aligned rotator (pulsar) radiate?
SpaceCore
# Why does an aligned rotator (pulsar) radiate?

(Asked by: username_0 on 2024-05-24)

It seems that the model of an "aligned" rotator is a common model to describe most features of isolated pulsars:

> Since the first works on pulsar magnetospheres, a stationary force-
> free magnetosphere of an aligned rotator has been considered as an
> underlying model for the real pulsar magnetosphere for more than
> 30 years.

(Quote and figure below are randomly somewhat randomly picked from [Timokhin, 2006](https://ui.adsabs.harvard.edu/abs/2006MNRAS.368.1055T/abstract).)

My very basic question is now: Why a rotating dipole field in vacuum should produce any radiation (or current)?

The whole geometry seems to have cylindrical symmetry, as rotation and dipole axis are supposed to be aligned:

[![enter image description here](https://i.sstatic.net/VCB7vket.png)](https://i.sstatic.net/VCB7vket.png)

So spinning it around its symmetry axis should not change the B-field anywhere in space. And without a varying B-field, no current or radiation.

Obviously I am missing something here.

**Tags:** neutron-star, magnetic-field, pulsar
> **Comments:**
> **username_1**: Although not an exact duplicate, the excellent answer in this question: https://astronomy.stackexchange.com/questions/98/what-causes-a-neutron-star-to-become-a-pulsar?rq=1 might answer yours; briefly, the dipole axis is normally not perfectly aligned with the spin axis.  

---

## 1 answers

### Answer by username_2 on 2024-05-29. Score: 1

What you describe would not appear as a *pulsar*. The usual model of a pulsar has non-aligned magnetic and rotation axes, in order to get a Doppler boosted and beamed cone of radiation to sweep across the direction of an observer at regular intervals.

The main radiation mechanisms are caused by particle acceleration from the neutron star surface along the magnetic field lines. Such particles can cause synchrotron or curvature radiation and this would occur even if the rotation and magnetic axes were aligned.

In the simple model proposed in the paper you reference, the magnetosphere is filled with plasma. Once you rotate the neutron star, this become inevitable because a large poloidal electric field (see equation 15 in the paper) drives a poloidal current (shown as $I$ in your diagram). The poloidal current generates a toroidal magnetic field (see equation 9 in the paper).

Since there is a poloidal electric field and a toroidal magnetic field (not shown in your diagram), there is a radial Poynting flux from their cross product, (${\bf E \times B}$) and hence radiation losses (discussed in Appendix B of the paper).


---

