# Why do pulsars turn "off" from rotation?

I was looking at the Pulsar wikipedia article and I came across an interesting aspect that said pulsars turn off from rotation:

When a pulsar's spin period slows down sufficiently, the radio pulsar mechanism is believed to turn off (the so-called "death line"). This turn-off seems to take place after about 10–100 million years, which means of all the neutron stars born in the 13.6 billion year age of the universe, around 99% no longer pulsate.

What I don't understand is why emission of EM waves would slow a pulsar down?

The first thing you need to recall is that electromagnetic waves do carry momentum as well as energy. This shows up in effects like light pressure. Specifically a photon of wavelength $\lambda$ carries momentum $h/\lambda$. In and of itself, that doesn't answer your question though, since you are asking about the rotation of the pulsar, and changed to its linear momentum don't affect that. However, there are two ways this can happen. First imagine a rotating sphere which is emitting radiation from its equator. Consider a point on that equator. The radiation it is emitting "forwards" (in the direction towards which it is rotating) will be blue shifted (as seen by a stationary distant observer) while the radiation emitted "backwards" will be correspondingly red-shifted. Since the blue-shifted radiation has shorter wavelength, it has more momentum, the net effect is a force on the source which tends to slow the rotation. (interestingly, the same effect is used at much lower energy levels to trap ultra-cold atoms in what is called "optical molasses").

The second effect is a bit more technical. The radiation which is emitted towards the poles of the pulsar has a property called "circular polarization" and a beam of circularly polarized light carries away angular momentum.

• How does a pulsar emit radiation towards its poles? Where is that radiation emitted from? Jun 23, 2021 at 23:10
• I'm confused why you bring up equatorial emission. I've never seen that invoked to attempt to explain a pulsar slowing down. Jun 24, 2021 at 14:10

I think there's been a little bit of confusion, both about the passage in Wikipedia and the phrasing in the question. Your post asks two distinct questions: Why an isolated pulsar's rotation slows down over time, and why this slowdown eventually leads to the end of radio emission. The gist of the answer to the first - rotational kinetic energy is transferred to radiation at various wavelengths$$^{\dagger}$$ - has been addressed, so I'll focus on the second.

Our understanding of the emission mechanism pulsars use isn't fantastic. While we know the basic ingredients - a powerful magnetic field, plasma in a corotating magnetosphere, etc. - things get a little hazy beyond that. A leading class of mechanisms involve radio emission by electron-positron pairs, which are in turn created by photons emitted by accelerating charged particles. The requirement that pairs be created in turn places constraints on the magnetic field, which is itself related to the pulsar's spin period $$P$$ and period time derivative $$\dot{P}$$.

As a pulsar spins down, eventually the above conditions cannot be satisfied, radio emission turns off, and the pulsar enters a graveyard of sorts in a $$P$$-$$\dot{P}$$ diagram. The critical line is referred to colloquially as the "death line", and its precise location and slope vary slightly based on your model of the cap around the pulsar's magnetic poles, where emission takes place. Chen & Ruderman 1993 present several different death lines based on different polar cap geometries and structures (although they plot theirs in terms of spin period and surface magnetic field, rather than period and period derivative).

Largely, the population of known pulsars fits this theory. That said, we have found a couple of pulsars under the death line. J0250+5854, the extremely slow-rotating pulsar (spin period 23.5 seconds) and J2144−3933 (8.5 seconds) really shouldn't be exhibiting radio emission. This means that either our assumption of the pair production emission mechanism is incorrect, or it's simply a bit more complicated.

(As a note: 10-100 million years is a bit low for some of the faster canonical - i.e. not re-spun up - pulsars, ones with periods of a few hundred milliseconds and low $$\dot{P}$$ values; these may last for up to ~1 billion years before emission turns off.)

$$^{\dagger}$$Emission in the radio part of the spectrum turns out to actually be pretty inefficient, and a lot of the spin-down energy is carried away at shorter wavelengths and higher energies.