<p>I'm not sure where you get the 17 km radius from. It's possible, although 10 km is a more usually assumed radius for a neutron star. It might be a <em>little</em> bigger because of the rotation rate.</p>
<p>Is it possible? Well, yes it is because the rotation rate is unambiguously 716 Hz and the radius of a neutron star cannot be much smaller than about 10 km before becoming unstable and collapsing into a black hole.</p>
<p>Millisecond pulsars spin very fast because they accrete material from a companion. The accreted material lands on the surface with angular momentum and this adds to the angular momentum of the neutron star, spinning it up. The angular rotation rate is just the total angular momentum divided by the moment of inertia, and because the latter is proportional to the square of the radius, and neutron stars are small, this leads to a very fast rotation rate.</p>
<p>You probably shouldn't be all that surprised. For comparison, if you drop something from a long way off onto the surface of the neutron star, it will be travelling at speeds of about <span class="math-container">$0.5c$</span> when it impacts the surface.</p>

CC BY-SA 4.0
2022-06-23T16:37:40.427Z
Yes, 17 should be 16 or less, according to wiki. Also, I'm wrong about the frequency, 716Hz is the correct one. But I was looking for the bigger picture. In that sense, your answer covers me
Stavros Souvatzis
CC BY-SA 4.0
2022-06-23T18:00:19.100Z
@Stavros [Physical Environment of Accreting Neutron Stars](https://doi.org/10.1155/2016/3424565), by J. Wang (2016) has lots of info about various spin-up & spin-down processes. It talks about millisecond pulsars in 2.4.4. Accretion-Induced Field Decay and Spin-Up
PM 2Ring
CC BY-SA 4.0
2022-06-23T18:43:45.530Z
@PM2Ring Some light reading... You do understand I'm not a physicist, right? :). I will take a look though, thanks
Stavros Souvatzis
CC BY-SA 4.0
2022-06-23T16:33:37.210Z
2022-06-23T16:44:03.023Z
2022-06-23T16:44:03.023Z
ProfRob
<p>I recently came upon millisecond pulsars. I knew of pulsars, I had never guessed though that they can spin so fast.</p>
<p>I believe I had read about a pulsar rotating at about 10-15Hz.</p>
<p>But I just read about J1748-2446ad, which rotates at the astonishing 716Hz.</p>
<p>Brief research and I find its radius is about 16km, making its rotation circumference:</p>
<p><span class="math-container">$c = 2πr ≈ 100.5km$</span></p>
<p>Given that the pulsar rotates at 716Hz, its linear velocity at the surface should be:</p>
<p><span class="math-container">$v = 716c/s ≈ 71900km/s$</span></p>
<p>Assuming these calculations are nearly correct, could it be that any point on the rotation circumference moves at about 24% of the speed of light? Can this be possible?</p>
<p>Thanks for any answers that will satisfy my curiosity.</p>

CC BY-SA 4.0
2022-06-23T18:06:48.573Z
BTW, you can write equations using MathJax on this site. See https://physics.stackexchange.com/help/notation & https://math.stackexchange.com/help/notation
PM 2Ring
CC BY-SA 4.0
2022-06-23T18:41:52.407Z
@PM2Ring Thanks, I didn't know that
Stavros Souvatzis
<pulsar>
Pulsar rotation linear velocity
Stavros Souvatzis
# Pulsar rotation linear velocity

(Asked by: username_0 on 2022-06-23)

I recently came upon millisecond pulsars. I knew of pulsars, I had never guessed though that they can spin so fast.

I believe I had read about a pulsar rotating at about 10-15Hz.

But I just read about J1748-2446ad, which rotates at the astonishing 716Hz.

Brief research and I find its radius is about 16km, making its rotation circumference:

$c = 2πr ≈ 100.5km$

Given that the pulsar rotates at 716Hz, its linear velocity at the surface should be:

$v = 716c/s ≈ 71900km/s$

Assuming these calculations are nearly correct, could it be that any point on the rotation circumference moves at about 24% of the speed of light? Can this be possible?

Thanks for any answers that will satisfy my curiosity.

**Tags:** pulsar
> **Comments:**
> **username_1**: BTW, you can write equations using MathJax on this site. See https://physics.stackexchange.com/help/notation & https://math.stackexchange.com/help/notation  
> **username_0**: @PM2Ring Thanks, I didn't know that  

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## 1 answers

### Answer by username_2 on 2022-06-23. Score: 3 | Accepted answer

I'm not sure where you get the 17 km radius from. It's possible, although 10 km is a more usually assumed radius for a neutron star. It might be a *little* bigger because of the rotation rate.

Is it possible? Well, yes it is because the rotation rate is unambiguously 716 Hz and the radius of a neutron star cannot be much smaller than about 10 km before becoming unstable and collapsing into a black hole.

Millisecond pulsars spin very fast because they accrete material from a companion. The accreted material lands on the surface with angular momentum and this adds to the angular momentum of the neutron star, spinning it up. The angular rotation rate is just the total angular momentum divided by the moment of inertia, and because the latter is proportional to the square of the radius, and neutron stars are small, this leads to a very fast rotation rate.

You probably shouldn't be all that surprised. For comparison, if you drop something from a long way off onto the surface of the neutron star, it will be travelling at speeds of about $0.5c$ when it impacts the surface.

> **Comments:**
> **username_0**: Yes, 17 should be 16 or less, according to wiki. Also, I'm wrong about the frequency, 716Hz is the correct one. But I was looking for the bigger picture. In that sense, your answer covers me  
> **username_1**: @Stavros [Physical Environment of Accreting Neutron Stars](https://doi.org/10.1155/2016/3424565), by J. Wang (2016) has lots of info about various spin-up & spin-down processes. It talks about millisecond pulsars in 2.4.4. Accretion-Induced Field Decay and Spin-Up  
> **username_0**: @PM2Ring Some light reading... You do understand I'm not a physicist, right? :). I will take a look though, thanks  

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