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Neutron stars are one type of remnant of a giant star's core after its collapse. Neutron stars tend to rotate at very high speed and the mismatch between its axis of rotation and magnetic pole make it a "pulsar". Over time, the rotational energy is lost and may come to a static state, no rotation.

Have we observed any static neutron star(s)?

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    $\begingroup$ The issue with this question might be similar to asking "Is anything exactly 1 meter long? Even when it's right in front of you, let alone thousands of light years away. Maybe draw a line somewhere in rotation? $\endgroup$
    – DKNguyen
    Commented Mar 3, 2022 at 18:32
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    $\begingroup$ This might be a duplicate of astronomy.stackexchange.com/q/19927/2153. $\endgroup$
    – HDE 226868
    Commented Mar 3, 2022 at 20:23
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    $\begingroup$ If the angular deceleration depends on the angular velocity, then only an exponential deceleration will happen and not a complete stall. $\endgroup$
    – peterh
    Commented Mar 3, 2022 at 22:41
  • $\begingroup$ @DKNguyen but rotational energy levels are quantized. Ortho-hydrogen must rotate. :) $\endgroup$
    – DavePhD
    Commented Mar 4, 2022 at 2:22
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    $\begingroup$ @HDE226868 I don't feel so. asking "will it work" is totally different from asking "have you saw it working" $\endgroup$ Commented Mar 4, 2022 at 9:57

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The absence of evidence of spin cannot be evidence for the absence of spin.

We lose the ability to measure the spin of single neutron stars when they slow down below the pulsar "death line" at rotation periods above about 5-10 seconds.

Neutron stars in binaries are often measured to be fast rotators, either as (millisecond) pulsars or by monitoring the rotation of accretion hot spots. Neutron stars in binaries can also be slowed by accretion torques and these have the slowest measured rotation rates.

The vast majority of neutron stars are not pulsars and are not in close binary systems. They are cool, small and relatively dark. The problem in answering your question is that neutron stars also cool down as they spin down and the slow rotators you seek might be members of this effectively invisible population.

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    $\begingroup$ at rotation periods above about 8 seconds; implying that some stars complete a full rotation faster than every 8 seconds - incredible. $\endgroup$
    – stevec
    Commented Mar 3, 2022 at 13:25
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    $\begingroup$ @stevec there are neutron stars that spin at a speed close to the speed of light $\endgroup$ Commented Mar 3, 2022 at 13:28
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    $\begingroup$ @stevec e.g. see astronomy.stackexchange.com/questions/1291/… - the term "milli-second pulsar" exists for a reason. $\endgroup$ Commented Mar 3, 2022 at 16:21
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    $\begingroup$ @stevec PSR B1919+21, the first pulsar to be discovered (by Jocelyn Bell Burnell on 28 November 1967), has a period of 1.3373 seconds. The period of the famous Crab pulsar PSR B0531+21 (discovered in 1968) is 33.5028583 milliseconds. $\endgroup$
    – PM 2Ring
    Commented Mar 4, 2022 at 0:27
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    $\begingroup$ Couldn't it be tidally locked? That is, a tidally locked neutron star would see changes to its orbital period different from one that is not tidally locked? Doppler shift of the radiation from a visible companion star could be used measure the orbital period. $\endgroup$ Commented Mar 5, 2022 at 2:26
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Everything rotates at some rate. The rotation-powered pulsars mentioned in ProfRob's answer need to spin fast to generate their radiation. Accretion-powered pulsars do not, so they may be observed at slower rotation rates. The slowest one known is AX J1910.7+0917, at a period of about 36,200 seconds. This is extremely slow for such a dense object, with angular momentum/mass of ~0.001% of Earth.

Added in response to comment:

The pulsed emission from an accretion-powered pulsar is thermal. The pulsar accretes matter from a binary companion. The pulsar's magnetic field channels the accreted matter, which impacts and heats the pulsar at hot spots. The changing visibility of the hot spots as the pulsar rotates is observed as pulsating x-rays. If the magnetic field is strong enough, it can also channel the x-rays into beams, enhancing the effect.

Over the short term, accretion-powered pulsars are very regular. Over the long term, the accretion torques the pulsar, changing its period. As an extreme example, GX1+4's period decreased at ~2% per year through the 1970's.

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  • $\begingroup$ Quite interesting. Could you provide an explanation of how accretion pulsars generate output, and what, if any kind of regularity these pulses follow (vs the sinus rhythm of rotation pulsars)? $\endgroup$ Commented Mar 3, 2022 at 15:06
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    $\begingroup$ @CarlWitthoft See edit. $\endgroup$
    – John Doty
    Commented Mar 3, 2022 at 16:37
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    $\begingroup$ @JohnDoty the 8s limit applies to single neutron stars; as I said. The slow rotators in binaries have been slowed by accretion torques from a close companion. $\endgroup$
    – ProfRob
    Commented Mar 3, 2022 at 18:07
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    $\begingroup$ And 36,000s is still rotating as fast as Jupiter. $\endgroup$
    – ProfRob
    Commented Mar 3, 2022 at 18:11
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    $\begingroup$ @ProfRob But it's extremely slow for such a compact, dense object. Very low specific angular momentum. $\endgroup$
    – John Doty
    Commented Mar 3, 2022 at 18:21

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