Editing Neutron star (section)

==Rotation==

Neutron stars rotate extremely rapidly after their formation due to the conservation of angular momentum; in analogy to spinning ice skaters pulling in their arms, the slow rotation of the original star's core speeds up as it shrinks. A newborn neutron star can rotate many times a second.

===Spin down===
[[Image:PPdot2.png|thumb|''P''–''P''-dot diagram for known [[rotation-powered pulsar]]s (red), anomalous X-ray pulsars (green), high-energy emission pulsars (blue) and [[binary pulsar]]s (pink)]]
Over time, neutron stars slow, as their rotating magnetic fields in effect radiate energy associated with the rotation; older neutron stars may take several seconds for each revolution. This is called ''spin down''. The rate at which a neutron star slows its rotation is usually constant and very small.

The [[periodic time]] (''P'') is the [[Rotation period|rotational period]], the time for one rotation of a neutron star. The spin-down rate, the rate of slowing of rotation, is then given the symbol <math>\dot{P}</math> (''P''-dot), the [[derivative]] of ''P'' with respect to time. It is defined as periodic time increase per unit time; it is a [[dimensionless quantity]], but can be given the units of s⋅s<sup>−1</sup> (seconds per second).<ref name="nrao">{{cite web |url=https://www.cv.nrao.edu/~sransom/web/Ch6.html |title=Pulsar Properties (Essential radio Astronomy) |publisher=National Radio Astronomy Observatory |access-date=24 March 2016 |first1=J. J. |last1=Condon |first2=S. M. |last2=Ransom |name-list-style=amp |archive-date=10 April 2016 |archive-url=https://web.archive.org/web/20160410113528/http://www.cv.nrao.edu/~sransom/web/Ch6.html |url-status=live }}</ref>

The spin-down rate (''P''-dot) of neutron stars usually falls within the range of {{val|e=−22}} to {{val|e=−9|u=s⋅s<sup>−1</sup>}}, with the shorter period (or faster rotating) observable neutron stars usually having smaller ''P''-dot. As a neutron star ages, its rotation slows (as ''P'' increases); eventually, the rate of rotation will become too slow to power the radio-emission mechanism, so radio emission from the neutron star no longer can be detected.<ref name="nrao" />

''P'' and ''P''-dot allow minimum magnetic fields of neutron stars to be estimated.<ref name="nrao" /> ''P'' and ''P''-dot can be also used to calculate the ''characteristic age'' of a pulsar, but gives an estimate which is somewhat larger than the true age when it is applied to young pulsars.<ref name="nrao" />

''P'' and ''P''-dot can also be combined with neutron star's [[moment of inertia]] to estimate a quantity called ''spin-down [[luminosity]]'', which is given the symbol <math>\dot{E}</math> (''E''-dot). It is not the measured luminosity, but rather the calculated loss rate of rotational energy that would manifest itself as radiation. For neutron stars where the spin-down luminosity is comparable to the actual [[luminosity]], the neutron stars are said to be "[[rotation powered pulsar|rotation powered]]".<ref name="nrao" /><ref name="pavlov" /> The observed luminosity of the [[Crab Pulsar]] is comparable to the spin-down luminosity, supporting the model that rotational kinetic energy powers the radiation from it.<ref name="nrao" /> With neutron stars such as magnetars, where the actual luminosity exceeds the spin-down luminosity by about a factor of one hundred, it is assumed that the luminosity is powered by magnetic dissipation, rather than being rotation powered.<ref name="ufrgs">{{cite web |url=http://www.if.ufrgs.br/hadrons/zhang.pdf |title=Spin-Down Power of Magnetars |publisher=Universidade Federal do Rio Grande do Sul |access-date=24 March 2016 |first=B. |last=Zhang |archive-date=6 February 2021 |archive-url=https://web.archive.org/web/20210206223627/http://www.if.ufrgs.br/hadrons/zhang.pdf |url-status=live }}</ref>

''P'' and ''P''-dot can also be plotted for neutron stars to create a ''P''–''P''-dot diagram. It encodes a tremendous amount of information about the pulsar population and its properties, and has been likened to the [[Hertzsprung–Russell diagram]] in its importance for neutron stars.<ref name="nrao" />

===Spin up===
[[File:Neutron Star X-ray beaming with accretion disk.jpg|thumb|A computer simulation depicting a neutron star with accretion disk, spewing out X-rays through the magnetic axis]]
{{Main|Neutron star spin-up}}
Neutron star rotational speeds can increase, a process known as spin up. Sometimes neutron stars absorb orbiting matter from companion stars, increasing the rotation rate and reshaping the neutron star into an [[oblate spheroid]]. This causes an increase in the rate of rotation of the neutron star of over a hundred times per second in the case of millisecond pulsars.

The most rapidly rotating neutron star currently known, [[PSR J1748-2446ad]], rotates at 716 revolutions per second.<ref>{{Cite journal |arxiv = astro-ph/0601337|last1 = Hessels|first1 = Jason W. T|title = A Radio Pulsar Spinning at 716 Hz|journal = Science|volume = 311|issue = 5769|pages = 1901–1904|last2 = Ransom|first2 = Scott M|last3 = Stairs|first3 = Ingrid H|last4 = Freire|first4 = Paulo C. C|last5 = Kaspi|first5 = Victoria M|last6 = Camilo|first6 = Fernando|year = 2006|doi = 10.1126/science.1123430|pmid = 16410486|citeseerx = 10.1.1.257.5174|bibcode = 2006Sci...311.1901H|s2cid = 14945340}}</ref> A 2007 paper reported the detection of an X-ray burst oscillation, which provides an indirect measure of spin, of 1122&nbsp;[[Hertz|Hz]] from the neutron star [[XTE J1739-285]],<ref name="KaaretPrieskorn2007">{{cite journal|last1=Kaaret|first1=P.|last2=Prieskorn|first2=Z.|last3=Zand|first3=J. J. M. in 't|last4=Brandt|first4=S.|last5=Lund|first5=N.|last6=Mereghetti|first6=S.|last7=Götz|first7=D.|last8=Kuulkers|first8=E.|last9=Tomsick|first9=J. A.|title=Evidence of 1122 Hz X-Ray Burst Oscillations from the Neutron Star X-Ray Transient XTE J1739-285|journal=The Astrophysical Journal|volume=657|issue=2|year=2007|pages=L97–L100|issn=0004-637X|doi=10.1086/513270|arxiv=astro-ph/0611716|bibcode=2007ApJ...657L..97K|s2cid=119405361}}</ref> suggesting 1122 rotations a second. However, at present, this signal has only been seen once, and should be regarded as tentative until confirmed in another burst from that star.

===Glitches and starquakes===
[[Image:2004 stellar quake full.jpg|thumb|NASA artist's conception of a "[[Starquake (astrophysics)#Starquake|starquake]]", or "stellar quake"]]
Sometimes a neutron star will undergo a [[glitch (astronomy)|glitch]], a sudden small increase of its rotational speed or spin up.<ref name=":0">{{Citation |last1=Antonelli |first1=Marco |title=Astrophysics in the XXI Century with Compact Stars |date=November 2022 |pages=219–281 |last2=Montoli |first2=Alessandro |last3=Pizzochero |first3=Pierre|chapter=Insights into the Physics of Neutron Star Interiors from Pulsar Glitches |doi=10.1142/9789811220944_0007 |arxiv=2301.12769 |isbn=978-981-12-2093-7 }}</ref> Glitches are thought to be the effect of a [[starquake (astrophysics)|starquake]]—as the rotation of the neutron star slows, its shape becomes more spherical. Due to the stiffness of the "neutron" crust, this happens as discrete events when the crust ruptures, creating a starquake similar to earthquakes. After the starquake, the star will have a smaller equatorial radius, and because angular momentum is conserved, its rotational speed has increased.

Starquakes occurring in [[magnetars]], with a resulting glitch, is the leading hypothesis for the gamma-ray sources known as soft gamma repeaters.<ref name="sa"/>

Recent work, however, suggests that a starquake would not release sufficient energy for a neutron star glitch; it has been suggested that glitches may instead be caused by transitions of vortices in the theoretical superfluid core of the neutron star from one metastable energy state to a lower one, thereby releasing energy that appears as an increase in the rotation rate.<ref>{{cite web |url=http://physicsworld.com/cws/article/print/1756 |date=1 January 1998 |title=Pulsars, glitches and superfluids |publisher=Physicsworld.com |first=M. Ali |last=Alpar |access-date=12 January 2009 |archive-date=6 December 2008 |archive-url=https://web.archive.org/web/20081206090618/http://physicsworld.com/cws/article/print/1756 |url-status=live }}</ref><ref name=":0" />

===Anti-glitches===

An anti-glitch, a sudden small decrease in rotational speed, or spin down, of a neutron star has also been reported.<ref name="nature">{{cite journal |title=An anti-glitch in a magnetar |journal=Nature |doi=10.1038/nature12159 |year=2013 |first1=R. F. |last1=Archibald |first2=V. M. |last2=Kaspi |first3=C. Y. |last3=Ng |first4=K. N. |last4=Gourgouliatos |first5=D. |last5=Tsang |first6=P. |last6=Scholz |first7=A. P. |last7=Beardmore |first8=N. |last8=Gehrels |first9=J. A. |last9=Kennea |pages=591–593 |volume=497 |issue=7451 |hdl=10722/186148 |pmid=23719460 |arxiv=1305.6894 |bibcode=2013Natur.497..591A |s2cid=4382559 }}</ref><ref>{{cite web |last1=Reddy |first1=Francis |title=NASA's Swift Reveals New Phenomenon in a Neutron Star |url=https://www.nasa.gov/universe/nasas-swift-reveals-new-phenomenon-in-a-neutron-star/ |website=NASA.gov |date=29 May 2013 |publisher=National Aeronautics and Space Administration |access-date=26 September 2024}}</ref> It occurred in the magnetar [[1E 2259+586]], that in one case produced an X-ray luminosity increase of a factor of 20, and a significant spin-down rate change. Current neutron star models do not predict this behavior. If the cause were internal this suggests differential rotation of the solid outer crust and the superfluid component of the magnetar's inner structure.<ref name="nature" /><ref name=":0" />