Editing Globular cluster (section)

===N-body simulations===
{{Main|N-body simulation}}

Computing the gravitational interactions between stars within a globular cluster requires solving the [[N-body problem]]. The naive computational cost for a dynamic simulation increases in proportion to ''N''<sup> 2</sup> (where N is the number of objects), so the computing requirements to accurately simulate a cluster of thousands of stars can be enormous.<ref>{{cite conference
 | first = D. C. | last = Heggie
 | author2 = Giersz, M.
 | author3 = Spurzem, R.
 | author4 = Takahashi, K.
 | date= 1998 | page = 591
 | title = Dynamical Simulations: Methods and Comparisons
 | work = Highlights of Astronomy Vol. 11A, as presented at the Joint Discussion 14 of the XXIIIrd General Assembly of the IAU, 1997
 | editor = Johannes Andersen
 | publisher = Kluwer Academic Publishers
 | bibcode = 1998HiA....11..591H
|arxiv = astro-ph/9711191 }}</ref><ref>{{cite journal |last1=Di Cintio |first1=Pierfrancesco |last2=Pasquato |first2=Mario |last3=Simon-Petit |first3=Alicia |last4=Yoon |first4=Suk-Jin |title=Introducing a new multi-particle collision method for the evolution of dense stellar systems |journal=Astronomy & Astrophysics |year=2022 |volume=659 |pages=A19 |doi=10.1051/0004-6361/202140710 |arxiv=2103.02424 |s2cid=240032727 }}</ref> A more efficient method of simulating the N-body dynamics of a globular cluster is done by subdivision into small volumes and velocity ranges, and using ''probabilities'' to describe the locations of the stars. Their motions are described by means of the [[Fokker–Planck equation]], often using a model describing the mass density as a function of radius, such as a [[Plummer model]]. The simulation becomes more difficult when the effects of binaries and the interaction with external gravitation forces (such as from the Milky Way galaxy) must also be included.<ref>{{cite journal
 |last         = Benacquista
 |first        = Matthew J.
 |date         = 2006
 |title        = Relativistic Binaries in Globular Clusters
 |journal      = Living Reviews in Relativity
 |url          = http://relativity.livingreviews.org/Articles/lrr-2006-2/
 |volume       = 9
 |issue        = 1
 |page        = 2
 |doi          = 10.12942/lrr-2006-2
 |doi-access = free
 |bibcode      = 2006LRR.....9....2B
 |pmc          = 5255526
 |pmid         = 28163652
 |access-date  = May 28, 2006
 |archive-date = March 3, 2006
 |archive-url  = https://web.archive.org/web/20060303104233/http://relativity.livingreviews.org/Articles/lrr-2006-2/
 
}}</ref> In 2010 a low-density globular cluster's lifetime evolution was able to be directly computed, star-by-star.<ref>{{cite journal|last=Hasani Zonoozi|first=Akram|display-authors=etal|date=March 2011|title=Direct ''N''-body simulations of globular clusters – I. Palomar 14|journal=Monthly Notices of the Royal Astronomical Society|volume=411|issue=3|pages=1989–2001|arxiv=1010.2210|bibcode=2011MNRAS.411.1989Z|doi=10.1111/j.1365-2966.2010.17831.x|doi-access=free |s2cid=54777932}}</ref>

Completed N-body simulations have shown that stars can follow unusual paths through the cluster, often forming loops and falling more directly toward the core than would a single star orbiting a central mass. Additionally, some stars gain sufficient energy to escape the cluster due to gravitational interactions that result in a sufficient increase in velocity. Over long periods of time this process leads to the dissipation of the cluster, a process termed evaporation.<ref>{{cite book
 |editor1=J. Goodman |editor2=P. Hut | date= 1985
 | title = Dynamics of Star Clusters (International Astronomical Union Symposia)
 | publisher = Springer | isbn=978-90-277-1963-8 }}</ref> The typical time scale for the evaporation of a globular cluster is 10<sup>10</sup> years.<ref name="structure" /> The ultimate fate of a globular cluster must be either to accrete stars at its core, causing its steady contraction,<ref>{{cite journal|author1=Zhou, Yuan|author2=Zhong, Xie Guang|date=June 1990|title=The core evolution of a globular cluster containing massive black holes|journal=Astrophysics and Space Science|volume=168|issue=2|pages=233–241|bibcode=1990Ap&SS.168..233Y|doi=10.1007/BF00636869|s2cid=122289977}}</ref> or gradual shedding of stars from its outer layers.<ref>{{cite web|last=Pooley|first=Dave|title=Globular Cluster Dynamics: the importance of close binaries in a real N-body system|url=http://www.deadlyastroninja.com/research/node1.html|url-status=live|archive-url=https://web.archive.org/web/20100619062440/http://www.astro.wisc.edu/~pooley/research/node1.html|archive-date=June 19, 2010|access-date=April 7, 2021|publisher=self-published}}</ref>

[[Binary stars]] form a significant portion of stellar systems, with up to half of all [[field star]]s and [[open cluster]] stars occurring in binary systems.<ref>{{cite journal |doi=10.1088/0004-637X/799/2/135 |title=Stellar Loci Ii. A Model-Free Estimate of the Binary Fraction for Field FGK Stars |year=2015 |last1=Yuan |first1=Haibo |last2=Liu |first2=Xiaowei |last3=Xiang |first3=Maosheng |last4=Huang |first4=Yang |last5=Chen |first5=Bingqiu |last6=Wu |first6=Yue |last7=Hou |first7=Yonghui |last8=Zhang |first8=Yong |journal=The Astrophysical Journal |volume=799 |issue=2 |page=135 |arxiv=1412.1233 |bibcode=2015ApJ...799..135Y |s2cid=118504277 }}</ref><ref>{{cite journal |doi=10.1093/mnras/stab347 |title=Binary-driven stellar rotation evolution at the main-sequence turn-off in star clusters |year=2021 |last1=Sun |first1=Weijia |last2=De Grijs |first2=Richard |last3=Deng |first3=Licai |last4=Albrow |first4=Michael D. |journal=Monthly Notices of the Royal Astronomical Society |volume=502 |issue=3 |pages=4350–4358 |doi-access=free | bibcode= 2021MNRAS.502.4350S | arxiv=2102.02352 }}</ref> The present-day binary fraction in globular clusters is difficult to measure, and any information about their initial binary fraction is lost by subsequent dynamical evolution.<ref>{{cite journal |last1=Duchêne |first1=Gaspard |last2=Kraus |first2=Adam |title=Stellar Multiplicity |journal=Annual Review of Astronomy and Astrophysics |date=August 18, 2013 |volume=51 |issue=1 |pages=269–310 |doi=10.1146/annurev-astro-081710-102602 |bibcode=2013ARA&A..51..269D |arxiv=1303.3028|s2cid=119275313 }}</ref> Numerical simulations of globular clusters have demonstrated that binaries can hinder and even reverse the process of core collapse in globular clusters. When a star in a cluster has a gravitational encounter with a binary system, a possible result is that the binary becomes more tightly bound and kinetic energy is added to the solitary star. When the massive stars in the cluster are sped up by this process, it reduces the contraction at the core and limits core collapse.<ref name="murphy" /><ref>{{cite journal |doi=10.1051/0004-6361/201936203 |title=A stellar census in globular clusters with MUSE: Binaries in NGC 3201 |year=2019 |last1=Giesers |first1=Benjamin |last2=Kamann |first2=Sebastian |last3=Dreizler |first3=Stefan |last4=Husser |first4=Tim-Oliver |last5=Askar |first5=Abbas |last6=Göttgens |first6=Fabian |last7=Brinchmann |first7=Jarle |last8=Latour |first8=Marilyn |last9=Weilbacher |first9=Peter M. |last10=Wendt |first10=Martin |last11=Roth |first11=Martin M. |journal=Astronomy & Astrophysics |volume=632 |pages=A3 |arxiv=1909.04050 |bibcode=2019A&A...632A...3G |s2cid=202542401 }}</ref>