Editing Globular cluster (section)

==Morphology==
{| class="wikitable" style="margin-top: 0px; margin-left: 0.5em;" align="right"
|+ '''Ellipticity of globular clusters'''
|-
!Galaxy
!Ellipticity<ref>{{cite journal
 |author1=Staneva, A. |author2=Spassova, N. |author3=Golev, V. | date= 1996
 | title = The Ellipticities of Globular Clusters in the Andromeda Galaxy
 | journal = Astronomy and Astrophysics Supplement
 | volume = 116
 | issue = 3 | pages = 447–461
 | bibcode = 1996A&AS..116..447S | doi = 10.1051/aas:1996127 | doi-access = free }}</ref>
|-
|Milky Way
|0.07±0.04
|-
|[[Large Magellanic Cloud|LMC]]
|0.16±0.05
|-
|[[Small Magellanic Cloud|SMC]]
|0.19±0.06
|-
|M31
|0.09±0.04
|}
In contrast to open clusters, most globular clusters remain gravitationally bound together for time periods comparable to the lifespans of most of their stars. Strong tidal interactions with other large masses result in the dispersal of some stars, leaving behind "tidal tails" of stars removed from the cluster.<ref>{{cite web |last1=Hensley |first1=Kerrin |title=Dating the Evaporation of Globular Clusters |url=https://astrobites.org/2018/06/20/dating-globular-clusters/ |website=Astrobites |date=June 20, 2018}}</ref><ref>{{cite journal |last1=Bose |first1=Sownak |last2=Ginsburg |first2=Idan |last3=Loeb |first3=Abraham |title=Dating the Tidal Disruption of Globular Clusters with GAIA Data on Their Stellar Streams |journal=The Astrophysical Journal |date=May 23, 2018 |volume=859 |issue=1 |pages=L13 |doi=10.3847/2041-8213/aac48c|arxiv=1804.07770 |bibcode=2018ApJ...859L..13B |s2cid=54514038 |doi-access=free }}</ref>

After formation, the stars in the globular cluster begin to interact gravitationally with each other. The velocities of the stars steadily change, and the stars lose any history of their original velocity. The characteristic interval for this to occur is the [[relaxation time]], related to the characteristic length of time a star needs to cross the cluster and the number of stellar masses.<ref name="structure">{{cite journal
 | last = Benacquista | first = Matthew J.
 | title=Globular cluster structure
 | journal=Living Reviews in Relativity | date=2006
 | doi=10.12942/lrr-2006-2
 | bibcode=2006LRR.....9....2B
 | volume=9| issue = 1
 | page = 2
 | doi-access = free
 | arxiv=astro-ph/0202056
 | pmid=28163652
 | pmc=5255526
 }}</ref> The relaxation time varies by cluster, but a typical value is on the order of one billion years.<ref>{{cite journal |last1=Baumgardt |first1=H |last2=Hilker |first2=M |title=A catalogue of masses, structural parameters, and velocity dispersion profiles of 112 Milky Way globular clusters |journal=Monthly Notices of the Royal Astronomical Society |date=August 1, 2018 |volume=478 |issue=2 |pages=1520–1557 |doi=10.1093/mnras/sty1057 |arxiv=1804.08359 |bibcode=2018MNRAS.478.1520B|doi-access=free }}</ref><ref>{{Cite journal|last1=Zocchi|first1=A.|last2=Varri|first2=A. L.|last3=Bertin|first3=Giuseppe|date=January 6, 2012|title=A dynamical study of Galactic globular clusters under different relaxation conditions|url=https://www.researchgate.net/publication/51978934|journal=[[Astronomy & Astrophysics]]|volume=539|pages=A65|arxiv=1201.1466|doi=10.1051/0004-6361/201117977|bibcode=2012A&A...539A..65Z|s2cid=54078666}}</ref>

Although globular clusters are generally spherical in form, ellipticity can form via tidal interactions. Clusters within the Milky Way and the Andromeda Galaxy are typically [[oblate spheroid]]s in shape, while those in the Large Magellanic Cloud are more elliptical.<ref>{{cite journal
 |author1=Frenk, C. S. |author2=White, S. D. M. | date= 1980
 | title = The ellipticities of Galactic and LMC globular clusters
 | journal = Monthly Notices of the Royal Astronomical Society
 | volume = 286 | issue = 3 | pages = L39–L42
 | bibcode = 1997MNRAS.286L..39G |arxiv = astro-ph/9702024
 | doi = 10.1093/mnras/286.3.l39 |doi-access=free |s2cid=353384 }}</ref>

{{anchor|core radius}}

===Radii===
{{redirect-distinguish|Tidal radius|Roche limit}}
[[File:Appearances can be deceptive.jpg|thumb|alt=Hundreds of white-ish dots scattered on a black background, concentrated towards the center, with some brighter red and blue dots scattered across the frame|[[NGC 411]] is classified as an open cluster.<ref>{{cite news|title=Appearances can be deceptive|url=http://www.spacetelescope.org/images/potw1303a/|access-date=February 12, 2013|newspaper=ESO Picture of the Week | id= potw1303a}}</ref>]]

Astronomers characterize the morphology (shape) of a globular cluster by means of standard radii: the core radius (''r''<sub>''c''</sub>), the [[half-light radius]] (''r''<sub>''h''</sub>), and the tidal or Jacobi radius (''r''<sub>''t''</sub>). The radius can be expressed as a physical distance or as a subtended angle in the sky. Considering a radius around the core, the surface luminosity of the cluster steadily decreases with distance, and the core radius is the distance at which the apparent surface luminosity has dropped by half.<ref name="star clusters">{{cite web | url=http://www.astro.caltech.edu/~george/ay20/eaa-starclus.pdf |archive-url=https://web.archive.org/web/20060923134045/http://www.astro.caltech.edu/~george/ay20/eaa-starclus.pdf |archive-date=2006-09-23 |url-status=live | title=Star Clusters | publisher=Encyclopedia of Astronomy and Astrophysics | date=November 2000 | access-date=March 26, 2014 | author=Kenneth Janes | page=2}}</ref> A comparable quantity is the half-light radius, or the distance from the core containing half the total luminosity of the cluster; the half-light radius is typically larger than the core radius.<ref>{{cite web |last1=Rosen |first1=Anna |title=Understanding the Dynamical State of Globular Clusters |url=https://astrobites.org/2012/07/18/understanding-the-dynamical-state-of-globular-clusters/ |website=astrobites |date=July 18, 2012}}</ref><ref>{{cite journal |last1=Chatterjee |first1=Sourav |last2=Umbreit |first2=Stefan |last3=Fregeau |first3=John M. |last4=Rasio |first4=Frederic A. |title=Understanding the dynamical state of globular clusters: core-collapsed versus non-core-collapsed |journal=Monthly Notices of the Royal Astronomical Society |date=March 11, 2013 |volume=429 |issue=4 |pages=2881–2893 |doi=10.1093/mnras/sts464 |doi-access=free |bibcode=2013MNRAS.429.2881C |arxiv=1207.3063}}</ref>

Most globular clusters have a half-light radius of less than ten parsecs (pc), although some globular clusters have very large radii, like [[NGC 2419]] (r<sub>h</sub>&nbsp;= 18&nbsp;pc) and [[Palomar 14]] (r<sub>h</sub>&nbsp;= 25&nbsp;pc).<ref name="Bergh2007">{{Cite journal|last=Van den Bergh|first=Sidney|author-link=Sidney van den Bergh|date=November 2007|title=Globular Clusters and Dwarf Spheroidal Galaxies|journal=[[Monthly Notices of the Royal Astronomical Society]]|volume=385|issue=1|pages=L20–L22|arxiv=0711.4795|bibcode=2008MNRAS.385L..20V|doi=10.1111/j.1745-3933.2008.00424.x|doi-access=free |s2cid=15093329}}</ref> The half-light radius includes stars in the outer part of the cluster that happen to lie along the line of sight, so theorists also use the half-mass radius (''r''<sub>''m''</sub>){{snd}}the radius from the core that contains half the total mass of the cluster. A small half-mass radius, relative to the overall size, indicates a dense core. [[Messier&nbsp;3]] (M3), for example, has an overall visible dimension of about 18 [[arc minute]]s, but a half-mass radius of only 1.12&nbsp;arc minutes.<ref>{{cite journal
 | last1 =Buonanno |first1=R. |last2=Corsi |first2=C. E. |last3=Buzzoni |first3=A. |last4=Cacciari |first4=C. |last5=Ferraro |first5=F. R. |last6=Fusi Pecci |first6=F.
 | date= 1994
 | title = The Stellar Population of the Globular Cluster M 3. I. Photographic Photometry of 10 000 Stars
 | journal = Astronomy and Astrophysics | volume = 290
 | pages = 69–103
 | bibcode = 1994A&A...290...69B
}}</ref>

The tidal radius, or [[Hill sphere]], is the distance from the center of the globular cluster at which the external gravitation of the galaxy has more influence over the stars in the cluster than does the cluster itself.<ref name=Piatti-2019>{{cite journal| title = Characteristic radii of the Milky Way globular clusters| year = 2019| doi = 10.1093/mnras/stz2499| arxiv = 1909.01718| last1 = Piatti| first1 = Andrés E.| last2 = Webb| first2 = Jeremy J.| last3 = Carlberg| first3 = Raymond G.| journal = Monthly Notices of the Royal Astronomical Society| volume = 489| issue = 3| pages = 4367–4377| doi-access = free}}</ref> This is the distance at which the individual stars belonging to a cluster can be separated away by the galaxy. The tidal radius of M3, for example, is about forty arc minutes,<ref name="DaCosta">{{cite journal
| last1       = Da Costa
| first1      = G. S.
| last2      = Freeman
| first2     = K. C.
| date       = May 1976
| title      = The structure and mass function of the globular cluster M3
| journal    = Astrophysical Journal
| volume     = 206
| issue      = 1
| pages      = 128–137
| bibcode    = 1976ApJ...206..128D
| doi        = 10.1086/154363
}}</ref> or about 113&nbsp;pc.<ref name=Brosche-1999>{{cite journal |last1=Brosche|first1=P. |last2=Odenkirchen|first2=M. |last3=Geffert|first3=M. |date=March 1999|title=Instantaneous and average tidal radii of globular clusters|journal=New Astronomy|volume=4|issue=2|pages=133–139 |bibcode=1999NewA....4..133B|doi=10.1016/S1384-1076(99)00014-7}}</ref>

===Mass segregation, luminosity and core collapse===
In most Milky Way clusters, the surface brightness of a globular cluster as a function of decreasing distance to the core first increases, then levels off at a distance typically 1–2 parsecs from the core. About 20% of the globular clusters have undergone a process termed "core collapse". The luminosity in such a cluster increases steadily all the way to the core region.<ref>{{cite journal |author1=Djorgovski, S. |author2=King, I. R. |date=1986 |title=A preliminary survey of collapsed cores in globular clusters |journal=Astrophysical Journal |volume=305 |pages=L61–L65 |bibcode=1986ApJ...305L..61D |doi=10.1086/184685 |s2cid=122668507 |url=https://authors.library.caltech.edu/97564/ |archive-url=https://web.archive.org/web/20200915023244/https://authors.library.caltech.edu/97564/ |url-status=dead |archive-date=September 15, 2020 }}</ref><ref>{{cite journal |last1=Bianchini |first1=P |last2=Webb |first2=J J |last3=Sills |first3=A |last4=Vesperini |first4=E |title=Kinematic fingerprint of core-collapsed globular clusters |journal=Monthly Notices of the Royal Astronomical Society: Letters |date=March 21, 2018 |volume=475 |issue=1 |pages=L96–L100 |doi=10.1093/mnrasl/sly013 |doi-access=free | bibcode=2018MNRAS.475L..96B | arxiv=1801.07781}}</ref>
[[File:Globular_cluster_47_Tucanae.jpg|thumb|right|alt=Thousands of white-ish dots scattered on a black background, strongly concentrated towards the center|[[47 Tucanae]] is the second most luminous globular cluster in the Milky Way, after Omega Centauri.]]

Models of globular clusters predict that core collapse occurs when the more massive stars in a globular cluster encounter their less massive counterparts. Over time, dynamic processes cause individual stars to migrate from the center of the cluster to the outside, resulting in a net loss of [[kinetic energy]] from the core region and leading the region's remaining stars to occupy a more compact volume. When this gravothermal instability occurs, the central region of the cluster becomes densely crowded with stars, and the [[surface brightness]] of the cluster forms a [[power-law]] cusp.<ref name=ashman_zepf1998>{{cite book
 |author1=Ashman, Keith M. |author2=Zepf, Stephen E. | title=Globular Cluster Systems | date=1998 | volume=30
 | series=Cambridge astrophysics series | page=29
 | publisher=Cambridge University Press | isbn=978-0-521-55057-4 }}</ref> A massive black hole at the core could also result in a luminosity cusp.<ref name=binney_merrifield1998>{{cite book
 |author1=Binney, James |author2=Merrifield, Michael | title=Galactic astronomy | date=1998 | page=371
 | series=Princeton series in astrophysics
 | publisher=Princeton University Press
 | isbn=978-0-691-02565-0 }}</ref> Over a long time, this leads to a concentration of massive stars near the core, a phenomenon called [[mass segregation]].<ref name=lymanspitzer1984>{{cite journal |last1=Spitzer |first1=Lyman |title=Dynamics of Globular Clusters |journal=Science |date=1984 |volume=225 |issue=4661 |pages=465–472 |doi=10.1126/science.225.4661.465 |jstor=1693970 |pmid=17750830 |bibcode=1984Sci...225..465S |s2cid=30929160 |issn=0036-8075}}</ref>

The dynamical heating effect of binary star systems works to prevent an initial core collapse of the cluster. When a star passes near a binary system, the orbit of the latter pair tends to contract, releasing energy. Only after this primordial supply of energy is exhausted can a deeper core collapse proceed.<ref name=vanbeveren2001>{{cite book
 | first=D. | last=Vanbeveren | date=2001
 | title=The Influence of Binaries on Stellar Population Studies | volume=264
 | series=Astrophysics and space science library
 | publisher=Springer | page=397 | isbn=978-0-7923-7104-5 }}</ref><ref name=spitzer1986>{{cite conference
 | title=Dynamical Evolution of Globular Clusters
 | last=Spitzer | first=L. Jr. | work=The Use of Supercomputers in Stellar Dynamics, Proceedings of a Workshop Held at the Institute for Advanced Study
 | series=Lecture Notes in Physics | location=Princeton, USA | date=June 2–4, 1986
 | volume=267 |editor1=P. Hut |editor2=S. McMillan | publisher=Springer-Verlag, Berlin Heidelberg New York
 | page=3 | doi=10.1007/BFb0116388
 | bibcode=1986LNP...267....3S | isbn=978-3-540-17196-6 }}</ref> In contrast, the effect of [[tidal shock]]s as a globular cluster repeatedly passes through the plane of a spiral galaxy tends to significantly accelerate core collapse.<ref name=apj522_2_935>{{cite journal
 | title=Effects of Tidal Shocks on the Evolution of Globular Clusters
 |author1=Gnedin, Oleg Y. |author2=Lee, Hyung Mok |author3=Ostriker, Jeremiah P. | journal=The Astrophysical Journal | volume=522
 | issue=2 | pages=935–949 |date=September 1999
 | doi=10.1086/307659 | bibcode=1999ApJ...522..935G
 | arxiv=astro-ph/9806245 |s2cid=11143134 }}</ref>

Core collapse may be divided into three phases. During a cluster's adolescence, core collapse begins with stars nearest the core. Interactions between [[binary star]] systems prevents further collapse as the cluster approaches middle age. The central binaries are either disrupted or ejected, resulting in a tighter concentration at the core.<ref name=pnas107_16_7164>{{cite journal | title=Effects of Tidal Shocks on the Evolution of Globular Clusters |author1=Pooley, David | journal=Proceedings of the National Academy of Sciences | volume=107 | issue= 16 | pages= 7164–7167 |date=April 2010 | doi= 10.1073/pnas.0913903107 |pmid=20404204 |pmc=2867700 | bibcode=2010PNAS..107.7164P| s2cid= 15402180 |doi-access=free }}</ref> The interaction of stars in the collapsed core region causes tight binary systems to form. As other stars interact with these tight binaries they increase the energy at the core, causing the cluster to re-expand. As the average time for a core collapse is typically less than the age of the galaxy, many of a galaxy's globular clusters may have passed through a core collapse stage, then re-expanded.<ref name=bahcall_piran_weinberg2004>{{cite book
 |author1=Bahcall, John N. |author2=Piran, Tsvi |author3=Weinberg, Steven | title=Dark Matter in the Universe | page=51 | edition=2nd
 | publisher=World Scientific | date=2004 | isbn=978-981-238-841-4 }}</ref>
[[File:The stars of the Large Magellanic Cloud.jpg|thumb|alt=Hundreds of white-ish dots scattered on a black background, concentrated towards the center|Globular cluster [[NGC 1854]] is located in the Large Magellanic Cloud.<ref>{{cite web |title=The stars of the Large Magellanic Cloud |url=https://esahubble.org/images/potw1625a/ |website=European Space Agency/Hubble |language=en |date=June 20, 2016 | id=potw1625a | access-date=April 7, 2021}}</ref>]]

The HST has provided convincing observational evidence of this stellar mass-sorting process in globular clusters. Heavier stars slow down and crowd at the cluster's core, while lighter stars pick up speed and tend to spend more time at the cluster's periphery. The cluster [[47&nbsp;Tucanae]], made up of about one million stars, is one of the densest globular clusters in the Southern Hemisphere. This cluster was subjected to an intensive photographic survey that obtained precise velocities for nearly fifteen thousand stars in this cluster.<ref>{{cite press release
 | title=Stellar Sorting in Globular Cluster 47
 | publisher=Hubble News Desk | date=October 4, 2006
| url=https://hubblesite.org/contents/news-releases/2006/news-2006-33.html
 | access-date=April 9, 2021 | id= 2006-33 }}</ref>

The overall luminosities of the globular clusters within the Milky Way and the Andromeda Galaxy each have a roughly [[Gaussian curve|Gaussian distribution]], with an average magnitude M<sub>v</sub> and a variance σ<sup>2</sup>. This distribution of globular cluster luminosities is called the Globular Cluster Luminosity Function (GCLF). For the Milky Way, M<sub>v</sub>&nbsp;= {{nowrap|−7.29 ± 0.13}}, σ&nbsp;= {{nowrap|1.1 ± 0.1}}. The GCLF has been used as a "[[standard candle]]" for measuring the distance to other galaxies, under the assumption that globular clusters in remote galaxies behave similarly to those in the Milky Way.<ref>{{cite journal
 | last = Secker | first = Jeff | date= 1992
 | title = A Statistical Investigation into the Shape of the Globular cluster Luminosity Distribution
 | journal = Astronomical Journal | volume = 104
 | issue = 4 | pages = 1472–1481
 | bibcode = 1992AJ....104.1472S | doi = 10.1086/116332 }}</ref>

===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>

===Intermediate forms===
[[File:Globular Cluster M10.jpg|thumb|alt=Thousands of white-ish dots scattered on a black background, strongly concentrated towards the center|[[Messier 10]] lies about 15,000 light-years from Earth, in the constellation of [[Ophiuchus (constellation)|Ophiuchus]].<ref>{{cite news|title=Globular Cluster M10|url=http://www.spacetelescope.org/images/potw1225a/|access-date=June 18, 2012|newspaper=ESA/Hubble Picture of the Week}}</ref>]]

Cluster classification is not always definitive; objects have been found that can be classified in more than one category. For example, BH 176 in the southern part of the Milky Way has properties of both an open and a globular cluster.<ref>{{cite journal | last1=Ortolani |first1=S. |last2=Bica |first2=E. |last3=Barbuy |first3=B.
 | title=BH 176 and AM-2: globular or open clusters? | journal=Astronomy and Astrophysics | date=1995 | volume=300 | page=726 | bibcode=1995A&A...300..726O}}</ref>

In 2005 astronomers discovered a new, "extended" type of star cluster in the Andromeda Galaxy's halo, similar to the globular cluster. The three new-found clusters have a similar star count to globular clusters and share other characteristics, such as stellar populations and metallicity, but are distinguished by their larger size{{snd}}several hundred light years across{{snd}}and some hundred times lower density. Their stars are separated by larger distances; parametrically, these clusters lie somewhere between a globular cluster and a [[dwarf spheroidal galaxy]].<ref name="extended">{{cite journal
 |author1=Huxor, A. P. |author2=Tanvir, N. R. |author3=Irwin, M. J. |author4=R. Ibata | title=A new population of extended, luminous, star clusters in the halo of M31
 | journal=Monthly Notices of the Royal Astronomical Society
 | date=2005 | volume=360
 | issue=3 | pages=993–1006
 | arxiv=astro-ph/0412223
 | doi=10.1111/j.1365-2966.2005.09086.x
|doi-access=free | bibcode=2005MNRAS.360.1007H|s2cid=6215035 }}</ref>
The formation of these extended clusters is likely related to accretion.<ref>{{cite journal |last1=Huxor |first1=A. P. |last2=Mackey |first2=A. D. |last3=Ferguson |first3=A. M. N. |last4=Irwin |first4=M. J. |last5=Martin |first5=N. F. |last6=Tanvir |first6=N. R. |last7=Veljanoski |first7=J. |last8=McConnachie |first8=A. |last9=Fishlock |first9=C. K. |last10=Ibata |first10=R. |last11=Lewis |first11=G. F. |title=The outer halo globular cluster system of M31 – I. The final PAndAS catalogue |journal=Monthly Notices of the Royal Astronomical Society |date=August 11, 2014 |volume=442 |issue=3 |pages=2165–2187 |doi=10.1093/mnras/stu771|doi-access=free |arxiv=1404.5807 }}</ref> It is unclear why the Milky Way lacks such clusters; Andromeda is unlikely to be the sole galaxy with them, but their presence in other galaxies remains unknown.<ref name="extended" />