Globular cluster#Mass segregation, luminosity and core collapse

The first known globular cluster, now called M 22, was discovered in 1665 by Abraham Ihle, a German amateur astronomer.Kirch, Gottfried (1682) Annus II. Ephemeridum Motuum Coelestium Ad Annum Aerae Christianae M. DC. LXXXII. … [Second year. Ephemerides of the celestial motions for the year of the Christian era 1682.] Leipzig, (Germany): Heirs of Friedrich Lanckisch. (in Latin) 54 pages. The pages of this book are not numbered. However, in the Appendix, section III. Stella nebulosa prope pedem borealem Ganymedis observata, Lipsia, die 1. Sept. 1681. (III. Nebula near the northern foot of Ganymede observed, Leipzig, 1. September 1681.), first paragraph, Kirch enumerated recently discovered nebulae: " […] & tertia in Sagittaris, quam Dn. Joh. Abrah. Ihle Anno 1665. deprehendit; […] " ([…] and the third [nebula] in Sagittarius, which Mr. Johann Abraham Ihle discovered in the year 1665; […]) Downloadable at: [https://opendata2.uni-halle.de/handle/1516514412012/32738 Digitale Sammlungen der Universitäts- und Landesbibliothek Sachsen-Anhalt] (Digital collections of the university- and state library of Sachsen-Anhalt){{cite journal |last=Lynn |first=W.T. |date=April 1886 |title=The discovery of the star-cluster 22 Messier in Sagittarius |journal=The Observatory |volume=9 |pages=163–164 |bibcode=1886Obs.....9..163L |url=https://books.google.com/books?id=XHEKAAAAIAAJ&pg=PA163}}{{cite web |last=Sharp |first=N.A. |title=M22, NGC 6656 |publisher=NOIRLab |url=https://noirlab.edu/public/images/noao-m22/ |access-date=August 23, 2021}} The cluster Omega Centauri, easily visible in the southern sky with the naked eye, was known to ancient astronomers like Ptolemy as a star, but was reclassified as a nebula by Edmond Halley in 1677,{{cite book |last1=Halley |first1=Edmond |title=Catalogus Stellarum Australium … |trans-title= Catalog of southern stars … |date=1679 |publisher=Thomas James |location=London, England |url=https://books.google.com/books?id=QVg4AAAAMAAJ&pg=PP26}}

This book's pages are not numbered. However in the "Centaurus" section, one entry is labeled "in dorso equino nebula" (nebula in the horse's back); the position of this nebula is consistent with Omega Centauri. then finally as a globular cluster in the early 19th century by John Herschel.{{cite book |last1=Herschel |first1=John F. W. |title=Results of astronomical observations made during the years 1834, 5, 6, 7, 8, at the Cape of Good Hope; being the completion of a telescopic survey of the whole surface of the visible heavens, commenced in 1825 |date=1847 |publisher=Smith, Elder and Co. |location=London, England |page=105 |bibcode=1847raom.book.....H |url=https://archive.org/details/resultsofastrono00hers/page/104/mode/2up}} See entry: 🜨 [symbol for globular cluster]; ω Centauri{{cite book |last=O'Meara |first=Stephen James |year=2012 |title=Deep-Sky Companions: Southern gems |publisher=Cambridge University Press |location=Cambridge |isbn=978-1-107-01501-2 |pages=243–245 |url=https://books.google.com/books?id=S5QIEKns33sC&pg=PA244 |access-date=September 24, 2021}}{{cite web |title=Omega Centauri |website=eso.org |language=en |publisher=European Southern Observatory |url=https://www.eso.org/public/france/images/b09/?lang |access-date=September 24, 2021}} The French astronomer Abbé Lacaille listed NGC 104, {{nobr|NGC 4833}}, M 55, M 69, and {{nobr|NGC 6397}} in his 1751–1752 catalogue.The label M before a number refers to Charles {{underline|M}}essier's catalogue, while NGC is from the New General Catalogue by John Dreyer. The low resolution of early telescopes prevented individual stars in a cluster from being visually separated until Charles Messier observed M 4 in 1764.{{cite journal |last=Messier |first=Charles |author-link=Charles Messier |year=1771 |title=Catalogue des Nébuleuses & des amas d'Étoiles, que l'on découvre parmi les Étoiles fixes sur l'horizon de Paris; observées à l'Observatoire de la Marine, avec differens instruments |trans-title=Catalog of nebulas and star clusters, that one discovers among the fixed stars on the horizon of Paris; observed at the Naval Observatory, with various instruments |language=fr |journal=Histoire de l'Académie Royale des Sciences ... Avec les Mémoires de Mathématique & de Physique, pour la même Année, ... [History of the Royal Academy of Sciences ... with the Mathematical and Physical Memoirs, for the same year, ...] |pages=435–461 |url=https://gallica.bnf.fr/ark:/12148/bpt6k35697/f613.image}}{{efn|

From page 437: Le 8 Mai 1764, j'ai découvert une nébuleuse ... de 25^d 55′ 40″ méridionale.

"On 8 May 1764, I discovered a nebula near Antares, and on its parallel; it is a [source of] light which has little extension, which is dim, and which is seen with difficulty; by using a good telescope to see it, one perceives very small stars in it. Its right ascension was determined to be 242° 16′ 56″, and its declination, 25° 55′ 40″ south."{{rp|style=ama|page= 437}}

}}{{cite book |last=Boyd |first=Richard N. |year=2008 |title=An Introduction to Nuclear Astrophysics |publisher=University of Chicago Press |isbn=978-0-226-06971-5 |page=376 |url=https://books.google.com/books?id=uoIyc538X9kC}}

When William Herschel began his comprehensive survey of the sky using large telescopes in 1782, there were 34 known globular clusters. Herschel discovered another 36 and was the first to resolve virtually all of them into stars. He coined the term globular cluster in his Catalogue of a Second Thousand New Nebulae and Clusters of Stars (1789).{{cite journal |last=Herschel |first=William |author-link=William Herschel |year=1789 |title=Catalogue of a second thousand of new nebulæ and clusters of stars, with a few introductory remarks on the construction of the heavens |journal=Philosophical Transactions of the Royal Society of London |volume=79 |pages=212–255 |bibcode=1789RSPT...79..212H |url=https://babel.hathitrust.org/cgi/pt?id=pst.000008680679;view=1up;seq=248 |access-date=April 28, 2021}}{{efn|

From page 218, discussing the shapes of star clusters, Herschel wrote:

"And thus, from the above-mentioned appearances, we come to know that there are globular clusters of stars nearly equal in size, which are scattered evenly at equal distances from the middle, but with an encreasing [sic] accumulation towards the center."{{rp|style=ama|page= 218}}

}}{{cite web |last1=Frommert |first1=Hartmut |last2=Kronberg |first2=Christine |title=Globular Star Clusters |website=The Messier Catalog |publisher=Students for the Exploration and Development of Space |url=http://messier.seds.org/glob.html |access-date=June 19, 2015 |archive-url=https://web.archive.org/web/20150430163307/http://messier.seds.org/glob.html |archive-date=April 30, 2015 }} In 1914, Harlow Shapley began a series of studies of globular clusters, published across about forty scientific papers. He examined the clusters' RR Lyrae variables (stars which he assumed were Cepheid variables) and used their luminosity and period of variability to estimate the distances to the clusters. RR Lyrae variables were later found to be fainter than Cepheid variables, causing Shapley to overestimate the distances.{{cite book |last1=Ashman |first1=Keith M. |author1-link=Keith M. Ashman |last2=Zepf |first2=Stephen E. |year=1998 |title=Globular Cluster Systems |series=Cambridge Astrophysics Series |volume=30 |page=2 |publisher=Cambridge, UK University Press |isbn=978-0-521-55057-4 |url=https://books.google.com/books?id=sXwXfSH6g90C}}

File:NGC 7006 (HST).jpg is a highly concentrated, Class I globular cluster.]]

A large majority of the Milky Way's globular clusters are found in the halo around the galactic core. In 1918, Shapley used this strongly asymmetrical distribution to determine the overall dimensions of the galaxy. Assuming a roughly spherical distribution of globular clusters around the galaxy's center, he used the positions of the clusters to estimate the position of the Sun relative to the Galactic Center.{{cite journal |last=Shapley |first=Harlow |author-link=Harlow Shapley |year=1918 |title=Globular clusters and the structure of the galactic system |journal=Publications of the Astronomical Society of the Pacific |volume=30 |issue=173 |pages=42–54 |bibcode=1918PASP...30...42S |doi=10.1086/122686 |doi-access=free }} He correctly concluded that the Milky Way's center is in the Sagittarius constellation and not near the Earth. He overestimated the distance, finding typical globular cluster distances of {{convert|10-30|kpc|ly}};{{cite journal |last=Trimble |first=V.L. |author-link=Virginia Louise Trimble |date=December 1995 |title=The 1920 Shapley-Curtis Discussion: Background, issues, and aftermath |journal=Publications of the Astronomical Society of the Pacific |volume=107 |page=1133 |doi=10.1086/133671|bibcode=1995PASP..107.1133T |s2cid=122365368 |url=https://escholarship.org/uc/item/1q68k7m0 }} the modern distance to the Galactic Center is roughly {{convert|8.5|kpc|ly}}.{{efn|

Harlow Shapley's error was aggravated by interstellar dust in the Milky Way, which absorbs and diminishes the amount of light from distant objects (such as globular clusters), thus making them appear to be farther away.

}}{{cite book |last1=Bennett |first1=Jeffrey O. |last2=Donahue |first2=Megan |last3=Schneider |first3=Nicholas |last4=Voit |first4=Mark |year=2020 |title=The Cosmic Perspective |publisher=Pearson |isbn=978-0-134-87436-4 |edition=9th}}{{cite book |last1=Zeilik |first1=Michael |last2=Gregory |first2=Stephen A |title=Introductory Astronomy & Astrophysics |year=1998 |publisher=Brooks/Cole, Cengage Learning |location=Belmont Drive, CA |isbn=978-0-03-006228-5 |page=277 |edition=4th}}{{cite book |last1=Ryden |first1=Barbara Sue |last2=Peterson |first2=Bradley M. |year=2010 |title=Foundations of Astrophysics |location=San Francisco, CA |isbn=978-0-321-59558-4 |page=436}} Shapley's measurements indicated the Sun is relatively far from the center of the galaxy, contrary to what had been inferred from the observed uniform distribution of ordinary stars. In reality most ordinary stars lie within the galaxy's disk and are thus obscured by gas and dust in the disk, whereas globular clusters lie outside the disk and can be seen at much greater distances.File:A Swarm of Ancient Stars - GPN-2000-000930.jpg globular cluster in the constellation Scorpius is located about 30,000 light-years from the Sun and contains hundreds of thousands of stars.{{cite web |title=Hubble images a swarm of ancient stars |url=https://esahubble.org/images/opo9926a/ |publisher=European Space Agency (ESA) |access-date=August 23, 2021}}]]

The count of known globular clusters in the Milky Way has continued to increase, reaching 83 in 1915, 93 in 1930, 97 by 1947, and 157 in 2010.{{cite web |last=Frommert |first=Hartmut |date=August 2007 |title=Milky Way Globular Clusters |publisher=Students for the Exploration and Development of Space | url=http://spider.seds.org/spider/MWGC/mwgc.html |access-date=February 26, 2008 }}{{cite book |last=Carroll |first=Bradley W. |year=2017 |title=An introduction to modern astrophysics |publisher=Cambridge University Press |location=Cambridge, United Kingdom |isbn=978-1-108-42216-1 |page=894 |edition=2nd |url=https://books.google.com/books?id=PY0wDwAAQBAJ&pg=PA894 |access-date=September 24, 2021}} The number of known globular clusters in the Milky Way reached 158 by the end of 2010, according to the European Southern Observatory, before two new globular clusters were discovered as part of the ESO’s VISTA (Visible and Infrared Survey Telescope for Astronomy) infrared survey, known as Variables in the Vía Láctea (VVV) survey, bringing the total to 160 known globular clusters.{{Cite web |last=information@eso.org |title=VISTA Finds New Globular Star Clusters - and sees right through the heart of the Milky Way |url=https://www.eso.org/public/news/eso1141/ |access-date=2025-02-09 |website=www.eso.org |language=en}} The two discovered by VISTA in 2011 are named VVV CL001 and VVV CL002.{{Cite journal |last=Minniti |first=D. |last2=Hempel |first2=M. |last3=Toledo |first3=I. |last4=Ivanov |first4=V. D. |last5=Alonso-García |first5=J. |last6=Saito |first6=R. K. |last7=Catelan |first7=M. |last8=Geisler |first8=D. |last9=Jordán |first9=A. |last10=Borissova |first10=J. |last11=Zoccali |first11=M. |last12=Kurtev |first12=R. |last13=Carraro |first13=G. |last14=Barbuy |first14=B. |last15=Clariá |first15=J. |date=2011-03-01 |title=Discovery of VVV CL001 - A low-mass globular cluster next to UKS 1 in the direction of the Galactic bulge |url=https://www.aanda.org/articles/aa/full_html/2011/03/aa15795-10/aa15795-10.html |journal=Astronomy & Astrophysics |language=en |volume=527 |pages=A81 |doi=10.1051/0004-6361/201015795 |issn=0004-6361|arxiv=1012.2450 }}{{Cite journal |last=Bidin |first=C. Moni |last2=Mauro |first2=F. |last3=Geisler |first3=D. |last4=Minniti |first4=D. |last5=Catelan |first5=M. |last6=Hempel |first6=M. |last7=Valenti |first7=E. |last8=Valcarce |first8=A. a. R. |last9=Alonso-García |first9=J. |last10=Borissova |first10=J. |last11=Carraro |first11=G. |last12=Lucas |first12=P. |last13=Chené |first13=A.-N. |last14=Zoccali |first14=M. |last15=Kurtev |first15=R. G. |date=2011-11-01 |title=Three Galactic globular cluster candidates |url=https://www.aanda.org/articles/aa/abs/2011/11/aa17488-11/aa17488-11.html |journal=Astronomy & Astrophysics |language=en |volume=535 |pages=A33 |doi=10.1051/0004-6361/201117488 |issn=0004-6361|arxiv=1109.1854 }}

Additional, undiscovered globular clusters are believed to be in the galactic bulge{{cite journal |last1=Camargo |first1=D. |last2=Minniti |first2=D. |year=2019 |title=Three candidate globular clusters discovered in the Galactic bulge |journal=Monthly Notices of the Royal Astronomical Society: Letters |volume=484 |pages=L90–L94 |arxiv=1901.08574 |doi=10.1093/mnrasl/slz010|doi-access=free }} or hidden by the gas and dust of the Milky Way.{{cite journal |last1=Ashman |first1=Keith M. |author-link1=Keith M. Ashman |last2=Zepf |first2=Stephen E. |year=1992 |title=The formation of globular clusters in merging and interacting galaxies, Part 1 |journal=Astrophysical Journal |volume=384 |pages=50–61 |bibcode=1992ApJ...384...50A |doi=10.1086/170850 }} For example, most of the Palomar Globular Clusters have only been discovered in the 1950s, with some located relatively close-by yet obscured by dust, while others reside in the very far reaches of the Milky Way halo. The Andromeda Galaxy, which is comparable in size to the Milky Way, may have as many as five hundred globulars.{{cite journal |last1=Barmby |first1=P. |author-link1=Pauline Barmby |last2=Huchra |first2=J.P. |author-link2=John Huchra |title=M31 globular clusters in the Hubble Space Telescope Archive. I. Cluster detection and completeleness |journal=The Astronomical Journal |year=2001 |volume=122 |issue=5 |pages=2458–2468 |doi = 10.1086/323457 | bibcode=2001AJ....122.2458B|arxiv = astro-ph/0107401 |s2cid=117895577 }} Every galaxy of sufficient mass in the Local Group has an associated system of globular clusters, as does almost every large galaxy surveyed.{{cite journal | last = Harris | first = William E. | year=1991 | title=Globular cluster systems in galaxies beyond the Local Group | journal=Annual Review of Astronomy and Astrophysics | volume=29 | issue = 1 | pages=543–579 | bibcode=1991ARA&A..29..543H | doi=10.1146/annurev.aa.29.090191.002551 }} Some giant elliptical galaxies (particularly those at the centers of galaxy clusters), such as M 87, have as many as 13,000 globular clusters.{{cite journal |author1=McLaughlin, Dean E. |author2=Harris, William E. |author3=Hanes, David A. | year=1994 | title=The spatial structure of the M87 globular cluster system | journal=Astrophysical Journal | volume=422 | issue=2 | pages=486–507 | bibcode=1994ApJ...422..486M | doi=10.1086/173744 }}

{{Main|Shapley–Sawyer Concentration Class}}

Shapley was later assisted in his studies of clusters by Henrietta Swope and Helen Sawyer Hogg. In 1927–1929, Shapley and Sawyer categorized clusters by the degree of concentration of stars toward each core. Their system, known as the Shapley–Sawyer Concentration Class, identifies the most concentrated clusters as Class I and ranges to the most diffuse Class XII.The Concentration Class is sometimes given with Arabic numerals (Classes 1–12) rather than Roman numerals.{{cite journal |last=Hogg |first=Helen Battles Sawyer |year=1965 |title=Harlow Shapley and globular glusters |journal=Publications of the Astronomical Society of the Pacific |volume=77 |issue=458 |pages=336–346 |bibcode=1965PASP...77..336S |doi=10.1086/128229 |doi-access=free }} Astronomers from the Pontifical Catholic University of Chile proposed a new type of globular cluster on the basis of observational data in 2015: Dark globular clusters.{{cite news |title=The Very Large Telescope discovers new kind of globular star cluster |date=May 13, 2015 |magazine=Astronomy |url=http://www.astronomy.com/news/2015/05/the-very-large-telescope-discovers-new-kind-of-globular-star-cluster |access-date=May 14, 2015 }}

{{clear}}

File:NGC 2808 HST.jpg contains three distinct generations of stars.{{cite journal |last1=Piotto |first1=G. |last2=Bedin |first2=L. R. |last3=Anderson |first3=J. |last4=King |first4=I. R. |last5=Cassisi |first5=S. |last6=Milone |first6=A.P. |last7=Villanova |first7=S. |last8=Pietrinferni |first8=A. |last9=Renzini |first9=A. | title=A Triple Main Sequence in the Globular Cluster NGC 2808

| journal=The Astrophysical Journal | volume=661| issue=1

| pages=L53–L56 |date=May 2007

| doi=10.1086/518503 | bibcode=2007ApJ...661L..53P |arxiv = astro-ph/0703767 |s2cid=119376556 }}
NASA image]]

The formation of globular clusters is poorly understood.{{cite journal |last1=Gratton |first1=Raffaele |last2=Bragaglia |first2=Angela |last3=Carretta |first3=Eugenio |last4=D'Orazi |first4=Valentina |last5=Lucatello |first5=Sara |last6=Sollima |first6=Antonio |title=What is a globular cluster? An observational perspective |journal=The Astronomy and Astrophysics Review |date=2019 |volume=27 |issue=1 |page=8 |doi=10.1007/s00159-019-0119-3 |bibcode=2019A&ARv..27....8G | arxiv=1911.02835|s2cid=207847491 }} Globular clusters have traditionally been described as a simple star population formed from a single giant molecular cloud, and thus with roughly uniform age and metallicity (proportion of heavy elements in their composition). Modern observations show that nearly all globular clusters contain multiple populations;{{cite journal |last1=Bastian |first1=Nate |last2=Lardo |first2=Carmela |title=Multiple Stellar Populations in Globular Clusters |journal=Annual Review of Astronomy and Astrophysics |date=September 14, 2018 |volume=56 |issue=1 |pages=83–136 |doi=10.1146/annurev-astro-081817-051839 |bibcode=2018ARA&A..56...83B|arxiv=1712.01286 |s2cid=59144325 }} the globular clusters in the Large Magellanic Cloud (LMC) exhibit a bimodal population, for example. During their youth, these LMC clusters may have encountered giant molecular clouds that triggered a second round of star formation.{{cite conference | last=Piotto | first=Giampaolo |date=June 2009 | title=Observations of multiple populations in star clusters | work=The Ages of Stars, Proceedings of the International Astronomical Union, IAU Symposium | volume=258 | pages=233–244 | doi=10.1017/S1743921309031883 | bibcode=2009IAUS..258..233P | arxiv=0902.1422}} This star-forming period is relatively brief, compared with the age of many globular clusters.{{cite news |author1=Weaver, D. |author2=Villard, R. |author3=Christensen, L. L. |author4=Piotto, G. |author5=Bedin, L. | title=Hubble Finds Multiple Stellar 'Baby Booms' in a Globular Cluster | publisher=Hubble News Desk | date=May 2, 2007 | url=http://hubblesite.org/newscenter/archive/releases/2007/18/full/ | access-date=May 1, 2007 }} It has been proposed that this multiplicity in stellar populations could have a dynamical origin. In the Antennae Galaxy, for example, the Hubble Space Telescope has observed clusters of clusters{{snd}}regions in the galaxy that span hundreds of parsecs, in which many of the clusters will eventually collide and merge. Their overall range of ages and (possibly) metallicities could lead to clusters with a bimodal, or even multimodal, distribution of populations.{{cite journal |author1=Amaro-Seoane, P. |author2=Konstantinidis, S. |author3=Brem, P. |author4=Catelan, M. | title=Mergers of multimetallic globular clusters: the role of dynamics | journal=Monthly Notices of the Royal Astronomical Society | date=2013 | volume=435 | issue=1 | pages=809–821 | bibcode=2013MNRAS.435..809A | doi=10.1093/mnras/stt1351 |doi-access=free |arxiv = 1108.5173 |s2cid=54177579 }}

File:The globular star cluster Messier 54.jpg{{cite press release |last1=Mucciarelli |first1=Alessio |last2=Christensen |first2=Lars Lindberg |title=This Star Cluster Is Not What It Seems|url=http://www.eso.org/public/news/eso1428/|publisher=European Southern Observatory|access-date=April 7, 2021 | date=September 10, 2014 | id=eso1428}}]]

Observations of globular clusters show that their stars primarily come from regions of more efficient star formation, and from where the interstellar medium is at a higher density, as compared to normal star-forming regions. Globular cluster formation is prevalent in starburst regions and in interacting galaxies.{{cite journal |author1=Elmegreen, B. G. |author2=Efremov, Y. N. | title=A Universal Formation Mechanism for Open and Globular Clusters in Turbulent Gas | journal=Astrophysical Journal | date=1999 | volume=480 | issue=2 | pages=235–245 | bibcode=1997ApJ...480..235E | doi=10.1086/303966 | doi-access=free }} Some globular clusters likely formed in dwarf galaxies and were removed by tidal forces to join the Milky Way.{{cite journal|last=Lotz|first=Jennifer M.|author-link=Jennifer Lotz|author2=Miller, Bryan W.|author3=Ferguson, Henry C.|date=September 2004|title=The Colors of Dwarf Elliptical Galaxy Globular Cluster Systems, Nuclei, and Stellar Halos|journal=The Astrophysical Journal|volume=613|issue=1|pages=262–278|arxiv=astro-ph/0406002|bibcode=2004ApJ...613..262L|doi=10.1086/422871|s2cid=10800774}} In elliptical and lenticular galaxies there is a correlation between the mass of the supermassive black holes (SMBHs) at their centers and the extent of their globular cluster systems. The mass of the SMBH in such a galaxy is often close to the combined mass of the galaxy's globular clusters.{{cite journal |author1=Burkert, Andreas |author2=Tremaine, Scott | title=A correlation between central supermassive black holes and the globular cluster systems of early-type galaxies

| date=April 1, 2010 | quote=A possible explanation is that both large black-hole masses and large globular cluster populations are associated with recent major mergers.

| arxiv=1004.0137 | doi=10.1088/0004-637X/720/1/516 | volume=720 |issue=1 | journal=The Astrophysical Journal | pages=516–521 | bibcode=2010ApJ...720..516B|s2cid=118632899 }}

No known globular clusters display active star formation, consistent with the hypothesis that globular clusters are typically the oldest objects in their galaxy and were among the first collections of stars to form. Very large regions of star formation known as super star clusters, such as Westerlund 1 in the Milky Way, may be the precursors of globular clusters.{{cite press release

|title=Young and Exotic Stellar Zoo: ESO's Telescopes Uncover Super Star Cluster in the Milky Way |last1=Negueruela |first1=Ignacio |last2=Clark |first2=Simon

|date=March 22, 2005

|publisher=European Southern Observatory

|url=https://www.eso.org/public/news/eso0510/

|access-date=April 7, 2021

|url-status=live

|archive-url=https://web.archive.org/web/20070409105105/http://eso.org/outreach/press-rel/pr-2005/pr-08-05.html

|archive-date=April 9, 2007 |id=eso0510

}}

Many of the Milky Way's globular clusters have a retrograde orbit (meaning that they revolve around the galaxy in the reverse of the direction the galaxy is rotating),{{cite journal

| first=V. V.

| last=Kravtsov

| title=Globular Clusters and Dwarf Spheroidal Galaxies of the Outer Galactic Halo: on the Putative Scenario of their Formation

| journal=Astronomical and Astrophysical Transactions

| volume=20

| issue=1

| pages=89–92

| doi=10.1080/10556790108208191

| bibcode=2001A&AT...20...89K

| date=2001

}} including the most massive, Omega Centauri. Its retrograde orbit suggests it may be a remnant of a dwarf galaxy captured by the Milky Way.{{cite journal |last1=Bekki |first1=K. |last2=Freeman |first2=K. C. |title=Formation of ω Centauri from an ancient nucleated dwarf galaxy in the young Galactic disc: Formation of ω Centauri |journal=Monthly Notices of the Royal Astronomical Society |date=2003 |volume=346 |issue=2 |pages=L11–L15 |doi=10.1046/j.1365-2966.2003.07275.x|arxiv=astro-ph/0310348|bibcode=2003MNRAS.346L..11B |doi-access=free }}{{cite journal |doi=10.3847/1538-3881/ab8819 |title=The Most Metal-poor Stars in Omega Centauri (NGC 5139) |year=2020 |last1=Johnson |first1=Christian I. |last2=Dupree |first2=Andrea K. |last3=Mateo |first3=Mario |last4=Bailey |first4=John I. |last5=Olszewski |first5=Edward W. |last6=Walker |first6=Matthew G. |journal=The Astronomical Journal |volume=159 |issue=6 |page=254 |arxiv=2004.09023 |bibcode=2020AJ....159..254J |s2cid=215827658 |doi-access=free }}

File:Djorgovski 1.jpg's stars contain hydrogen and helium, but not much else. In astronomical terms they are metal-poor.{{cite web |publisher=European Space Agency (ESA) |title=Engulfed by Stars Near the Milky Way's Heart |url=http://www.spacetelescope.org/images/potw1126a/ |access-date=June 28, 2011 }}]]

Globular clusters are generally composed of hundreds of thousands of low-metal, old stars. The stars found in a globular cluster are similar to those in the bulge of a spiral galaxy but confined to a spheroid in which half the light is emitted within a radius of only a few to a few tens of parsecs. They are free of gas and dust,{{cite journal |last1=Bastian |first1=N. |last2=Strader |first2=J. |title=Constraining globular cluster formation through studies of young massive clusters – III. A lack of gas and dust in massive stellar clusters in the LMC and SMC |journal=Monthly Notices of the Royal Astronomical Society |date=October 1, 2014 |volume=443 |issue=4 |pages=3594–3600 |doi=10.1093/mnras/stu1407|doi-access=free |arxiv=1407.2726 }} and it is presumed that all the gas and dust was long ago either turned into stars or blown out of the cluster by the massive first-generation stars.

Globular clusters can contain a high density of stars; on average about 0.4{{spaces}}stars per cubic parsec, increasing to 100 or 1000{{spaces}}stars/pc{{Sup|3}} in the core of the cluster.{{cite web |last=Talpur |first=Jon |year=1997 |url=http://www.astro.keele.ac.uk/workx/globulars/globulars.html |title=A Guide to Globular Clusters |publisher=Keele University |access-date=April 25, 2007 | archive-url=https://web.archive.org/web/20210404045753/https://www.astro.keele.ac.uk/workx/globulars/globulars.html | archive-date=April 4, 2021 | url-status=live }} In comparison, the stellar density around the Sun is roughly 0.1 stars/pc{{Sup|3}}.{{cite web |last1=Mamajek |first1=Eric |title=Number Densities of Stars of Different Types in the Solar Vicinity |url=http://www.pas.rochester.edu/~emamajek/memo_star_dens.html |department=Department of Physics and Astronomy |publisher=University of Rochester |access-date=September 5, 2021}} The typical distance between stars in a globular cluster is about one light year,{{cite web |url=http://www.dur.ac.uk/ian.smail/gcCm/gcCm_intro.html |last=Smail|first=Ian| access-date=September 5, 2021 |publisher=University of Durham |department=Department of Physics |title=The Hertzsprung-Russell Diagram of a Globular Cluster}} but at its core the separation between stars averages about a third of a light year{{snd}}thirteen times closer than the Sun is to its nearest neighbor, Proxima Centauri.{{cite web |url=https://www.nasa.gov/mission_pages/hubble/multimedia/ero/ero_omega_centauri.html |publisher=NASA |date=September 9, 2009 |title=Colorful Stars Galore Inside Globular Star Cluster Omega Centauri |access-date=April 28, 2021 |archive-date=January 26, 2021 |archive-url=https://web.archive.org/web/20210126021258/https://www.nasa.gov/mission_pages/hubble/multimedia/ero/ero_omega_centauri.html |url-status=dead }}

Globular clusters are thought to be unfavorable locations for planetary systems. Planetary orbits are dynamically unstable within the cores of dense clusters because of the gravitational perturbations of passing stars. A planet orbiting at one astronomical unit around a star that is within the core of a dense cluster, such as 47 Tucanae, would survive only on the order of a hundred million years.{{cite journal |last=Sigurdsson |first=Steinn |title=Planets in globular clusters? |journal=Astrophysical Journal |year=1992 |volume=399 |issue=1 |pages=L95–L97 |bibcode=1992ApJ...399L..95S |doi=10.1086/186615}} There is a planetary system orbiting a pulsar (PSR{{spaces}}B1620−26) that belongs to the globular cluster M4, but these planets likely formed after the event that created the pulsar.{{cite journal |title=Orbital Parameters of the PSR B1620-26 Triple System |journal=Proceedings of the 160th Colloquium of the International Astronomical Union |year=1999 |volume=105 |bibcode=1996ASPC..105..525A |arxiv=astro-ph/9605141 |author1=Arzoumanian, Z. |author2=Joshi, K. |author3=Rasio, F. A. |author4=Thorsett, S.E. |page=525 }}

Some globular clusters, like Omega Centauri in the Milky Way and Mayall II in the Andromeda Galaxy, are extraordinarily massive, measuring several million solar masses ({{Solar mass}}) and having multiple stellar populations. Both are evidence that supermassive globular clusters formed from the cores of dwarf galaxies that have been consumed by larger galaxies.{{cite journal |author1=Bekki, K. |author2=Freeman, K.C. |author-link2=Ken Freeman (astronomer) |title=Formation of ω Centauri from an ancient nucleated dwarf galaxy in the young Galactic disc |journal=Monthly Notices of the Royal Astronomical Society |volume=346 |issue=2 |pages=L11–L15 |date=December 2003 |doi=10.1046/j.1365-2966.2003.07275.x| arxiv=astro-ph/0310348 |bibcode=2003MNRAS.346L..11B |s2cid=119466098 }} About a quarter of the globular cluster population in the Milky Way may have been accreted this way,{{cite journal |author1=Forbes, Duncan A. |author2=Bridges, Terry |title=Accreted versus in situ Milky Way globular clusters |date=January 25, 2010 |arxiv=1001.4289 |doi=10.1111/j.1365-2966.2010.16373.x |journal=Monthly Notices of the Royal Astronomical Society |volume=404 |issue=3 |page=1203 |doi-access=free |bibcode=2010MNRAS.404.1203F |s2cid=51825384 }} as with more than 60% of the globular clusters in the outer halo of Andromeda.{{cite journal |last1=Forbes |first1=Duncan A. |last2=Bastian |first2=Nate |last3=Gieles |first3=Mark |last4=Crain |first4=Robert A. |last5=Kruijssen |first5=J. M. Diederik |last6=Larsen |first6=Søren S. |last7=Ploeckinger |first7=Sylvia |last8=Agertz |first8=Oscar |last9=Trenti |first9=Michele |last10=Ferguson |first10=Annette M. N. |last11=Pfeffer |first11=Joel |last12=Gnedin |first12=Oleg Y. |title=Globular cluster formation and evolution in the context of cosmological galaxy assembly: open questions |journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=February 2018 |volume=474 |issue=2210 |page=20170616 |doi=10.1098/rspa.2017.0616|pmid=29507511 |pmc=5832832 |arxiv=1801.05818 |bibcode=2018RSPSA.47470616F |doi-access=free }}

Globular clusters normally consist of Population II stars which, compared with Population I stars such as the Sun, have a higher proportion of hydrogen and helium and a lower proportion of heavier elements. Astronomers refer to these heavier elements as metals (distinct from the material concept) and to the proportions of these elements as the metallicity. Produced by stellar nucleosynthesis, the metals are recycled into the interstellar medium and enter a new generation of stars. The proportion of metals can thus be an indication of the age of a star in simple models, with older stars typically having a lower metallicity.{{cite book |title=An Introduction to the Sun and Stars |page=240 |publisher=Cambridge University Press |year=2004 |isbn=978-0-521-54622-5 |author1=Green, Simon F. |author2=Jones, Mark H. |author3=Burnell, S. Jocelyn}}

The Dutch astronomer Pieter Oosterhoff observed two special populations of globular clusters, which became known as Oosterhoff groups. The second group has a slightly longer period of RR Lyrae variable stars.{{cite journal |title=On the Two Oosterhoff Groups of Globular Clusters |journal=Astrophysical Journal |volume=185 |year=1973 |pages=477–498 |doi=10.1086/152434 |author1=van Albada, T. S. |author2=Baker, Norman |bibcode=1973ApJ...185..477V}} While both groups have a low proportion of metallic elements as measured by spectroscopy, the metal spectral lines in the stars of Oosterhoff type{{spaces}}I (Oo{{spaces}}I) cluster are not quite as weak as those in type{{spaces}}II (Oo{{spaces}}II), and so type{{spaces}}I stars are referred to as metal-rich (e.g. Terzan 7{{cite journal |title=ESO 280-SC06 |journal=Astronomical Journal |volume=109 |page=663 |year=1995 |author1=Buonanno, R. |author2=Corsi, C.E. |author3=Pulone, L. |bibcode=1995AJ....109..663B |doi=10.1086/117309}}), while type{{spaces}}II stars are metal-poor (e.g. ESO 280-SC06{{cite web |last=Frommert |first=Hartmut | title=Globular cluster ESO 280-S C06, in Ara | website=Students for the Exploration and Development of Space |url=http://spider.seds.org/spider/MWGC/eso280sc06.html |access-date=April 9, 2021 }}). These two distinct populations have been observed in many galaxies, especially massive elliptical galaxies. Both groups are nearly as old as the universe itself and are of similar ages. Suggested scenarios to explain these subpopulations include violent gas-rich galaxy mergers, the accretion of dwarf galaxies, and multiple phases of star formation in a single galaxy. In the Milky Way, the metal-poor clusters are associated with the halo and the metal-rich clusters with the bulge.{{cite journal |last=Harris |first=W.E. |title=Spatial structure of the globular cluster system and the distance to the galactic center |journal=Astronomical Journal |year=1976 |volume=81 |pages=1095–1116 |bibcode=1976AJ.....81.1095H |doi=10.1086/111991}}

A large majority of the metal-poor clusters in the Milky Way are aligned on a plane in the outer part of the galaxy's halo. This observation supports the view that type{{spaces}}II clusters were captured from a satellite galaxy, rather than being the oldest members of the Milky Way's globular cluster system as was previously thought. The difference between the two cluster types would then be explained by a time delay between when the two galaxies formed their cluster systems.{{cite journal |author1=Lee, Y.W. |author2=Yoon, S.J. | title=On the Construction of the Heavens |journal=An Aligned Stream of Low-Metallicity Clusters in the Halo of the Milky Way |volume=297 |year=2002 |pages=578–581 |bibcode=2002Sci...297..578Y |doi=10.1126/science.1073090 |pmid=12142530 |issue=5581 |arxiv=astro-ph/0207607|s2cid=9702759 }}

File:Messier 53 HST.jpg contains an unusually large number of a type of star called blue stragglers.{{cite web |title=Spot the Difference – Hubble spies another globular cluster, but with a secret |url=http://spacetelescope.org/images/potw1140a/ |work=Picture of the Week |publisher=ESA/Hubble |access-date=October 5, 2011}}{{cite web |title=APOD: 2021 February 7 – Blue Straggler Stars in Globular Cluster M53 |url=https://apod.nasa.gov/apod/ap210207.html |website=Astronomy Picture of the Day |access-date=February 28, 2021}}]]

Close interactions and near-collisions of stars occur relatively often in globular clusters because of their high star density. These chance encounters give rise to some exotic classes of stars{{snd}}such as blue stragglers, millisecond pulsars, and low-mass X-ray binaries{{snd}}which are much more common in globular clusters. How blue stragglers form remains unclear, but most models attribute them to interactions between stars, such as stellar mergers, the transfer of material from one star to another, or even an encounter between two binary systems.{{cite journal

| author=Leonard, Peter J. T. | date= 1989

| title=Stellar collisions in globular clusters and the blue straggler problem

| journal=The Astronomical Journal | volume=98

| pages=217–226 | doi=10.1086/115138

| bibcode=1989AJ.....98..217L }}{{cite journal|last1=Ferraro|first1=F. R.|last2=Lanzoni|first2=B.|last3=Raso|first3=S.|last4=Nardiello|first4=D.|last5=Dalessandro|first5=E.|last6=Vesperini|first6=E.|last7=Piotto|first7=G.|last8=Pallanca|first8=C.|last9=Beccari|first9=G.|last10=Bellini|first10=A.|last11=Libralato|first11=M.|date=June 8, 2018|title=The Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters. XV. The Dynamical Clock: Reading Cluster Dynamical Evolution from the Segregation Level of Blue Straggler Stars|journal=The Astrophysical Journal|volume=860|issue=1|page=36|arxiv=1805.00968|bibcode=2018ApJ...860...36F|doi=10.3847/1538-4357/aac01c|first15=S.|last15=Cassisi|last12=Anderson|first12=J.|first13=A.|last14=Bedin|first14=L. R.|first20=R. P.|last16=Milone|last20=van der Marel|first19=M.|last19=Salaris|first18=A.|last18=Renzini|first17=S.|last17=Ortolani|first16=A. P.|last13=Aparicio|s2cid=119435307 |doi-access=free }} The resulting star has a higher temperature than other stars in the cluster with comparable luminosity and thus differs from the main-sequence stars formed early in the cluster's existence.{{cite journal |author1=Rubin, V.C. |author2=Ford, W.K.J. |author-link1=Vera Rubin |title=A Thousand Blazing Suns: The Inner Life of Globular Clusters |journal=Mercury |year=1999 |volume=28 |issue=4 |page=26 |url=http://www.astrosociety.org/pubs/mercury/9904/murphy.html |access-date=June 2, 2006 |bibcode=1999Mercu..28d..26M |archive-date=May 21, 2006 |archive-url=https://web.archive.org/web/20060521044631/http://www.astrosociety.org/pubs/mercury/9904/murphy.html }} Some clusters have two distinct sequences of blue stragglers, one bluer than the other.

File:STSci-2002-18.jpg at its core,{{cite press release |title=Hubble Discovers Black Holes in Unexpected Places |url=https://hubblesite.org/contents/news-releases/2002/news-2002-18.html |publisher=Space Telescope Science Institute |language=en | id=2002-18 | date=September 17, 2002}} but this claim is contested.]]

File:STScI-01H0MY22SC4HPS3SYE78B4EZ4F AdobeExpress.gif, where astronomers suspect that an intermediate-mass black hole could be present.{{cite journal|last=Vitral|first=E.|display-authors=etal|title=An elusive dark central mass in the globular cluster M4|journal=Monthly Notices of the Royal Astronomical Society|date=2023|volume=522|issue=4 |pages=5740–5757|doi=10.1093/mnras/stad1068|doi-access=free |arxiv =2305.12702 |bibcode = 2023MNRAS.522.5740V }}{{cite news |date=23 May 2023|title=NASA's Hubble Hunts for Intermediate-Sized Black Hole Close to Home | url=https://www.nasa.gov/feature/goddard/2023/nasas-hubble-hunts-for-intermediate-sized-black-hole-close-to-home/ |work=NASA|access-date=23 May 2023}} If confirmed, the black hole would be in the center of the cluster, and would have a sphere of influence (black hole) limited by the red circle.]]

Astronomers have searched for black holes within globular clusters since the 1970s. The required resolution for this task is exacting; it is only with the Hubble Space Telescope (HST) that the first claimed discoveries were made, in 2002 and 2003. Based on HST observations, other researchers suggested the existence of a {{Solar mass|4,000}}(solar masses) intermediate-mass black hole in the globular cluster M15 and a {{Solar mass|20,000}} black hole in the Mayall II cluster of the Andromeda Galaxy.{{cite news|author1=Savage, D.|author2=Neal, N.|author3=Villard, R.|author4=Johnson, R.|author5=Lebo, H.|date=September 17, 2002|title=Hubble discovers black holes in unexpected places|publisher=Space Telescope Science Institute|url=http://hubblesite.org/newscenter/newsdesk/archive/releases/2002/18/text/|access-date=May 25, 2006|archive-url=https://web.archive.org/web/20031119083627/http://hubblesite.org/newscenter/newsdesk/archive/releases/2002/18/text/|archive-date=November 19, 2003}} Both X-ray and radio emissions from Mayall{{spaces}}II appear consistent with an intermediate-mass black hole;{{cite news |first=Dave |last=Finley |title=Star cluster holds midweight black hole, VLA indicates |publisher=NRAO |date=May 28, 2007 |url=http://www.nrao.edu/pr/2007/globularbh/ |access-date=May 29, 2007 }} however, these claimed detections are controversial.{{cite journal |last1=Greene |first1=Jenny E. |last2=Strader |first2=Jay |last3=Ho |first3=Luis C. |title=Intermediate-Mass Black Holes |journal=Annual Review of Astronomy and Astrophysics |date=August 18, 2020 |volume=58 |issue=1 |pages=257–312 |doi=10.1146/annurev-astro-032620-021835 |bibcode=2020ARA&A..58..257G|arxiv=1911.09678 |s2cid=208202069 }}

The heaviest objects in globular clusters are expected to migrate to the cluster center due to mass segregation. One research group pointed out that the mass-to-light ratio should rise sharply towards the center of the cluster, even without a black hole, in both M15{{cite journal |author1=Baumgardt, Holger |author2=Hut, Piet |author3=Makino, Junichiro |author4=McMillan, Steve |author5=Portegies Zwart, Simon |title=On the Central Structure of M15 |journal=Astrophysical Journal Letters |year=2003 |volume=582 |issue=1 |page=21 |bibcode=2003ApJ...582L..21B |doi=10.1086/367537 |arxiv=astro-ph/0210133|s2cid=16216186 }} and Mayall II.{{Cite journal |author1=Baumgardt, Holger |author2=Hut, Piet |author3=Makino, Junichiro |author4=McMillan, Steve |author5=Portegies Zwart, Simon | title=A dynamical model for the globular cluster G1 |journal=Astrophysical Journal Letters |year=2003 |volume=589 |issue=1 |page=25 |doi=10.1086/375802 |bibcode=2003ApJ...589L..25B |arxiv=astro-ph/0301469 |s2cid=119464795 }} Observations from 2018 find no evidence for an intermediate-mass black hole in any globular cluster, including M15, but cannot definitively rule out one with a mass of {{Solar mass|500–1000}}.{{cite journal |last1=Tremou |first1=Evangelia |last2=Strader |first2=Jay |last3=Chomiuk |first3=Laura |last4=Shishkovsky |first4=Laura |last5=Maccarone |first5=Thomas J. |last6=Miller-Jones |first6=James C. A. |last7=Tudor |first7=Vlad |last8=Heinke |first8=Craig O. |last9=Sivakoff |first9=Gregory R. |last10=Seth |first10=Anil C. |last11=Noyola |first11=Eva |title=The MAVERIC Survey: Still No Evidence for Accreting Intermediate-mass Black Holes in Globular Clusters |journal=The Astrophysical Journal |date=July 18, 2018 |volume=862 |issue=1 |page=16 |doi=10.3847/1538-4357/aac9b9 |bibcode=2018ApJ...862...16T | arxiv=1806.00259|s2cid=119367485 |doi-access=free }} Finally, in 2023, an analysis of HST and the Gaia spacecraft data from the closest globular cluster, Messier 4, revealed an excess mass of roughly {{Solar mass|800}} in the center of this cluster, which appears to not be extended. This could thus be considered as kinematic evidence for an intermediate-mass black hole (even if an unusually compact cluster of compact objects like white dwarfs, neutron stars or stellar-mass black holes cannot be completely discounted).

The confirmation of intermediate-mass black holes in globular clusters would have important ramifications for theories of galaxy development as being possible sources for the supermassive black holes at their centers. The mass of these supposed intermediate-mass black holes is proportional to the mass of their surrounding clusters, following a pattern previously discovered between supermassive black holes and their surrounding galaxies.{{cite journal |bibcode=2019MNRAS.488.5340B |title=No evidence for intermediate-mass black holes in the globular clusters ω Cen and NGC 6624 |last1=Baumgardt |first1=H. |last2=He |first2=C. |last3=Sweet |first3=S. M. |last4=Drinkwater |first4=M. |last5=Sollima |first5=A. |last6=Hurley |first6=J. |last7=Usher |first7=C. |last8=Kamann |first8=S. |last9=Dalgleish |first9=H. |last10=Dreizler |first10=S. |last11=Husser |first11=T. -O. |journal=Monthly Notices of the Royal Astronomical Society |year=2019 |volume=488 |issue=4 |page=5340 |doi=10.1093/mnras/stz2060 |doi-access=free |arxiv=1907.10845 }}

File:M3 color magnitude diagram.jpg. There is a characteristic "knee" in the curve at magnitude 19 where stars begin entering the giant stage of their evolutionary path, the main-sequence turnoff.]]

Hertzsprung–Russell diagrams (H–R diagrams) of globular clusters allow astronomers to determine many of the properties of their populations of stars. An H–R diagram is a graph of a large sample of stars plotting their absolute magnitude (their luminosity, or brightness measured from a standard distance), as a function of their color index. The color index, roughly speaking, measures the color of the star; positive color indices indicate a reddish star with a cool surface temperature, while negative values indicate a bluer star with a hotter surface. Stars on an H–R diagram mostly lie along a roughly diagonal line sloping from hot, luminous stars in the upper left to cool, faint stars in the lower right. This line is known as the main sequence and represents the primary stage of stellar evolution. The diagram also includes stars in later evolutionary stages such as the cool but luminous red giants.{{cite journal |last1=Woodrow |first1=Janice |title=The Hertzsprung-Russell Diagram: Explaining a difficult concept |journal=The Science Teacher |date=1991 |volume=58 |issue=8 |pages=52–57 |jstor=24146262 |issn=0036-8555}}

Constructing an H–R diagram requires knowing the distance to the observed stars to convert apparent into absolute magnitude. Because all the stars in a globular cluster have about the same distance from Earth, a color–magnitude diagram using their observed magnitudes looks like a shifted H–R diagram (because of the roughly constant difference between their apparent and absolute magnitudes).{{cite book |last1=Carroll |first1=Bradley W. |last2=Ostlie |first2=Dale A. |title=An Introduction to Modern Astrophysics |date=2017 |location=Cambridge, United Kingdom |isbn=978-1-108-42216-1 |pages=475–476 |edition=Second}} This shift is called the distance modulus and can be used to calculate the distance to the cluster. The modulus is determined by comparing features (like the main sequence) of the cluster's color–magnitude diagram to corresponding features in an H–R diagram of another set of stars, a method known as spectroscopic parallax or main-sequence fitting.{{cite book | first=Martin | last=Schwarzschild | author-link=Martin Schwarzschild | date=1958 | title=Structure and Evolution of Stars | publisher=Princeton University Press | isbn=978-0-486-61479-3 | url-access=registration | url=https://archive.org/details/StructureAndEvolutionOfTheStars }}

Since globular clusters form at once from a single giant molecular cloud, a cluster's stars have roughly the same age and composition. A star's evolution is primarily determined by its initial mass, so the positions of stars in a cluster's H–R or color–magnitude diagram mostly reflect their initial masses. A cluster's H–R diagram, therefore, appears quite different from H–R diagrams containing stars of a wide variety of ages. Almost all stars fall on a well-defined curve in globular cluster H–R diagrams, and that curve's shape indicates the age of the cluster.{{cite journal

| author=Sandage, A. R. | author-link=Allan Sandage

| title=Observational Approach to Evolution. III. Semiempirical Evolution Tracks for M67 and M3

| journal=Astrophysical Journal | volume=126

| page=326 | date=1957

| bibcode=1957ApJ...126..326S | doi=10.1086/146405 }} A more detailed H–R diagram often reveals multiple stellar populations as indicated by the presence of closely separated curves, each corresponding to a distinct population of stars with a slightly different age or composition. Observations with the Wide Field Camera 3, installed in 2009 on the Hubble Space Telescope, made it possible to distinguish these slightly different curves.{{cite journal |last1=Piotto |first1=G. |last2=Milone |first2=A. P. |last3=Bedin |first3=L. R. |last4=Anderson |first4=J. |last5=King |first5=I. R. |last6=Marino |first6=A. F. |last7=Nardiello |first7=D. |last8=Aparicio |first8=A. |last9=Barbuy |first9=B. |last10=Bellini |first10=A. |last11=Brown |first11=T. M. |last12=Cassisi |first12=S. |last13=Cool |first13=A. M. |last14=Cunial |first14=A. |last15=Dalessandro |first15=E. |last16=D'Antona |first16=F. |last17=Ferraro |first17=F. R. |last18=Hidalgo |first18=S. |last19=Lanzoni |first19=B. |last20=Monelli |first20=M. |last21=Ortolani |first21=S. |last22=Renzini |first22=A. |last23=Salaris |first23=M. |last24=Sarajedini |first24=A. |last25=Marel |first25=R. P. van der |last26=Vesperini |first26=E. |last27=Zoccali |first27=M.|author27-link=Manuela Zoccali |title=The Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters. I. Overview of the Project and Detection of Multiple Stellar Populations |journal=The Astronomical Journal |date=February 5, 2015 |volume=149 |issue=3 |page=91 |doi=10.1088/0004-6256/149/3/91|arxiv=1410.4564 |bibcode=2015AJ....149...91P |s2cid=119194870 }}

The most massive main-sequence stars have the highest luminosity and will be the first to evolve into the giant star stage. As the cluster ages, stars of successively lower masses will do the same. Therefore, the age of a single-population cluster can be measured by looking for those stars just beginning to enter the giant star stage, which form a "knee" in the H–R diagram called the main-sequence turnoff, bending to the upper right from the main-sequence line. The absolute magnitude at this bend is directly a function of the cluster's age; an age scale can be plotted on an axis parallel to the magnitude.

The morphology and luminosity of globular cluster stars in H–R diagrams are influenced by numerous parameters, many of which are still actively researched. Recent observations have overturned the historical paradigm that all globular clusters consist of stars born at exactly the same time, or sharing exactly the same chemical abundance. Some clusters feature multiple populations, slightly differing in composition and age; for example, high-precision imagery of cluster NGC 2808 discerned three close, but distinct, main sequences.{{cite journal |bibcode=2010RSPTA.368..755K |title=Star clusters as laboratories for stellar and dynamical evolution |last1=Kalirai |first1=J. S. |last2=Richer |first2=H. B. |journal=Philosophical Transactions of the Royal Society of London, Series A |year=2010 |volume=368 |issue=1913 |pages=755–82 |doi=10.1098/rsta.2009.0257 |pmid=20083505 |arxiv=0911.0789 |s2cid=5561270 |quote=Verification of the picture above came from extremely precise HST/ACS imaging observations of NGC 2808 by Piotto et al. (2007), who resolve three main sequences in the cluster for a single turnoff (see figure 3). This remarkable observation is consistent with multiple stellar populations of approximately the same age with varying helium abundances}} Further, the placements of the cluster stars in an H–R diagram (including the brightnesses of distance indicators) can be influenced by observational biases. One such effect, called blending, arises when the cores of globular clusters are so dense that observations see multiple stars as a single target. The brightness measured for that seemingly single star is thus incorrect{{snd}}too bright, given that multiple stars contributed.{{cite journal |bibcode=2012ApJ...752L..10M |title=The Impact of Contaminated RR Lyrae/Globular Cluster Photometry on the Distance Scale |last1=Majaess |first1=D. |last2=Turner |first2=D. |last3=Gieren |first3=W. |last4=Lane |first4=D. |journal=The Astrophysical Journal |year=2012 |volume=752 |issue=1 |pages=L10 |doi=10.1088/2041-8205/752/1/L10 |arxiv=1205.0255 |s2cid=118528078 }} In turn, the computed distance is incorrect, so the blending effect can introduce a systematic uncertainty into the cosmic distance ladder and may bias the estimated age of the universe and the Hubble constant.{{cite journal |bibcode=2014ApJS..210....6L |title=Toward a Better Understanding of the Distance Scale from RR Lyrae Variable Stars: A Case Study for the Inner Halo Globular Cluster NGC 6723 |last1=Lee |first1=Jae-Woo |last2=López-Morales |first2=Mercedes |last3=Hong |first3=Kyeongsoo |last4=Kang |first4=Young-Woon |last5=Pohl |first5=Brian L. |last6=Walker |first6=Alistair |journal=The Astrophysical Journal Supplement Series |year=2014 |volume=210 |issue=1 |page=6 |doi=10.1088/0067-0049/210/1/6 |arxiv=1311.2054 |s2cid=119280050 }}

The blue stragglers appear on the H–R diagram as a series diverging from the main sequence in the direction of brighter, bluer stars. White dwarfs (the final remnants of some Sun-like stars), which are much fainter and somewhat hotter than the main-sequence stars, lie on the bottom-left of an H–R diagram. Globular clusters can be dated by looking at the temperatures of the coolest white dwarfs, often giving results as old as 12.7 billion years.{{cite journal

|author1=Hansen, B. M. S. |author2=Brewer, J. |author3=Fahlman, G. G. |author4=Gibson, B. K. |author5=Ibata, R. |author6=Limongi, M. |author7=Rich, R. M. |author8=Richer, H. B. |author9=Shara, M. M. |author10=Stetson, P. B. | title=The White Dwarf Cooling Sequence of the Globular Cluster Messier 4

| date=2002 | journal=Astrophysical Journal Letters

| volume=574

| issue=2 | pages=L155

| arxiv=astro-ph/0205087 | doi=10.1086/342528 | bibcode=2002ApJ...574L.155H|s2cid=118954762 }} In comparison, open clusters are rarely older than about half a billion years.{{cite journal |last1=Soderblom |first1=David R. |title=The Ages of Stars |journal=Annual Review of Astronomy and Astrophysics |date=August 2010 |volume=48 |issue=1 |pages=581–629 |doi=10.1146/annurev-astro-081309-130806 |bibcode=2010ARA&A..48..581S |arxiv=1003.6074|s2cid=119102781 }} The ages of globular clusters place a lower bound on the age of the entire universe, presenting a significant constraint in cosmology. Astronomers were historically faced with age estimates of clusters older than their cosmological models would allow,{{cite journal |doi=10.1086/187847 |title=Absolute ages of globular clusters and the age of the universe |year=1995 |last1=Chaboyer |first1=Brian |journal=The Astrophysical Journal |volume=444 |pages=L9 |arxiv=astro-ph/9412015 |bibcode=1995ApJ...444L...9C |s2cid=2416004 }} but better measurements of cosmological parameters, through deep sky surveys and satellites, appear to have resolved this issue.{{cite journal |doi=10.1088/1475-7516/2020/12/002 |title=Inferring the age of the universe with globular clusters |year=2020 |last1=Valcin |first1=David |last2=Bernal |first2=José Luis |last3=Jimenez |first3=Raul |last4=Verde |first4=Licia |last5=Wandelt |first5=Benjamin D. |journal=Journal of Cosmology and Astroparticle Physics |volume=2020 |issue=12 |page=002 |arxiv=2007.06594 |bibcode=2020JCAP...12..002V |s2cid=220514389 }}{{cite news

|author=Majaess, D.

|date=February 23, 2013

|title=Nearby Ancient Star is Almost as Old as the Universe

|url=http://www.universetoday.com/100147/nearby-ancient-star-is-almost-as-old-as-the-universe/

|work=Universe Today

|access-date=November 29, 2014 }}

Studying globular clusters sheds light on how the composition of the formational gas and dust affects stellar evolution; the stars' evolutionary tracks vary depending on the abundance of heavy elements. Data obtained from these studies are then used to study the evolution of the Milky Way as a whole.{{cite press release |url=http://www.eso.org/public/news/eso0107/ |publisher=European Southern Observatory |date=March 2, 2001 |title=Ashes from the Elder Brethren |access-date=April 7, 2021 | id=eso0107}}

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.{{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}}{{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 }}

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.{{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

}} The relaxation time varies by cluster, but a typical value is on the order of one billion years.{{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 }}{{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}}

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 spheroids in shape, while those in the Large Magellanic Cloud are more elliptical.{{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 }}

{{anchor|core radius}}

{{redirect-distinguish|Tidal radius|Roche limit}}

File:Appearances can be deceptive.jpg is classified as an open cluster.{{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}}]]

Astronomers characterize the morphology (shape) of a globular cluster by means of standard radii: the core radius (r_c), the half-light radius (r_h), and the tidal or Jacobi radius (r_t). 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.{{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}} 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.{{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}}{{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}}

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_h = 18 pc) and Palomar 14 (r_h = 25 pc).{{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}} 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_m){{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 3 (M3), for example, has an overall visible dimension of about 18 arc minutes, but a half-mass radius of only 1.12 arc minutes.{{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

}}

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.{{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}} 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,{{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

}} or about 113 pc.{{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}}

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.{{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 }}{{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}}

File:Globular_cluster_47_Tucanae.jpg 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.{{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 }} A massive black hole at the core could also result in a luminosity cusp.{{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 }} Over a long time, this leads to a concentration of massive stars near the core, a phenomenon called mass segregation.{{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}}

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.{{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 }}{{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 }} In contrast, the effect of tidal shocks as a globular cluster repeatedly passes through the plane of a spiral galaxy tends to significantly accelerate core collapse.{{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 }}

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.{{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 }} 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.{{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 }}

File:The stars of the Large Magellanic Cloud.jpg is located in the Large Magellanic Cloud.{{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}}]]

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 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.{{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 }}

The overall luminosities of the globular clusters within the Milky Way and the Andromeda Galaxy each have a roughly Gaussian distribution, with an average magnitude M_v and a variance σ². This distribution of globular cluster luminosities is called the Globular Cluster Luminosity Function (GCLF). For the Milky Way, M_v = {{nowrap|−7.29 ± 0.13}}, σ = {{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.{{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 }}

{{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 ² (where N is the number of objects), so the computing requirements to accurately simulate a cluster of thousands of stars can be enormous.{{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 }}{{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 }} 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.{{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/

}} In 2010 a low-density globular cluster's lifetime evolution was able to be directly computed, star-by-star.{{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}}

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.{{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 }} The typical time scale for the evaporation of a globular cluster is 10¹⁰ years. The ultimate fate of a globular cluster must be either to accrete stars at its core, causing its steady contraction,{{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}} or gradual shedding of stars from its outer layers.{{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}}

Binary stars form a significant portion of stellar systems, with up to half of all field stars and open cluster stars occurring in binary systems.{{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 }}{{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 }} 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.{{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 }} 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.{{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 }}

File:Globular Cluster M10.jpg lies about 15,000 light-years from Earth, in the constellation of Ophiuchus.{{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}}]]

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.{{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}}

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.{{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 }}

The formation of these extended clusters is likely related to accretion.{{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 }} 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.

When a globular cluster comes close to a large mass, such as the core region of a galaxy, it undergoes a tidal interaction. The difference in gravitational strength between the nearer and further parts of the cluster results in an asymmetric, tidal force. A "tidal shock" occurs whenever the orbit of a cluster takes it through the plane of a galaxy.{{cite journal |last1=Ostriker |first1=Jeremiah P. |last2=Spitzer |first2=Lyman Jr. |last3=Chevalier |first3=Roger A. |date=September 1972 |title=On the Evolution of Globular Clusters |journal=Astrophysical Journal |doi=10.1086/181018 |bibcode=1972ApJ...176L..51O |volume=176 |page=L51}}

Tidal shocks can pull stars away from the cluster halo, leaving only the core part of the cluster; these trails of stars can extend several degrees away from the cluster.{{cite conference |last1=Lauchner |first1=A. |last2=Wilhelm |first2=R. |last3=Beers |first3=T. C. |last4=Allende Prieto |first4=C. |date=December 2003 |title=A Search for Kinematic Evidence of Tidal Tails in Globular Clusters |work=American Astronomical Society Meeting 203, #112.26 |bibcode=2003AAS...20311226L}} These tails typically both precede and follow the cluster along its orbit and can accumulate significant portions of the original mass of the cluster, forming clump-like features.{{cite conference |last1=Di Matteo |first1=P. |last2=Miocchi |first2=P. |last3=Capuzzo Dolcetta |first3=R. |date=May 2004 |title=Formation and Evolution of Clumpy Tidal Tails in Globular Clusters |work=American Astronomical Society, DDA meeting #35, #03.03 |bibcode=2004DDA....35.0303D |url=https://www.researchgate.net/publication/1799679}} The globular cluster Palomar 5, for example, is near the apogalactic point of its orbit after passing through the Milky Way. Streams of stars extend outward toward the front and rear of the orbital path of this cluster, stretching to distances of 13,000 light years. Tidal interactions have stripped away much of Palomar{{spaces}}5's mass; further interactions with the galactic core are expected to transform it into a long stream of stars orbiting the Milky Way in its halo.{{cite press release

| last=Staude

| first=Jakob

| date=June 3, 2002

| url=http://classic.sdss.org/news/releases/20020603.pal5.html

| title=Sky Survey Unveils Star Cluster Shredded By The Milky Way

| work=Image of the Week

| publisher=Sloan Digital Sky Survey

| access-date=April 9, 2021

| archive-url=https://web.archive.org/web/20060629091731/http://www.sdss.org/news/releases/20020603.pal5.html

| archive-date=June 29, 2006

| url-status=live

}}

The Milky Way is in the process of tidally stripping the Sagittarius Dwarf Spheroidal Galaxy of stars and globular clusters through the Sagittarius Stream. As many as 20% of the globular clusters in the Milky Way's outer halo may have originated in that galaxy.{{cite journal |last1=Carballo-Bello |first1=J. A. |last2=Corral-Santana |first2=J. M. |last3=Martínez-Delgado |first3=D. |last4=Sollima |first4=A. |last5=Muñoz |first5=R. R. |last6=Côté |first6=P. |last7=Duffau |first7=S. |last8=Catelan |first8=M. |last9=Grebel |first9=E. K. |title=The southern leading and trailing wraps of the Sagittarius tidal stream around the globular cluster Whiting 1 |journal=Monthly Notices of the Royal Astronomical Society: Letters |date=January 24, 2017 |volume=467 |issue=1 |pages=L91–L94 |doi=10.1093/mnrasl/slx006 |doi-access=free |bibcode=2017MNRAS.467L..91C |arxiv=1612.08745}} Palomar 12, for example, most likely originated in the Sagittarius Dwarf Spheroidal but is now associated with the Milky Way.{{cite journal

|author1=Dinescu, D. I. |author2=Majewski, S. R. |author3=Girard, T. M. |author4=Cudworth, K. M. | title=The Absolute Proper Motion of Palomar 12: A Case for Tidal Capture from the Sagittarius Dwarf Spheroidal Galaxy

| journal=The Astronomical Journal | date=2000

| volume=120 | issue=4 | pages=1892–1905

| bibcode=2000AJ....120.1892D

| doi=10.1086/301552 |arxiv = astro-ph/0006314 |s2cid=118898193 }}{{cite journal |last1=Sbordone |first1=L. |last2=Bonifacio |first2=P. |last3=Buonanno |first3=R. |last4=Marconi |first4=G. |last5=Monaco |first5=L. |last6=Zaggia |first6=S. |title=The exotic chemical composition of the Sagittarius dwarf spheroidal galaxy |journal=Astronomy & Astrophysics |date=April 2007 |volume=465 |issue=3 |pages=815–824 |doi=10.1051/0004-6361:20066385|arxiv=astro-ph/0612125 |bibcode=2007A&A...465..815S |doi-access=free }} Tidal interactions like these add kinetic energy into a globular cluster, dramatically increasing the evaporation rate and shrinking the size of the cluster. The increased evaporation accelerates the process of core collapse.{{cite journal |last1=Gnedin |first1=Oleg Y. |last2=Ostriker |first2=Jeremiah P. |title=Destruction of the Galactic Globular Cluster System |journal=The Astrophysical Journal |date=January 1997 |volume=474 |issue=1 |pages=223–255 |doi=10.1086/303441|arxiv=astro-ph/9603042 |bibcode=1997ApJ...474..223G |doi-access=free }}

Astronomers are searching for exoplanets of stars in globular star clusters.{{cite news |last=Ricard |first=Elise |date=15 January 2016 |title=Planet locations, a supernova, and a black hole |department=Space Friday |publisher=California Academy of Sciences |url=https://www.calacademy.org/explore-science/space-friday-planet-locations-a-supernova-and-a-black-hole |access-date=May 15, 2016}} A search in 2000 for giant planets in the globular cluster {{nobr|47 Tucanae}} came up negative, suggesting that the abundance of heavier elements – low in globular clusters – necessary to build these planets may need to be at least 40% of the Sun's abundance. Because terrestrial planets are built from heavier elements such as silicon, iron and magnesium, member stars have a far lower likelihood of hosting Earth-mass planets than stars in the solar neighborhood. Globular clusters are thus unlikely to host habitable terrestrial planets.{{cite journal | last1=Gonzalez | first1=Guillermo | author-link1=Guillermo Gonzalez (astronomer) | last2=Brownlee | first2=Donald | author-link2=Donald E. Brownlee |last3=Ward | first3=Peter |date=July 2001 | title=The galactic habitable zone: Galactic chemical evolution | journal=Icarus | volume=152 | issue=1 | pages=185–200 | doi=10.1006/icar.2001.6617 | bibcode=2001Icar..152..185G | arxiv = astro-ph/0103165 | s2cid=18179704 }}

A giant planet was found in the globular cluster {{nobr|Messier 4}}, orbiting a pulsar in the binary star system {{nobr|PSR B1620-26}}. The planet's eccentric and highly inclined orbit suggests it may have been formed around another star in the cluster, then "exchanged" into its current arrangement.{{cite book | last1=Sigurdsson | first1=S. | last2=Stairs | first2=I.H. | author-link2=Ingrid Stairs | last3=Moody | first3=K. | last4=Arzoumanian | first4=K.M.Z. | last5=Thorsett | first5=S.E. |author-link5=Stephen Thorsett | year=2008 | chapter=Planets around pulsars in globular clusters | editor1-first=D. | editor1-last=Fischer | editor2-first=F.A. | editor2-last=Rasio | editor3-first=S.E. | editor3-last=Thorsett | editor-link3=Stephen Thorsett |editor4-first=A. | editor4-last=Wolszczan |editor-link4=Aleksander Wolszczan | title=Extreme Solar Systems |series=ASP Conference Series | volume=398 | page=119 | publisher=Astronomical Society of the Pacific | bibcode=2008ASPC..398..119S }} The likelihood of close encounters between stars in a globular cluster can disrupt planetary systems; some planets break free to become rogue planets, orbiting the galaxy. Planets orbiting close to their star can become disrupted, potentially leading to orbital decay and an increase in orbital eccentricity and tidal effects.{{cite journal | display-authors=1 | last1=Spurzem | first1=R. |author-link1=Rainer Spurzem | last2=Giersz | first2=M. | last3=Heggie | first3=D.C. | author-link3=Douglas C. Heggie |last4=Lin | first4=D.N.C. |date=May 2009 | title=Dynamics of planetary systems in star clusters | journal=The Astrophysical Journal | volume=697 | issue=1 | pages=458–482 | doi=10.1088/0004-637X/697/1/458 | bibcode=2009ApJ...697..458S |arxiv = astro-ph/0612757 | s2cid=119083161 }} In 2024, a gas giant or brown dwarf was found to closely orbit the pulsar "M62H", where the name indicates that the planetary system belongs to the globular cluster Messier 62.{{Cite journal |last1=Vleeschower |first1=L. |last2=Corongiu |first2=A. |last3=Stappers |first3=B. W. |last4=Freire |first4=P. C. C. |last5=Ridolfi |first5=A. |last6=Abbate |first6=F. |last7=Ransom |first7=S. M. |last8=Possenti |first8=A. |last9=Padmanabh |first9=P. V. |last10=Balakrishnan |first10=V. |last11=Kramer |first11=M. |last12=Krishnan |first12=V. Venkatraman |last13=Zhang |first13=L. |last14=Bailes |first14=M. |last15=Barr |first15=E. D. |date=2024-03-01 |title=Discoveries and timing of pulsars in M62 |url=https://ui.adsabs.harvard.edu/abs/2024MNRAS.tmp..838V |journal=Monthly Notices of the Royal Astronomical Society |volume=530 |issue=2 |pages=1436–1456 |doi=10.1093/mnras/stae816 |doi-access=free |arxiv=2403.12137 |bibcode=2024MNRAS.530.1436V |issn=0035-8711}}

{{cmn|colwidth=30em|

• List of globular clusters
• Extragalactic Distance Scale
• Kraken galaxy
• Leonard-Merritt mass estimator
• Polytrope

}}

{{notelist}}

{{reflist|30em}}

• {{cite book |last1=Binney |first1=James |author-link1=James Binney |last2=Tremaine |first2=Scott |author-link2=Scott Tremaine |title=Galactic Dynamics |date=2008 |publisher=Princeton University Press |isbn=978-0-691-08444-2 |edition=2nd |url=https://books.google.com/books?id=qxWt20TH--cC |ref=none}}
• {{cite book |last1=Heggie |first1=Douglas |last2=Hut |first2=Piet |author1-link=Douglas C. Heggie |author2-link=Piet Hut |title=The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics |date=2003 |publisher=Cambridge University Press |isbn=978-0-521-77486-4 |url-access=registration |url=https://archive.org/details/gravitationalmil0000hegg |ref=none}}
• {{cite book |last1=Spitzer |first1=Lyman |author1-link=Lyman Spitzer |title=Dynamical Evolution of Globular Clusters |date=1987 |publisher=Princeton University Press |isbn=978-0-691-08460-2 |url-access=registration |url=https://archive.org/details/dynamicalevoluti0000spit/page/n5/mode/2up |ref=none}}

• {{cite journal | last1 = Elson | first1 = Rebecca | last2 = Hut | first2 = Piet | last3 = Inagaki | first3 = Shogo | year = 1987 | title = Dynamical evolution of globular clusters | journal = Annual Review of Astronomy and Astrophysics | volume = 25 | page = 565 | bibcode = 1987ARA&A..25..565E | doi = 10.1146/annurev.aa.25.090187.003025 | ref=none}}
• {{cite journal | last1 = Gratton | first1 = R. | last2 = Bragaglia | first2 = A. | last3 = Carretta | first3 = E. | display-authors = etal | year = 2019 | title = What is a globular cluster? An observational perspective | journal = The Astronomy and Astrophysics Review | volume = 27| issue = 1| page = 8| doi = 10.1007/s00159-019-0119-3 | arxiv = 1911.02835 | bibcode = 2019A&ARv..27....8G | s2cid = 207847491 | ref=none }}
• {{cite journal | last1 = Meylan | first1 = G. | last2 = Heggie | first2 = D. C. | year = 1997 | title = Internal dynamics of globular clusters | journal = The Astronomy and Astrophysics Review | volume = 8 | issue = 1–2| pages = 1–143 |bibcode = 1997A&ARv...8....1M | doi = 10.1007/s001590050008| arxiv = astro-ph/9610076 | s2cid = 119059312 | ref=none}}

{{Commons category|Globular clusters}}

• [http://messier.seds.org/glob.html Globular Clusters], Students for the Exploration and Development of Space Messier pages
• [http://spider.seds.org/spider/MWGC/mwgc.html Milky Way Globular Clusters]
• [https://web.archive.org/web/20061002033908/http://www.physics.mcmaster.ca/Globular.html Catalogue of Milky Way Globular Cluster Parameters] by William E. Harris, McMaster University, Ontario, Canada
• [https://web.archive.org/web/20110128035351/http://gclusters.altervista.org/ A galactic globular cluster database] by Marco Castellani, Rome Astronomical Observatory, Italy
• [https://people.smp.uq.edu.au/HolgerBaumgardt/globular/ Catalogue of structural and kinematic parameters and galactic orbits of globular clusters] by Holger Baumgardt, University of Queensland, Australia
• [https://scyon.univie.ac.at/ SCYON], a newsletter dedicated to star clusters.
• [http://www.manybody.org/modest/ MODEST], a loose collaboration of scientists working on star clusters.

{{Stellar system}}

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Category:Star clusters