Globular cluster

's from the Sun and contains hundreds of thousands of stars. [cite news
coauthors =The Hubble Heritage team
url = http://hubblesite.org/newscenter/newsdesk/archive/releases/1999/26/
title = Hubble Images a Swarm of Ancient Stars
work = HubbleSite News Desk
publisher = Space Telescope Science Institute
date =1999-07-01 | accessdate = 2006-05-26 ] ] A globular cluster is a spherical collection of stars that orbits a galactic core as a satellite. Globular clusters are very tightly bound by gravity, which gives them their spherical shapes and relatively high stellar densities toward their centers. The name of this category of star cluster is derived from the Latin "globulus"—a small sphere. A globular cluster is sometimes known more simply as a "globular".

Globular clusters, which are found in the halo of a galaxy, contain considerably more stars and are much older than the less dense galactic, or open clusters, which are found in the disk. Globular clusters are fairly common; there are about 158 [cite web
last=Frommert | first=Hartmut | month=August | year=2007
url=http://www.seds.org/~spider/spider/MWGC/mwgc.html
title=Milky Way Globular Clusters
publisher=SEDS | accessdate=2008-02-26 ] currently known globular clusters in the Milky Way, with perhaps 10–20 more undiscovered.cite journal
author = Ashman, Keith M.; Zepf, Stephen E.
year = 1992
title = The formation of globular clusters in merging and interacting galaxies
journal = Astrophysical Journal, Part 1
volume = 384 | pages = 50–61
url = http://adsabs.harvard.edu/cgi-bin/bib_query?1992ApJ...384...50A
accessdate = 2006-05-27 | doi = 10.1086/170850 ] Large galaxies can have more: Andromeda, for instance, may have as many as 500. [cite journal
author = Barmby, P.; Huchra, J. P.
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
url=http://www.journals.uchicago.edu/doi/full/10.1086/323457 | doi = 10.1086/323457 ] Some giant elliptical galaxies, such as M87, [cite journal
author=Strom, S. E.; Strom, K. M.; Wells, D. C.; Forte, J. C.; Smith, M. G.; Harris, W. E.
title=The halo globular clusters of the giant elliptical galaxy Messier 87
journal=Astrophysical Journal | year=1981
volume=245 | issue=5457 | pages=416–453
url=http://adsabs.harvard.edu/abs/1981ApJ...245..416S
doi=10.1086/158820 | accessdate=2008-06-23 ] may have as many as 10,000 globular clusters. These globular clusters orbit the galaxy out to large radii, 40 kiloparsecs (approximately 131 thousand light-years) or more. [cite journal
author = Dauphole, B.; Geffert, M.; Colin, J.; Ducourant, C.; Odenkirchen, M.; Tucholke, H.-J.
title=The kinematics of globular clusters, apocentric distances and a halo metallicity gradient
journal=Astronomy and Astrophysics | year=1996
volume=313 | pages=119–128 | accessdate=2008-06-23
url=http://adsabs.harvard.edu/abs/1996A&A...313..119D ]

Every galaxy of sufficient mass in the Local Group has an associated group of globular clusters, and almost every large galaxy surveyed has been found to possess a system of globular clusters. [cite journal
last = Harris | first = William E.
title=Globular cluster systems in galaxies beyond the Local Group
journal=Annual Review of Astronomy and Astrophysics
year=1991 | volume=29 | pages=543–579
url=http://adsabs.harvard.edu/abs/1991ARA&A..29..543H
accessdate=2006-06-02
doi=10.1146/annurev.aa.29.090191.002551 ] The Sagittarius Dwarf and Canis Major Dwarf galaxies appear to be in the process of donating their associated globular clusters (such as Palomar 12) to the Milky Way. [cite journal
author=Dinescu, D. I.; Majewski, S. R.; Girard, T. M.; 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 | year=2000
volume=120 | issue=4 | pages=1892–1905
url=http://adsabs.harvard.edu/abs/2000astro.ph..6314D
doi=10.1086/301552 | accessdate=2006-06-02 ] This demonstrates how many of this galaxy's globular clusters were acquired in the past.

Although it appears that globular clusters contain some of the first stars to be produced in the galaxy, their origins and their role in galactic evolution are still unclear. It does appear clear that globular clusters are significantly different from dwarf elliptical galaxies and were formed as part of the star formation of the parent galaxy rather than as a separate galaxy.Fact|date=January 2008 However, recent conjectures by astronomers suggest that globular clusters and dwarf spheroidals may not be clearly separate and distinct types of objects.citation
last = van den Bergh | first = Sidney
authorlink = Sidney van den Bergh
title = Globular Clusters and Dwarf Spheroidal Galaxies
year = 2007 | date = November 2007
journal = MNRAS (Letters), in press
url = http://adsabs.harvard.edu/abs/2007arXiv0711.4795V
accessdate=2006-06-02
doi = 10.1111/j.1745-3933.2008.00424.x
volume = 385
pages = L20 ]

Observation history

The first globular cluster discovered was M22 in 1665 by Abraham Ihle, a German amateur astronomer. [cite web
author = Sharp, N. A.
url = http://www.noao.edu/image_gallery/html/im0575.html
title = M22, NGC6656
publisher = REU program/NOAO/AURA/NSF
accessdate = 2006-08-16 ] However, given the small aperture of early telescopes, individual stars within a globular cluster were not resolved until Charles Messier observed M4. The first eight globular clusters discovered are shown in the table. Subsequently, Abbé Lacaille would list NGC 104, NGC 4833, M55, M69, and NGC 6397 in his 1751–52 catalogue. The "M" before a number refers to the catalogue of Charles Messier, while "NGC" is from the New General Catalogue by John Dreyer.

William Herschel began a survey program in 1782 using larger telescopes and was able to resolve the stars in all 33 of the known globular clusters. In addition he found 37 additional clusters. In Herschel's 1789 catalog of deep sky objects, his second such, he became the first to use the name "globular cluster" as their description.

The number of globular clusters discovered continued to increase, reaching 83 in 1915, 93 in 1930 and 97 by 1947. A total of 151 globular clusters have now been discovered in the Milky Way galaxy, out of an estimated total of 180 ± 20. These additional, undiscovered globular clusters are believed to be hidden behind the gas and dust of the Milky Way.

Beginning in 1914, Harlow Shapley began a series of studies of globular clusters, published in about 40 scientific papers. He examined the cepheid variables in the clusters and would use their period–luminosity relationship for distance estimates.

Of the globular clusters within our Milky Way, the majority are found in the vicinity of the galactic core, and the large majority lie on the side of the celestial sky centered on the core. In 1918 this strongly asymmetrical distribution was used by Harlow Shapley to make a determination of the overall dimensions of the galaxy. By 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+
url = http://adsabs.harvard.edu/abs/1918PASP...30...42S
accessdate = 2006-05-30 | doi = 10.1086/122686 ] While his distance estimate was significantly in error, it did demonstrate that the dimensions of the galaxy were much greater than had been previously thought. His error was due to the fact that dust in the Milky Way diminished the amount of light from a globular cluster that reached the earth, thus making it appear farther away. Shapley's estimate was, however, within the same order of magnitude of the currently accepted value.

Shapley's measurements also indicated that the Sun was relatively far from the center of the galaxy, contrary to what had previously been inferred from the apparently nearly even distribution of ordinary stars. In reality, ordinary stars lie within the galaxy's disk and are thus often obscured by gas and dust, whereas globular clusters lie outside the disk and can be seen at much further distances.

Shapley was subsequently assisted in his studies of clusters by Henrietta Swope and Helen Battles Sawyer (later Hogg). In 1927–29, Harlow Shapley and Helen Sawyer began categorizing clusters according to the degree of concentration the system has toward the core. The most concentrated clusters were identified as Class I, with successively diminishing concentrations ranging to Class XII. This became known as the "Shapley–Sawyer Concentration Class". (It is sometimes given with numbers [Class 1–12] rather than Roman numerals.)cite journal
last = Hogg | first = Helen Battles Sawyer | year = 1965
title = Harlow Shapley and Globular Clusters
journal = Publications of the Astronomical Society of the Pacific
volume = 77 | issue = 458 | pages = 336–46
url = http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1965PASP...77..336S | doi = 10.1086/128229 ]

Composition

Globular clusters are generally composed of hundreds of thousands of low-metal, old stars. The type of stars found in a globular cluster are similar to those in the bulge of a spiral galaxy but confined to a volume of only a few cubic parsecs. They are free of gas and dust and it is presumed that all of the gas and dust was long ago turned into stars.

While globular clusters can contain a high density of stars (on average about 0.4 stars per cubic parsec, increasing to 100 or 1000 stars per cubic parsec 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
accessdate = 2007-04-25 ] they are not thought to be favorable locations for the survival of planetary systems. Planetary orbits are dynamically unstable within the cores of dense clusters because of the perturbations of passing stars. A planet orbiting at 1 astronomical unit around a star that is within the core of a dense cluster such as 47 Tucanae would only survive on the order of 10⁸ years. [cite journal
last = Sigurdsson | first = Steinn
title=Planets in globular clusters?
journal=Astrophysical Journal | year=1992 | volume=399
issue=1 | pages=L95–L97
url=http://adsabs.harvard.edu/abs/1992ApJ...399L..95S
accessdate=2006-08-20 | doi=10.1086/186615 ] However, there has been at least one planetary system found orbiting a pulsar (PSR B1620−26) that belongs to the globular cluster M4. [cite journal
author = Arzoumanian, Z.; Joshi, K.; Rasio, F. A.; Thorsett, S. E.
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 | pages=525
accessdate=2008-06-23
url=http://adsabs.harvard.edu/abs/1996astro.ph..5141A ]

With a few notable exceptions, each globular cluster appears to have a definite age. That is, most of the stars in a cluster are at approximately the same stage in stellar evolution, suggesting that they formed at about the same time. All known globular clusters appear to have no active star formation, which is consistent with the view that globular clusters are typically the oldest objects in the 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 news
title=Young and Exotic Stellar Zoo: ESO's Telescopes Uncover Super Star Cluster in the Milky Way
date=2005-03-22 | publisher=ESO
url=http://www.eso.org/outreach/press-rel/pr-2005/pr-08-05.html
accessdate=2007-03-20 ]

Some globular clusters, like Omega Centauri in our Milky Way and G1 in M31, are extraordinarily massive (several million solar masses) and contain multiple stellar populations. Both can be regarded as evidence that supermassive globular clusters are in fact the cores of dwarf galaxies that are consumed by the larger galaxies. Several globular clusters (like M15) have extremely massive cores which may harbor black holes, [cite web
first=Roeland | last=van der Marel | date =2002-03-03
url = http://www-int.stsci.edu/~marel/m15release.html
title = Black Holes in Globular Clusters
publisher = Space Telescope Science Institute
accessdate = 2006-06-08 ] although simulations suggest that a less massive black hole or central concentration of neutron stars or massive white dwarfs explain observations equally well.

Metallic content

Globular clusters normally consist of Population IIstars, which have a low metallic content compared to
Population I stars such as the Sun. (To astronomers, "metals" includes all elements heavier than helium, such as lithium and carbon.)

The Dutch astronomer Pieter Oosterhoff noticed that there appear to be two 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
author=van Albada, T. S.; Baker, Norman ] Both groups have weak lines of metallic elements. But the lines in the stars of Oosterhoff type I (OoI) cluster are not quite as weak as those in type II (OoII). Hence type I are referred to as "metal-rich" while type II are "metal-poor".

These two populations have been observed in many galaxies (especially massive elliptical galaxies). Both groups are of similar ages (nearly as old as the universe itself) but differ in their metal abundances. Many scenarios have been suggested to explain these subpopulations, including violent gas-rich galaxy mergers, the accretion of dwarf galaxies, and multiple phases of star formation in a single galaxy. In our 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
url=http://adsabs.harvard.edu/abs/1976AJ.....81.1095H
doi=10.1086/111991 ]

In the Milky Way it has been discovered that the large majority of the low metallicity clusters are aligned along a plane in the outer part of the galaxy's halo. This result argues in favor of the view that type II clusters in the galaxy were captured from a satellite galaxy, rather than being the oldest members of the Milky Way's globular cluster system as had been 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
author=Lee, Y. W.; 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
url=http://adsabs.harvard.edu/abs/2002astro.ph..7607Y
accessdate = 2006-06-01 ]

Exotic components

Globular clusters have a very high star density, and therefore close interactions and near-collisions of stars occur relatively often. Due to these chance encounters, some exotic classes of stars, such as blue stragglers, millisecond pulsars and low-mass X-ray binaries, are much more common in globular clusters. A blue straggler is formed from the merger of two stars, possibly as a result of an encounter with a binary system. The resulting star has a higher temperature than comparable stars in the cluster with the same luminosity, and thus differs from the main sequence stars formed at the beginning of the cluster.cite journal
author=Rubin, V. C.; Ford, W. K. J.
title=A Thousand Blazing Suns: The Inner Life of Globular Clusters
journal=Mercury | year=1999 | volume=28 | pages=26
url=http://www.astrosociety.org/pubs/mercury/9904/murphy.html
accessdate=2006-06-02 ]

Astronomers have searched for black holes within globular clusters since the 1970s. The resolution requirements for this task, however, are exacting, and it is only with the Hubble space telescope that the first confirmed discoveries have been made. In independent programs, a 4,000 solar mass intermediate-mass black hole has been suggested to exist based on HST observations in the globular cluster M15 and a 20,000 solar mass black hole in the Mayall II cluster in the Andromeda Galaxy. [cite news
author=Savage, D.; Neal, N.; Villard, R.; Johnson, R.; Lebo, H.
url=http://hubblesite.org/newscenter/newsdesk/archive/releases/2002/18/text/
title=Hubble Discovers Black Holes in Unexpected Places
date=2002-09-17 | work=HubbleSite
publisher=Space Telescope Science Institute
accessdate=2006-05-25 ] Both x-ray and radio emissions from Mayall II appear to be 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=2007-05-28
url=http://www.nrao.edu/pr/2007/globularbh/
accessdate=2007-05-29 ]

These are of particular interest because they are the first black holes discovered that were intermediate in mass between the conventional stellar-mass black hole and the supermassive black holes discovered at the cores of galaxies. The mass of these intermediate mass black holes is proportional to the mass of the clusters, following a pattern previously discovered between supermassive black holes and their surrounding galaxies.

Claims of intermediate mass black holes have been met with some skepticism. The densest objects in globular clusters are expected to migrate to the cluster center due to mass segregation. These will be white dwarfs and neutron stars in an old stellar population like a globular cluster. As pointed out in two papers by Holger Baumgardt and collaborators, the mass-to-light ratio should rise sharply towards the center of the cluster, even without a black hole, in both M15 [cite journal
author=Baumgardt, Holger; Hut, Piet; Makino, Junichiro; McMillan, Steve; Portegies Zwart, Simon
title=On the Central Structure of M15
journal=Astrophysical Journal Letters | year=2003
volume=582 | pages=21
url=http://adsabs.harvard.edu/abs/2003ApJ...582L..21B
accessdate=2006-09-13 | doi=10.1086/367537 ] and Mayall II. [Cite journal
author=Baumgardt, Holger; Hut, Piet; Makino, Junichiro; McMillan, Steve; Portegies Zwart, Simon | title=A Dynamical Model for the Globular Cluster G1
journal=Astrophysical Journal Letters | year=2003
volume=589 | pages=25
url=http://www.astro.uni-bonn.de/~holger/preprints/g1.html
accessdate=2006-09-13 | doi=10.1086/375802 ]

Color-magnitude diagram

The Hertzsprung-Russell diagram (HR-diagram) is a graph of a large sample of stars that plots their visual
absolute magnitude against their color index. Thecolor index, B−V, is the difference between the magnitude of the star in blue light, or B, and the magnitude in visual light (green-yellow), or V. Large positive values indicate a red star with a cool surface temperature, while negative values imply a blue star with a hotter surface.

When the stars near the Sun are plotted on an HR diagram, it displays a distribution of stars of various masses, ages, and compositions. Many of the stars lie relatively close to a sloping curve with increasing absolute magnitude as the stars are hotter, known as main sequence stars. However the diagram also typically includes stars that are in later stages of their evolution and have wandered away from this main sequence curve.

As all the stars of a globular cluster are at approximately the same distance from us, their absolute magnitudes differ from their visual magnitude by about the same amount. The main sequence stars in the globular cluster will fall along a line that is believed to be comparable to similar stars in the solar neighborhood. (The accuracy of this assumption is confirmed by comparable results obtained by comparing the magnitudes of nearby short-period variables, such as RR Lyrae stars and cepheid variables, with those in the cluster.) [cite journal
author = Shapley, H. | authorlink = Harlow Shapley
year = 1917 | title = Studies based on the colors and magnitudes in stellar clusters. I,II,III
journal = Astrophysical Journal | volume = 45
pages = 118–141
url = http://adsabs.harvard.edu/abs/1917ApJ....45..118S
accessdate = 2006-05-26 | doi = 10.1086/142314 ]

By matching up these curves on the HR diagram the absolute magnitude of main sequence stars in the cluster can also be determined. This in turn provides a distance estimate to the cluster, based on the visual magnitude of the stars. The difference between the relative and absolute magnitude, the "distance modulus", yields this estimate of the distance. [cite book
last = Martin | first = Schwarzschild | year = 1958
title = Structure and Evolution of Stars
publisher = Princeton University Press ]

When the stars of a particular globular cluster are plotted on an HR diagram, nearly all of the stars fall upon a relatively well defined curve. This differs from the HR diagram of stars near the Sun, which lumps together stars of differing ages and origins. The shape of the curve for a globular cluster is characteristic of a grouping of stars that were formed at approximately the same time and from the same materials, differing only in their initial mass. As the position of each star in the HR diagram varies with age, the shape of the curve for a globular cluster can be used to measure the overall age of the collected stars. [cite journal
author = Sandage, A.R. | authorlink = Allan Sandage
year = 1957
title = Observational Approach to Evolution. III. Semiempirical Evolution Tracks for M67 and M3
journal = Astrophysical Journal | volume = 126
pages = 326
url = http://adsabs.harvard.edu/abs/1957ApJ...126..326S
accessdate = 2006-05-26 | doi = 10.1086/146405 ]

The most massive main sequence stars in a globular cluster will also have the highest absolute magnitude, and these will be the first to evolve into the giant star stage. As the cluster ages, stars of successively lower masses will also enter the giant star stage. Thus the age of a cluster can be measured by looking for the stars that are just beginning to enter the giant star stage. This forms a "knee" in the HR diagram, bending to the upper right from the main sequence line. The absolute magnitude at this bend is directly a function of the age of globular cluster, so an age scale can be plotted on an axis parallel to the magnitude.

In addition, globular clusters can be dated by looking at the temperatures of the coolest white dwarfs. Typical results for globular clusters are that they may be as old as 12.7 billion years. [cite journal
author = Hansen, B. M. S.; Brewer, J.; Fahlman, G. G.; Gibson, B. K.; Ibata, R.; Limongi, M.; Rich, R. M.; Richer, H. B.; Shara, M. M.; Stetson, P. B.
year = 2002
title = The White Dwarf Cooling Sequence of the Globular Cluster Messier 4
journal = Astrophysical Journal Letters
volume = 574 | pages = L155
url = http://arxiv.org/abs/astro-ph/0205087
accessdate = 2006-05-26 | doi = 10.1086/342528 ] This is in contrast to open clusters which are only tens of millions of years old.

The ages of globular clusters place a bound on the age limit of the entire universe. This lower limit has been a significant constraint in cosmology. During the early 1990s, astronomers were faced with age estimates of globular clusters that appeared older than cosmological models would allow. However, better measurements of cosmological parameters through deep sky surveys and satellites such as COBE have resolved this issue as have computer models of stellar evolution that have different models of mixing.

Evolutionary studies of globular clusters can also be used to determine changes due to the starting composition of the gas and dust that formed the cluster. That is, the change in the evolutionary tracks due to the abundance of heavy elements. (Heavy elements in astronomy are considered to be all elements more massive than helium.) The data obtained from studies of globular clusters are then used to study the evolution of the Milky Way as a whole. [Cite press release
date=2001-03-01
url=http://www.eso.org/outreach/press-rel/pr-2001/pr-03-01.html
title=Ashes from the Elder Brethren — UVES Observes Stellar Abundance Anomalies in Globular Clusters
accessdate=2006-05-26 ]

In globular clusters a few stars known as blue stragglers are observed, apparently continuing the main sequence in the direction of brighter, bluer stars. The origins of these stars is still unclear, but most models suggest that these stars are the result of mass transfer in multiple star systems.

Morphology

In contrast to open clusters, most globular clusters remain gravitationally bound for time periods comparable to the life spans of the majority of their stars. (A possible exception is when strong tidal interactions with other large masses result in the dispersal of the stars.)

At present the formation of globular clusters remains a poorly understood phenomenon. It remains uncertain whether the stars in a globular cluster form in a single generation, or are spawned across multiple generations over a period of several hundred million years. This star-forming period is relatively brief, however, compared to the age of many globular clusters. [cite news
author=Weaver, D.; Villard, R.; Christensen, L. L.; Piotto, G.; Bedin, L.
title=Hubble Finds Multiple Stellar 'Baby Booms' in a Globular Cluster
publisher=Hubble News Desk | date=2007-05-02
url=http://hubblesite.org/newscenter/archive/releases/2007/18/full/
accessdate=2007-05-01 ] Observations of globular clusters show that these stellar formations arise primarily in regions of efficient star formation, and where the interstellar medium is at a higher density than in normal star-forming regions. Globular cluster formation is prevalent in starburst regions and in interacting galaxies. [cite journal
author = Elmegreen, B. G.; Efremov, Y. N.
title=A Universal Formation Mechanism for Open and Globular Clusters in Turbulent Gas
journal=Astrophysical Journal | year=1999 | volume=480
issue=2 | pages=235
url=http://adsabs.harvard.edu/abs/1997ApJ...480..235E
doi=10.1086/303966 ]

After they are formed, the stars in the globular cluster begin to gravitationally interact with each other. As a result the velocity vectors of the stars are steadily modified, and the stars lose any history of their original velocity. The characteristic interval for this to occur is the relaxation time. This is related to the characteristic length of time a star needs to cross the cluster as well as the number of stellar masses in the system.cite journal
last = Benacquista | first = Matthew J.
title=Globular cluster structure
journal=Living Reviews in Relativity | year=2006
url=http://relativity.livingreviews.org/open?pubNo=lrr-2006-2&page=articlesu2.html
accessdate=2006-08-14 ] The value of the relaxation time varies by cluster, but the mean value is on the order of 10⁹ years.

Although globular clusters generally appear spherical in form, ellipticities can occur due to 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
author = Frenk, C. S.; White, S. D. M. | year = 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
url = http://adsabs.harvard.edu/abs/1997astro.ph..2024G
accessdate = 2006-05-31 ]

Radii

Astronomers characterize the morphology of a globular cluster by means of standard radii. These are the core radius ("r"_"c"), the half-light radius ("r"_"h") and the tidal radius ("r"_"t"). The overall luminosity of the cluster steadily decreases with distance from the core, and the core radius is the distance at which the apparent surface luminosity has dropped by half. A comparable quantity is the half-light radius, or the distance from the core within which half the total luminosity from the cluster is received. This is typically larger than the core radius.

Note that the half-light radius includes stars in the outer part of the cluster that happen to lie along the line of sight, so theorists will also use the half-mass radius ("r"_"m")—the radius from the core that contains half the total mass of the cluster. When the half-mass radius of a cluster is small relative to the overall size, it has a dense core. An example of this is Messier 3 (M3), which has an overall visible dimension of about 18 arc minutes, but a half-mass radius of only 1.12 arc minutes. [cite journal
author =Buonanno, R.; Corsi, C. E.; Buzzoni, A.; Cacciari, C.; Ferraro, F. R.; Fusi Pecci, F.
year = 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
url = http://adsabs.harvard.edu/abs/1994A&A...290...69B
accessdate = 2006-05-29 ]

Almost all globular clusters have a half-light radius of less than 10 pc. Although there are well-established globular clusters with very large radii (i.e. NGC 2419 (R_h = 18 pc) and Palomar 14 (R_h = 25 pc).

Finally the tidal radius 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. 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 is about 38 arc minutes.

Mass segregation and luminosity

In measuring the luminosity curve of a given globular cluster as a function of distance from the core, most clusters in the Milky Way steadily increase in luminosity as this distance decreases, up to a certain distance from the core, then the luminosity levels off. Typically this distance is about 1–2 parsecs from the core. However about 20% of the globular clusters have undergone a process termed "core collapse". In this type of cluster, the luminosity continues to steadily increase all the way to the core region. [cite journal
author = Djorgovski, S.; King, I. R. | year = 1986
title = A preliminary survey of collapsed cores in globular clusters
journal = Astrophysical Journal | volume = 305
pages = L61–L65
url = http://adsabs.harvard.edu/abs/1986ApJ...305L..61D
accessdate = 2006-05-29 | doi = 10.1086/184685 ] An example of a core-collapsed globular is
M15.

Core-collapse is thought to occur when the more massive stars in a globular encounter their less massive companions. As a result of the encounters the larger stars tend to lose kinetic energy and start to settle toward the core. Over a lengthy period of time this leads to a concentration of massive stars near the core, a phenomenon called mass segregation.

The Hubble Space Telescope has been used to provide 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 globular star cluster 47 Tucanae, which is made up of about 1 million stars, is one of the densest globular clusters in the Southern Hemisphere. This cluster was subjected to an intensive photographic survey, which allowed astronomers to track the motion of its stars. Precise velocities were obtained for nearly 15,000 stars in this cluster. [cite news
title=Stellar Sorting in Globular Cluster 47
publisher=Hubble News Desk | date=2006-10-04
url=http://hubblesite.org/newscenter/newsdesk/archive/releases/2006/33/
accessdate=2006-10-24 ]

The different stages of core-collapse may be divided into three phases. During a globular cluster's adolescence, the process of core-collapse begins with stars near the core. However, the interactions between binary star systems prevents further collapse as the cluster approaches middle age. Finally, the central binaries are either disrupted or ejected, resulting in a tighter concentration at the core.

A 2008 study by Dr. John Fregeau of 13 globular clusters in the Milky Way shows that three of them have unusually large number of X-ray sources, or X-ray binaries, suggesting the clusters are middle-aged. Previously, these globular clusters had been classified as being in old age because they had very tight concentrations of stars in their centers, another litmus test of age used by astronomers. The implication is that most globular clusters, including the other ten studied by Fregeau, are not in middle age, as previously thought, but are actually in adolescence.

"It's remarkable that these objects, which are thought to be some of the oldest in the Universe, may really be very immature," said Fregeau whose paper appears in The Astrophysical Journal. "This would represent a major change in thinking about the current evolutionary status of globular clusters."cite news
last=Baldwin | first=Emily | date=2008-04-29
title=Old globular clusters surprisingly young
publisher=Astronomy Now Online
url=http://www.astronomynow.com/Oldglobularclusterssurprisinglyyoung.html
accessdate=2008-05-02 ]

The overall luminosities of the globular clusters within the Milky Way and M31 can be modeled by means of a gaussian curve. This gaussian can be represented by means of 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 = −7.20±0.13, σ=1.1±0.1 magnitudes.) [cite journal
last = Secker | first = Jeff | year = 1992
title = A Statistical Investigation into the Shape of the Globular cluster Luminosity Distribution
journal = Astronomical Journal | volume = 104
issue = 4 | pages = 1472–1481
url = http://adsabs.harvard.edu/abs/1992AJ....104.1472S
accessdate = 2006-05-28 | doi = 10.1086/116332 ] The GCLF has also been used as a "standard candle" for measuring the distance to other galaxies, under the assumption that the globular clusters in remote galaxies follow the same principles as they do in the Milky Way.

N-body simulations

Computing the interactions between the stars within a globular cluster requires solving what is termed the N-body problem. That is, each of the stars within the cluster continually interacts with the other "N"−1 stars, where "N" is the total number of stars in the cluster. The naive CPU computational "cost" for a dynamic simulation increases in proportion to "N"³, [cite web
last = Benacquista | first = Matthew J.
date = 2002-02-20
url = http://relativity.livingreviews.org/open?pubNo=lrr-2002-2&page=articlesu11.html
title = Relativistic Binaries in Globular Clusters: 5.1 N-body
publisher = Living Reviews in Relativity
accessdate = 2006-10-25 ] so the potential computing requirements to accurately simulate such a cluster can be enormous. [cite conference
first = D. C. | last = Heggie
coauthors = Giersz, M.; Spurzem, R.; Takahashi, K.
year = 1998 | pages = 591
title = Dynamical Simulations: Methods and Comparisons
booktitle = 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
url = http://adsabs.harvard.edu/abs/1997astro.ph.11191H
accessdate = 2006-05-28 ] An efficient method of mathematically simulating the N-body dynamics of a globular cluster is done by subdividing into small volumes and velocity ranges, and using probabilities to describe the locations of the stars. The motions are then described by means of a formula called the Fokker-Planck equation. This can be solved by a simplified form of the equation, or by running Monte Carlo simulations and using random values. However 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. | year = 2006
title = Relativistic Binaries in Globular Clusters
journal = Living Reviews in Relativity
issue = lrr-2006-2
url = http://relativity.livingreviews.org/Articles/lrr-2006-2/
accessdate = 2006-05-28 ]

The results of N-body simulations have shown that the stars can follow unusual paths through the cluster, often forming loops and often falling more directly toward the core than would a single star orbiting a central mass. In addition, due to interactions with other stars that result in an increase in velocity, some of the stars gain sufficient energy to escape the cluster. Over long periods of time this will result in a dissipation of the cluster, a process termed evaporation. [cite book
editor = J. Goodman and P. Hut | year = 1985
title = Dynamics of Star Clusters (International Astronomical Union Symposia)
publisher = Springer | isbn=90-277-1963-2 ] The typical time scale for the evaporation of a globular cluster is 10¹⁰ years.

Binary stars form a significant portion of the total population of stellar systems, with up to half of all stars occurring in binary systems. 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.

Intermediate forms

The distinction between cluster types is not alwaysclear-cut, and objects have been found that blur thelines between the categories. For example, BH 176in the southern part of the Milky Way has propertiesof both an open and a globular cluster. [cite journal
author=Ortolani, S.; Bica, E.; Barbuy, B.
title=BH 176 and AM-2: globular or open clusters?
journal=Astronomy and Astrophysics | year=1995
volume=300 | pages=726
url=http://adsabs.harvard.edu/abs/1995A&A...300..726O
accessdate=2008-06-23 ]

In 2005, astronomers discovered a completely new type of star cluster in the Andromeda Galaxy, which is, in several ways, very similar to globular clusters. The new-found clusters contain hundreds of thousands of stars, a similar number of stars that can be found in globular clusters. The clusters also share other characteristics with globular clusters, "e.g." the stellar populations and metallicity. What distinguishes them from the globular clusters is that they are much larger – several hundred light-years across – and hundreds of times less dense. The distances between the stars are, therefore, much greater within the newly discovered extended clusters. Parametrically, these clusters lie somewhere between a (low dark-matter) globular cluster and a (dark matter-dominated) dwarf spheroidal galaxy.cite journal
author=Huxor, A. P.; Tanvir, N. R.; Irwin, M. J.; R. Ibata
title=A new population of extended, luminous, star clusters in the halo of M31
journal=Monthly Notices of the Royal Astronomical Society
year=2005 | volume=360 | pages=993–1006
url=http://arxiv.org/abs/astro-ph/0412223
doi=10.1111/j.1365-2966.2005.09086.x ]

How these clusters are formed is not yet known, but their formation might well be related to that of globular clusters. Why M31 has such clusters, while the Milky Way does not, is not yet known. It is also unknown if any other galaxy contains these types of clusters, but it would be very unlikely that M31 is the sole galaxy with extended clusters.

Tidal encounters

When a globular cluster has a close encounter with a large mass, such as the core region of a galaxy, it undergoes a tidal interaction. The difference in the pull of gravity between the part of the cluster nearest the mass and the pull on the furthest part of the cluster results in a tidal force. A "tidal shock" occurs whenever the orbit of a cluster takes it through the plane of a galaxy.

As a result of a tidal shock, streams of stars can be pulled away from the cluster halo, leaving only the core part of the cluster. These tidal interaction effects create tails of stars that can extend up to several degrees of arc away from the cluster. [cite conference
author = Lauchner, A.; Wilhelm, R.; Beers, T. C.; Allende Prieto, C.
date = December 2003
title = A Search for Kinematic Evidence of Tidal Tails in Globular Clusters
booktitle = American Astronomical Society Meeting 203, #112.26
publisher = American Astronomical Society
url = http://adsabs.harvard.edu/abs/2003AAS...20311226L
accessdate = 2006-06-02 ] These tails typically both precede and follow the cluster along its orbit. The tails can accumulate significant portions of the original mass of the cluster, and can form clumplike features. [cite conference
author = Di Matteo, P.; Miocchi, P.; Capuzzo Dolcetta, R.
date = May 2004
title = Formation and Evolution of Clumpy Tidal Tails in Globular Clusters
booktitle = American Astronomical Society, DDA meeting #35, #03.03
publisher = American Astronomical Society
url = http://adsabs.harvard.edu/abs/2004DDA....35.0303D
accessdate = 2006-06-02 ]

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 out to distances of 13,000 light-years. [cite web
last = Staude | first = Jakob | date = 2002-06-03
url = http://www.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
accessdate = 2006-06-02 ] Tidal interactions have stripped away much of the mass from Palomar 5, and further interactions as it passes through the galactic core are expected to transform it into a long stream of stars orbiting the Milky Way halo.

Tidal interactions add kinetic energy into a globular cluster, dramatically increasing the evaporation rate and shrinking the size of the cluster. Not only does tidal shock strip off the outer stars from a globular cluster, but the increased evaporation accelerates the process of core collapse. The same physical mechanism may be at work in Dwarf spheroidal galaxies such as the Sagittarius Dwarf, which appears to be undergoing tidal disruption due to its proximity to the Milky Way.

ee also

*List of globular clusters
*Plummer model
*Extragalactic Distance Scale
*Polytrope
*Leonard-Merritt mass estimator

References

General resources

* [http://adswww.harvard.edu/ NASA Astrophysics Data System] has a collection of past articles, from all major astrophysics journals and many conference proceedings.
* [http://astro.u-strasbg.fr/scyon/ SCYON] is a newsletter dedicated to star clusters.
* [http://www.manybody.org/modest/ MODEST] is a loose collaboration of scientists working on star clusters.

Books

* cite book
author=Binney, James; Tremaine, Scott
year=1987 | title=Galactic Dynamics
edition=First edition
publisher=Princeton University Press
location=Princeton, New Jersey | isbn=0691084440
* cite book
author=Heggie, Douglas; Hut, Piet | year=2003
title=The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics
publisher=Cambridge University Press | isbn=0521774861
* cite book
author=Spitzer, Lyman | year=1987
title=Dynamical Evolution of Globular Clusters
publisher=Princeton University Press
location=Princeton, New Jersey | isbn=0691084602

Review Articles

* Elson, Rebecca; Hut, Piet; Inagaki, Shogo (1987). Dynamical evolution of globular clusters. "Annual review of astronomy and astrophysics" 25 565. [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1987ARA%26A..25..565E NASA ADS]
* Meylan, G.; Heggie, D. C. (1997). Internal dynamics of globular clusters. "The Astronomy and Astrophysics Review" 8 1. [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1997A%26ARv...8....1M NASA ADS]

External links

* [http://www.seds.org/messier/glob.html Globular Clusters] , SEDS Messier pages
* [http://www.seds.org/~spider/spider/MWGC/mwgc.html Milky Way Globular Clusters]
* [http://www.physics.mcmaster.ca/Globular.html Catalogue of Milky Way Globular Cluster Parameters] by William E. Harris, McMaster University, Ontario, Canada
* [http://www.mporzio.astro.it/~marco/gc/ A galactic globular cluster database] by Marco Castellani, Rome Astronomical Observatory, Italy
* [http://www.nature.com/news/2006/060821/full/060821-13.html Key stars have different birthdays] article describes how stars in globular clusters are born in several bursts, rather than all at once
* [http://globularclusters.wordpress.com Globular Clusters Blog] News, papers and preprints on Galactic Globular Clusters
* [http://www.space-and-telescope.com/MessierObjects.aspx Clickable Messier Object table including globular clusters]

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