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Globular cluster: Encyclopedia BETAFree Encyclopedia |
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RadiiAstronomers characterize the morphology of a globular cluster by means of standard radii. These are the core radius (rc), the half-light radius (rh) and the tidal radius (rc). 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 at 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 (rm)—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 the Globular Cluster M3, which has an overall visible dimension of about 18″, but a half-mass radius of only 1.12″. 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″. LuminosityIn measuring the luminosity curve of a globular cluster as a function of radius, most clusters in the Milky Way steadily increase in luminosity 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. An example of a core-collapsed globular is M15.[[Image:47tuc_salt.jpg|left|thumb|240px|{{47 Tucanae}} is thesecond most luminous globular cluster in the Milky Way, after {{Omega Centauri}}.]]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. The overall luminosities of the globular clusters within the Milky Way and M31 can be modelled by means of a gaussian curve. This gaussian can be represented by means of an average magnitude Mv and a variance σ. This distribution of globular cluster luminosities is called the Globular Cluster Luminosity Function (GCLF). (For the Milky Way, Mv = âˆ'7.20±0.13, σ=1.1±0.1 magnitudes.) 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 simulationsComputing 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 CPU computational "cost" for a simulation increases in proportion to N3', so the potential computing requirements to accurately simulate such a cluster can be enormous. An efficient method of mathematically simulating the N-body dynamics of a globular cluster is done by sub-dividing 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.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 results in an increase in velocity, some of the stars gain sufficient energy to be able to depart the cluster. Over long periods of time this will result in a dissipation of the cluster, a process termed evaporation. 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 clump-like features. The globular cluster Palomar 5, for example, is near the perihelion 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 will 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. See also*List of globular clusters*Plummer model *Relaxation time ReferencesGeneral resources* NASA Astrophysics Data System has a collection of past articles, from all major astrophysics journals and many conference proceedings.* SCYON is a newsletter dedicated to star clusters. * MODEST is a loose collaboration of scientists working on star clusters. Books* Binney, James; Tremaine, Scott (1987). Galactic Dynamics, Princeton University Press, Princeton, New Jersey.* Heggie, Douglas; Hut, Piet (2003). The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics, Cambridge University Press. * Spitzer, Lyman (1987). Dynamical Evolution of Globular Clusters, Princeton University Press, Princeton, New Jersey. Review Articles* Elson, Rebecca; Hut, Piet; Inagaki, Shogo (1987). Dynamical evolution of globular clusters. Annual review of astronomy and astrophysics 25 565. NASA ADS* Meylan, G.; Heggie, D. C. (1997). Internal dynamics of globular clusters. The Astronomy and Astrophysics Review 8 1. NASA ADS External links* Globular Clusters, SEDS Messier pages* Milky Way Globular Clusters * Catalogue of Milky Way Globular Cluster Parameters by William E. Harris, McMaster University, Ontario, Canada. * A galactic globular cluster database by Marco Castellani, Rome Astronomical Observatory, Italy.
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