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Star Cluster Star Cluster Shashikant Joint Astronomy Program Student Department Of Physics Indian Institute Of Science,Bangalore. December 10, 2003 1 Contents 1 Introduction 4 2 Color Magnitude Diagram Of Globular Cluster 4 2.1 Main Sequence . 4 2.2 Red Giant Branch . 6 2.3 Horizontal Branch . 7 2.4 Asymptotic Giant Branch and Beyond . 8 2.5 Blue Stragglers . 8 3 Globular Cluster Ages 9 4 Chemical Properties 10 5 binaries and stellar remnants 10 6 radii of globular clusters 11 6.1 core radius . 11 6.2 median radius . 12 6.3 tidal radius . 12 7 time scales in the evolution of globular clusters 13 7.1 orbital time scale . 13 7.2 relaxation time . 13 8 Fokker Planck description and evaporation time of cluster 14 8.1 Fokker Planck description . 14 8.2 evaporation of globular cluster . 16 9 binary stars in globular clusters 17 10 disk shocking 18 11 formation of globular clusters 19 2 Abstract In this article i am introducing some features of star clusters.I have discussed mostly globular clusters as open Custer's are open question today.Globular clusters are the oldest in milky way , their chemical properties are almost similar. Finally i have tried to discus the theoretical models to describe the main properties of globular clusters. 3 1 Introduction We know that stars are formed in gaseous clouds. When stars formed in a cloud it seems reasonable to expect that there will be a tendency for a large number of them to be close together and hence they form star clusters. Clusters are divided into two broad categories known as open cluster and globular cluster. Open clusters are made up of population I stars. These clusters are found in galactic disk. They are relatively young objects. Their median age is around 108 years. Some observations suggests that formation of open clusters is an ongoing process. These clusters are small in size . They contain 102 to 103 stars in a region of size 1 to 10 pc. There are 105 open clusters in milky way. Since these clusters are found in galactic disk, it is hard to identify them.This is the reason that we do not have much more knowledge about open clusters. On the other hand globular clusters are quite old.They are made up of population II stars. A typical globular cluster contain 104 106 stars ! within a median radius of 10 pc. There age is around 1010 years. Glob- ular clusters are spherical in shape but these spheres are inhomogeneous and concentrated toward center. 2 Color Magnitude Diagram Of Globular Clus- ter Figure 1 shows the C.M. diagram of a globular cluster. It illustrates a number of basic features of globular cluster C.M. diagram. These include the main sequence, The giant branch, and the horizontal branch, each of which is discussed in the following subsections. 2.1 Main Sequence One of the key features of globular clusters is the well-defined Main Sequence extending from the turn-off to fainter magnitudes and redder colors. Globu- lar cluster stars on the main sequence derive their energy from the conversion of hydrogen to helium in the stellar core. the low luminosity end of the main sequence is determined by the magnitude limit of the observations. (there is 4 Figure 1: this figure shows the color magnitude diagram of M5 globular cluster also a theoretical lower limit to the main sequence corresponding to a stel- lar mass around 0:08M , Below which hydrogen burning no longer takes place in the stellar core.) A characteristic feature of the color-magnitude di- agrams of galactic globular clusters is that the turn-off of the main sequence occurs at fainter luminosities than for most star clusters in the solar neigh- borhood. This was first established by sandage arp, and others [1]. It was soon realized that the fainter luminosity of the main-sequence turn-off indi- cated that these globular clusters are old [2, 21] In the cores of more massive stars,Hydrogen is exhausted more rapidly,so that older stellar populations have main-sequence turn-offs at lower stellar masses and thus luminosities. As discussed in more detail later studies of the location of the main-sequence turn off in well studied galactic globular clusters give turn off masses of about 0:8M and corresponding ages of roughly 15 gyr. The sharp main sequence turn off of M5 is typical of globular cluster color-magnitude diagrams, Indicating that the stars within an individual globular cluster all formed at roughly the same time. another well studied cluster is M92 . The form of the main sequence turn off in M92 limits the age 5 spread between the constituent stars to about2:4% of the age of this cluster, or around 0:4 Gyr . Figure 1 illustrates another characteristic of globular cluster main sequences- they are very narrow. This narrowness indicates that all the stars in the globular cluster have a very similar chemical composition. It also constrains the fraction of binary stars within globular clusters. Unresolved binaries are expected to produce a population just above the main sequence, since the combined luminosity of the two stars exceeds that of a single star at the same color. (however, if the primary and secondary have significantly differ- ent masses, this effect is difficult to detect.) There are globular clusters where such a population of binaries has been detected, Such as NGC288 , where the inferred binary fraction is around 10% [5].Future observations,particularly with Hubble Space Telescope are likely to result in better constraints on the binary fraction in more globular clusters [6]. 2.2 Red Giant Branch - The red giant branch (RGB) in globular clusters extends from the subgiants which connect it to the main sequence to brighter magnitudes and redder colors until the tip of the RGB is reached. Observational properties and characteristics of the RGB , As well as a survey of earlier literature, are given by stetson (1993) . While the detailed evolution of stars on the RGB is a complicated topic, The salient feature is that such stars possess hydrogen- burning shells, which advance outward as they ascend the giant branch. the ascent is terminated by the ignition of the degenerate helium core which forms in the center of a star during this period of its evolution. Details of theoretical studies of this process are reviewed by Iben (1974) and Renzini (1977) . Like the main sequence, the RGB of most individual globular clusters is narrow and well defined, placing limits on chemical in homogeneities, and on variation in stellar physics among stars on the RGB. A comparison of the RGBs of different clusters reveals that globular clusters of higher metallicity exhibit giant branches that are shallower and redder than low metallicity clusters [7]. Like stars on the main sequence, higher metallicity giant stars have increased opacity, due to electrons from metals, which allows stars to maintain equilibrium at a lower temperature. the astrophysics of stars on the RGB is complex, and the exact location of the RGB is dependent on mass 6 loss rates and the details of the convective processes within such stars, often treated in terms of\mixing length theory" [8]. 2.3 Horizontal Branch The horizontal branch is composed of stars with helium burning cores which have evolved off the RGB. The horizontal branch is identified on color mag- nitude diagrams as a strip of stars. bluer than the RGB and brighter than the main sequence, which have a range of colors but similar luminosities(thus horizontal on the usual color magnitude diagram). The presence of RR Lyrae variables within the instability strip or RR Lyre gap on the horizontal branch is a defining feature of population II stars. A color magnitude diagram of the population I stars of the galactic disk is free of stars in this region. The horizontal branch of globular clusters has a particular importance on understanding these systems,As well as shedding light on stellar and galactic evolution. a simple method of describing the morphology of the horizontal branch is through a measure of the relative numbers of stars blueward and redward of the RR Lyrae gap. One way of quantifying this is through the parameter: C = (B R)=(B + V + R) (1) − Where B is the number of stars on the horizontal branch on the blue side of the RR Lyrae gap, R the number of stars on the red side, and V is the number of variables on the horizontal branch . In order to explain the detailed location of stars on the horizontal branch, it has been known for some time that mass loss during the earlier RGB phase must be invoked [9]. Observationally, the horizontal branch morphology (i.e., the color distri- bution of horizontal branch stars) of milky way globulars exhibits a broad range, and is determined by a number of physical effects. in general, the most important parameter is the metallicity of the cluster. Horizontal branch stars of higher metallicity are redder than those of lower metallicity as a re- sult of higher opacity on their envelopes. Metallicity is therefore the ”first parameter" in determining horizontal branch morphology. There are other parameters like age, helium abundance etc. 7 2.4 Asymptotic Giant Branch and Beyond When the helium in the core of a horizontal branch star is exhausted, The core contracts and helium begins burning in a shell around the core. Beyond this helium shell is the hydrogen burning shell. The increase in energy gen- eration means that the star ascends the giant branch for the second time. This second ascent is known as the asymptotic giant branch (AGB) phase of stellar evolution.
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