{"id":191,"date":"2018-11-19T05:23:29","date_gmt":"2018-11-19T05:23:29","guid":{"rendered":"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=191"},"modified":"2018-11-19T05:57:57","modified_gmt":"2018-11-19T05:57:57","slug":"h-r-diagram-colour-magnitude-diagram","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/chapter\/h-r-diagram-colour-magnitude-diagram\/","title":{"rendered":"H. R. Diagram \u2013 Colour- Magnitude Diagram"},"content":{"raw":"<div>\r\n\r\n&nbsp;\r\n\r\n<strong>1.\u00a0\u00a0Learning Outcomes<\/strong>\r\n\r\n&nbsp;\r\n\r\nAfter studying this module, you should be able to\r\n<ul>\r\n \t<li>recognize the colour-magnitude diagrams of star clusters<\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">note the turn-off points in CM diagrams<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">understand the evolutionary track of a star on the CM diagram<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">calculate the life-time of star on the Main Sequence<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">explain the connection between the turn-off point and the age of a cluster<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">Describe the nature of blue stragglers<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n\r\n<strong><span style=\"text-align: initial;font-size: 1em\">2.\u00a0\u00a0<\/span><\/strong><strong style=\"text-align: initial;font-size: 1em\">Introduction<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In the last few modules we have been discussing H. R. Diagrams and its importance for the astronomer. We found that all the characteristics of a star can be found once the position of the star is known on the H. R. Diagram.\u00a0 If, for example, a star is located on the giant branch then we know it surface temperature, spectral class, mass, radius and the kind of nuclear reactions that are going on in the core of the star. That is why when a new star is discovered, the attempt is to determine its location of the H. R. Diagram.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Since a star of a given spectral class could be a dwarf, giant or a supergiant, we had to find some way to supplement the spectral classification with a classification which would allow us to describe more comprehensively the class of a star. This supplementary classification is called the luminosity classification which we discussed in the last module. The luminosity classification classifies the stars as: I \u2013 Bright Supergiants; II \u2013 Normal Supergiants; III \u2013 Giants; IV \u2013 Subgiants; V \u2013 Main Sequence; VI \u2013 Subdwarfs and VII (or suffix wd) \u2013 White Dwarfs. When we include luminosity classification, a star of spectral class G2 on the main sequence is designated as G2 V.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">We also found that it is easier to find accurately the colour of a star than determining its surface temperature. Moreover, the colour is found to follow faithfully the surface temperature of stars, as we have discussed in earlier modules. Therefore, astronomers find it easier to draw a colour- magnitude diagram rather than the usual H.R. Diagram. \u00a0It turns out that such diagrams for\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">stellar clusters lead to the determination of the ages of clusters. Since the stars of a cluster can be reasonably assumed to have been born together, the stars can differ only in their mass and, to a small extent, chemical composition. The last two characteristics of the stars of a cluster allow us to estimate the ages of clusters, which is the subject of discussion in this module.<\/span><\/p>\r\n\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>3.\u00a0 Colour- Magnitude Diagrams of Stellar Clusters\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Figures 16.1 to 16.4 show the colour\u2013magnitude (CM) diagrams of stellar clusters such as Pleiades, Praesepe (M44), M92, and M67.<\/p>\r\n\r\n<\/div>\r\n<img class=\"aligncenter wp-image-194 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_03-e1542605412998.jpg\" alt=\"\" width=\"1938\" height=\"1518\" \/>\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Fig. 16.1. Colour-Magnitude Diagrams of Pleiades and Praesepe clusters. The turn-off point is shown by an orange dot. (Source: <\/span>http:\/\/www.astronomy.ohio- state.edu\/~pogge\/Ast162\/Unit3\/tests.html<span style=\"text-align: initial;font-size: 1em\">)<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In the case of Pleiades cluster, all the stars appear to lie on the Main Sequence. In the case of Praesepe and other clusters most of the stars again lie on the Main Sequence, but an important point to notice is that a few stars have turned to the right from the main Sequence towards the giant branch.\u00a0 The point at which the stars turn to the right from the Main Sequence is called the <\/span><strong style=\"text-align: initial;font-size: 1em\">turn-off point.\u00a0 <\/strong><span style=\"text-align: initial;font-size: 1em\">In the following figures these points are indicated by orange dots.<\/span><\/p>\r\n<img class=\"aligncenter wp-image-196 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_04-e1542605499111.jpg\" alt=\"\" width=\"1625\" height=\"1526\" \/>\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Fig. 16.2.\u00a0 Colour-Magnitude diagram of open cluster Praesepe (M44). The turn-off is\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">shown by an orange dot. Notice that the y-axis has apparent magnitude. As explained below, each star of the cluster has the same distance modulus; therefore, the apparent magnitude has to be adjusted by a fixed amount to get the absolute magnitude. This adjustment does not affect the shape of the diagram. The stars in the pink strip are giants. The presence of the blue star is important; we shall discuss it later. (Source: <\/span>http:\/\/www.starobserver.eu\/openclusters\/m44.html<span style=\"text-align: initial;font-size: 1em\">)<\/span><\/p>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter wp-image-195 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-e1542605550933.jpg\" alt=\"\" width=\"1402\" height=\"1386\" \/>\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Fig. 16.3.\u00a0 Colour Magnitude diagram of globular cluster M92.\u00a0 Note the turn off point at around colour 0.4. The overlying curves are called the isochrones. They will be discussed below.\u00a0 (Source:\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">http:\/\/www.pnas.org\/<\/span> <span style=\"text-align: initial;font-size: 1em\">content\/94\/13\/6579\/<\/span><span style=\"text-align: initial;font-size: 1em\">F2.expansion.html<\/span><span style=\"text-align: initial;font-size: 1em\">)<\/span><\/p>\r\n\r\n<div>\r\n\r\n<img class=\"aligncenter wp-image-197 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-1-e1542605593100.jpg\" alt=\"\" width=\"1188\" height=\"940\" \/>\r\n\r\n&nbsp;\r\n\r\nFig. 16.4.\u00a0 H. R. Diagram of clusters M67 and NGC188. (Source: https:\/\/en.wikipedia.org\/wiki\/Messier_67#\/media\/File:Open_cluster_HR_diagram_ages.gif)\r\n\r\n<\/div>\r\n<img class=\"aligncenter wp-image-198 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_06-e1542605676455.jpg\" alt=\"\" width=\"2013\" height=\"2565\" \/>\r\n<div>\r\n\r\n<img class=\"aligncenter wp-image-207 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_07-e1542605759876.jpg\" alt=\"\" width=\"1996\" height=\"2376\" \/> <img class=\"aligncenter wp-image-206 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_08-e1542605794461.jpg\" alt=\"\" width=\"1971\" height=\"2615\" \/> <img class=\"aligncenter wp-image-205 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_09-e1542605820585.jpg\" alt=\"\" width=\"1988\" height=\"2714\" \/> <img class=\"aligncenter wp-image-204 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_10-e1542605850538.jpg\" alt=\"\" width=\"1955\" height=\"2475\" \/> <img class=\"aligncenter wp-image-203 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_11-e1542605879319.jpg\" alt=\"\" width=\"2128\" height=\"2475\" \/> <img class=\"aligncenter wp-image-202 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_12-e1542605912486.jpg\" alt=\"\" width=\"1980\" height=\"2681\" \/> <img class=\"aligncenter wp-image-201 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_13-e1542605948185.jpg\" alt=\"\" width=\"1971\" height=\"2763\" \/> <img class=\"aligncenter wp-image-200 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_14-e1542605974767.jpg\" alt=\"\" width=\"1996\" height=\"2392\" \/> <img class=\"aligncenter wp-image-199 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_15-e1542605997588.jpg\" alt=\"\" width=\"2004\" height=\"1971\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n<strong>7.\u00a0 Summary<\/strong>\r\n<ul>\r\n \t<li style=\"text-align: justify\">Stars of a cluster can be assumed to have been born at the same time, so they have the same age. However, stars can differ in their masses. There can be small differences in chemical composition, too.<\/li>\r\n \t<li style=\"text-align: justify\">Stars of different masses have different life-times on the Main Sequence.<\/li>\r\n \t<li style=\"text-align: justify\">After residing on the main sequence, the stars evolve away from the Main Sequence towards the giant branch.<\/li>\r\n \t<li style=\"text-align: justify\">High mass stars evolve faster than the low mass stars.<\/li>\r\n \t<li style=\"text-align: justify\">The turn-off point in the colour-magnitude diagram of a cluster gives the mass of the stars that have started evolving away.<\/li>\r\n \t<li style=\"text-align: justify\">Since the time spent by these stars on the Main Sequence is known, the turn-off point determines the age of the cluster.<\/li>\r\n \t<li style=\"text-align: justify\">A few stars are found on the Main Sequence above the turn-off point. These stars are called blue stragglers, because they are not expected at that position.<\/li>\r\n \t<li style=\"text-align: justify\">It is thought that these stars were initially less massive than the stars at the turn-off point, but accreted mass from their binary companions and found themselves above the turn-off point.<\/li>\r\n \t<li style=\"text-align: justify\">The open or galactic clusters are much younger than the globular cluster populating the central bulge of the galaxy. Their ages vary from a few million to a few billion years.<\/li>\r\n \t<li style=\"text-align: justify\">The ages of globular clusters are in the range 12 \u2013 14 billion years, uncomfortably close the age of the universe itself.<\/li>\r\n \t<li style=\"text-align: justify\">Efforts are being made to determine the ages of clusters more precisely to avoid conflict with the age of the universe.<\/li>\r\n<\/ul>\r\n<div class=\"textLayer\">\r\n\r\n&nbsp;\r\n\r\n<strong>Know More<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The basic material is from Astronomy and Astrophysics with Elements of Cosmology, V. B. Bhatia, Narosa Publishing House, New Delhi, which has been substantially augmented by material from the following sources:<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">http:\/\/www.astronomy.ohio-state.edu\/~pogge\/Ast162\/Unit3\/tests.html<\/p>\r\n<p style=\"text-align: justify\">http:\/\/www.starobserver.eu\/openclusters\/m44.html<\/p>\r\n<p style=\"text-align: justify\">http:\/\/www.pnas.org\/content\/94\/13\/6579\/F2.expansion.html<\/p>\r\n<p style=\"text-align: justify\">https:\/\/en.wikipedia.org\/wiki\/Messier_67#\/media\/File:Open_cluster_HR_diagram_ages.gif<\/p>\r\n<p style=\"text-align: justify\">http:\/\/sci.esa.int\/education\/36828-stellar-processes-and-evolution\/?fbodylongid=1742<\/p>\r\n<p style=\"text-align: justify\">Australia Telescope Outreach and Education<\/p>\r\n<p style=\"text-align: justify\">https:\/\/www.wikiwand.com\/en\/Red-giant_branch<\/p>\r\n<p style=\"text-align: justify\">http:\/\/abyss.uoregon.edu\/~js\/ast122\/lectures\/lec15.html<\/p>\r\n<p style=\"text-align: justify\">https:\/\/ned.ipac.caltech.edu\/level5\/March03\/Vandenberg\/Vandenberg3.html<\/p>\r\n<p style=\"text-align: justify\">http:\/\/rml3.com\/a20p\/mainseqfitting.htm<\/p>\r\n<p style=\"text-align: justify\">http:\/\/www.astro.caltech.edu\/~george\/ay1\/lec_pdf\/Ay1_Lec09.pdf<\/p>\r\n<p style=\"text-align: justify\">http:\/\/burro.cwru.edu\/academics\/Astr221\/LifeCycle\/clusters.html<\/p>\r\n<p style=\"text-align: justify\">https:\/\/www.e-education.psu.edu\/astro801\/content\/l7_p6.html<\/p>\r\n<p style=\"text-align: justify\">http:\/\/applet-magic.com\/virialth.htm<\/p>\r\n<p style=\"text-align: justify\">http:\/\/coolcosmos.ipac.caltech.edu\/cosmic_classroom\/cosmic_reference\/molecular_clouds.html<\/p>\r\n\r\n<\/div>\r\n<div class=\"annotationLayer\"><\/div>","rendered":"<div>\n<p>&nbsp;<\/p>\n<p><strong>1.\u00a0\u00a0Learning Outcomes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>After studying this module, you should be able to<\/p>\n<ul>\n<li>recognize the colour-magnitude diagrams of star clusters<\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">note the turn-off points in CM diagrams<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">understand the evolutionary track of a star on the CM diagram<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">calculate the life-time of star on the Main Sequence<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">explain the connection between the turn-off point and the age of a cluster<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">Describe the nature of blue stragglers<\/span><\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<p><strong><span style=\"text-align: initial;font-size: 1em\">2.\u00a0\u00a0<\/span><\/strong><strong style=\"text-align: initial;font-size: 1em\">Introduction<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In the last few modules we have been discussing H. R. Diagrams and its importance for the astronomer. We found that all the characteristics of a star can be found once the position of the star is known on the H. R. Diagram.\u00a0 If, for example, a star is located on the giant branch then we know it surface temperature, spectral class, mass, radius and the kind of nuclear reactions that are going on in the core of the star. That is why when a new star is discovered, the attempt is to determine its location of the H. R. Diagram.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Since a star of a given spectral class could be a dwarf, giant or a supergiant, we had to find some way to supplement the spectral classification with a classification which would allow us to describe more comprehensively the class of a star. This supplementary classification is called the luminosity classification which we discussed in the last module. The luminosity classification classifies the stars as: I \u2013 Bright Supergiants; II \u2013 Normal Supergiants; III \u2013 Giants; IV \u2013 Subgiants; V \u2013 Main Sequence; VI \u2013 Subdwarfs and VII (or suffix wd) \u2013 White Dwarfs. When we include luminosity classification, a star of spectral class G2 on the main sequence is designated as G2 V.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">We also found that it is easier to find accurately the colour of a star than determining its surface temperature. Moreover, the colour is found to follow faithfully the surface temperature of stars, as we have discussed in earlier modules. Therefore, astronomers find it easier to draw a colour- magnitude diagram rather than the usual H.R. Diagram. \u00a0It turns out that such diagrams for\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">stellar clusters lead to the determination of the ages of clusters. Since the stars of a cluster can be reasonably assumed to have been born together, the stars can differ only in their mass and, to a small extent, chemical composition. The last two characteristics of the stars of a cluster allow us to estimate the ages of clusters, which is the subject of discussion in this module.<\/span><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>3.\u00a0 Colour- Magnitude Diagrams of Stellar Clusters\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Figures 16.1 to 16.4 show the colour\u2013magnitude (CM) diagrams of stellar clusters such as Pleiades, Praesepe (M44), M92, and M67.<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-194 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_03-e1542605412998.jpg\" alt=\"\" width=\"1938\" height=\"1518\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_03-e1542605412998.jpg 1938w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_03-e1542605412998-300x235.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_03-e1542605412998-768x602.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_03-e1542605412998-1024x802.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_03-e1542605412998-65x51.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_03-e1542605412998-225x176.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_03-e1542605412998-350x274.jpg 350w\" sizes=\"auto, (max-width: 1938px) 100vw, 1938px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Fig. 16.1. Colour-Magnitude Diagrams of Pleiades and Praesepe clusters. The turn-off point is shown by an orange dot. (Source: <\/span>http:\/\/www.astronomy.ohio- state.edu\/~pogge\/Ast162\/Unit3\/tests.html<span style=\"text-align: initial;font-size: 1em\">)<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In the case of Pleiades cluster, all the stars appear to lie on the Main Sequence. In the case of Praesepe and other clusters most of the stars again lie on the Main Sequence, but an important point to notice is that a few stars have turned to the right from the main Sequence towards the giant branch.\u00a0 The point at which the stars turn to the right from the Main Sequence is called the <\/span><strong style=\"text-align: initial;font-size: 1em\">turn-off point.\u00a0 <\/strong><span style=\"text-align: initial;font-size: 1em\">In the following figures these points are indicated by orange dots.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-196 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_04-e1542605499111.jpg\" alt=\"\" width=\"1625\" height=\"1526\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_04-e1542605499111.jpg 1625w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_04-e1542605499111-300x282.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_04-e1542605499111-768x721.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_04-e1542605499111-1024x962.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_04-e1542605499111-65x61.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_04-e1542605499111-225x211.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_04-e1542605499111-350x329.jpg 350w\" sizes=\"auto, (max-width: 1625px) 100vw, 1625px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Fig. 16.2.\u00a0 Colour-Magnitude diagram of open cluster Praesepe (M44). The turn-off is\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">shown by an orange dot. Notice that the y-axis has apparent magnitude. As explained below, each star of the cluster has the same distance modulus; therefore, the apparent magnitude has to be adjusted by a fixed amount to get the absolute magnitude. This adjustment does not affect the shape of the diagram. The stars in the pink strip are giants. The presence of the blue star is important; we shall discuss it later. (Source: <\/span>http:\/\/www.starobserver.eu\/openclusters\/m44.html<span style=\"text-align: initial;font-size: 1em\">)<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-195 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-e1542605550933.jpg\" alt=\"\" width=\"1402\" height=\"1386\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-e1542605550933.jpg 1402w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-e1542605550933-300x297.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-e1542605550933-768x759.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-e1542605550933-1024x1012.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-e1542605550933-65x64.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-e1542605550933-225x222.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-e1542605550933-350x346.jpg 350w\" sizes=\"auto, (max-width: 1402px) 100vw, 1402px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Fig. 16.3.\u00a0 Colour Magnitude diagram of globular cluster M92.\u00a0 Note the turn off point at around colour 0.4. The overlying curves are called the isochrones. They will be discussed below.\u00a0 (Source:\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">http:\/\/www.pnas.org\/<\/span> <span style=\"text-align: initial;font-size: 1em\">content\/94\/13\/6579\/<\/span><span style=\"text-align: initial;font-size: 1em\">F2.expansion.html<\/span><span style=\"text-align: initial;font-size: 1em\">)<\/span><\/p>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-197 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-1-e1542605593100.jpg\" alt=\"\" width=\"1188\" height=\"940\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-1-e1542605593100.jpg 1188w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-1-e1542605593100-300x237.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-1-e1542605593100-768x608.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-1-e1542605593100-1024x810.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-1-e1542605593100-65x51.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-1-e1542605593100-225x178.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_05-1-e1542605593100-350x277.jpg 350w\" sizes=\"auto, (max-width: 1188px) 100vw, 1188px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Fig. 16.4.\u00a0 H. R. Diagram of clusters M67 and NGC188. (Source: https:\/\/en.wikipedia.org\/wiki\/Messier_67#\/media\/File:Open_cluster_HR_diagram_ages.gif)<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-198 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_06-e1542605676455.jpg\" alt=\"\" width=\"2013\" height=\"2565\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_06-e1542605676455.jpg 2013w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_06-e1542605676455-235x300.jpg 235w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_06-e1542605676455-768x979.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_06-e1542605676455-804x1024.jpg 804w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_06-e1542605676455-65x83.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_06-e1542605676455-225x287.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_06-e1542605676455-350x446.jpg 350w\" sizes=\"auto, (max-width: 2013px) 100vw, 2013px\" \/><\/p>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-207 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_07-e1542605759876.jpg\" alt=\"\" width=\"1996\" height=\"2376\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_07-e1542605759876.jpg 1996w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_07-e1542605759876-252x300.jpg 252w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_07-e1542605759876-768x914.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_07-e1542605759876-860x1024.jpg 860w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_07-e1542605759876-65x77.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_07-e1542605759876-225x268.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_07-e1542605759876-350x417.jpg 350w\" sizes=\"auto, (max-width: 1996px) 100vw, 1996px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-206 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_08-e1542605794461.jpg\" alt=\"\" width=\"1971\" height=\"2615\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_08-e1542605794461.jpg 1971w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_08-e1542605794461-226x300.jpg 226w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_08-e1542605794461-768x1019.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_08-e1542605794461-772x1024.jpg 772w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_08-e1542605794461-65x86.jpg 65w, 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src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_10-e1542605850538.jpg\" alt=\"\" width=\"1955\" height=\"2475\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_10-e1542605850538.jpg 1955w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_10-e1542605850538-237x300.jpg 237w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_10-e1542605850538-768x972.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_10-e1542605850538-809x1024.jpg 809w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_10-e1542605850538-65x82.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_10-e1542605850538-225x285.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_10-e1542605850538-350x443.jpg 350w\" sizes=\"auto, (max-width: 1955px) 100vw, 1955px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-203 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_11-e1542605879319.jpg\" alt=\"\" width=\"2128\" height=\"2475\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_11-e1542605879319.jpg 2128w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_11-e1542605879319-258x300.jpg 258w, 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src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_12-e1542605912486.jpg\" alt=\"\" width=\"1980\" height=\"2681\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_12-e1542605912486.jpg 1980w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_12-e1542605912486-222x300.jpg 222w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_12-e1542605912486-768x1040.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_12-e1542605912486-756x1024.jpg 756w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_12-e1542605912486-65x88.jpg 65w, 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https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_13-e1542605948185-768x1077.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_13-e1542605948185-730x1024.jpg 730w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_13-e1542605948185-65x91.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_13-e1542605948185-225x315.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_13-e1542605948185-350x491.jpg 350w\" sizes=\"auto, (max-width: 1971px) 100vw, 1971px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-200 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_14-e1542605974767.jpg\" alt=\"\" width=\"1996\" height=\"2392\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_14-e1542605974767.jpg 1996w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_14-e1542605974767-250x300.jpg 250w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_14-e1542605974767-768x920.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_14-e1542605974767-854x1024.jpg 854w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_14-e1542605974767-65x78.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_14-e1542605974767-225x270.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_14-e1542605974767-350x419.jpg 350w\" sizes=\"auto, (max-width: 1996px) 100vw, 1996px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-199 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_15-e1542605997588.jpg\" alt=\"\" width=\"2004\" height=\"1971\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_15-e1542605997588.jpg 2004w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_15-e1542605997588-300x295.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_15-e1542605997588-768x755.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_15-e1542605997588-1024x1007.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_15-e1542605997588-65x64.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_15-e1542605997588-225x221.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530564Module16Text_Page_15-e1542605997588-350x344.jpg 350w\" sizes=\"auto, (max-width: 2004px) 100vw, 2004px\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p><strong>7.\u00a0 Summary<\/strong><\/p>\n<ul>\n<li style=\"text-align: justify\">Stars of a cluster can be assumed to have been born at the same time, so they have the same age. However, stars can differ in their masses. There can be small differences in chemical composition, too.<\/li>\n<li style=\"text-align: justify\">Stars of different masses have different life-times on the Main Sequence.<\/li>\n<li style=\"text-align: justify\">After residing on the main sequence, the stars evolve away from the Main Sequence towards the giant branch.<\/li>\n<li style=\"text-align: justify\">High mass stars evolve faster than the low mass stars.<\/li>\n<li style=\"text-align: justify\">The turn-off point in the colour-magnitude diagram of a cluster gives the mass of the stars that have started evolving away.<\/li>\n<li style=\"text-align: justify\">Since the time spent by these stars on the Main Sequence is known, the turn-off point determines the age of the cluster.<\/li>\n<li style=\"text-align: justify\">A few stars are found on the Main Sequence above the turn-off point. These stars are called blue stragglers, because they are not expected at that position.<\/li>\n<li style=\"text-align: justify\">It is thought that these stars were initially less massive than the stars at the turn-off point, but accreted mass from their binary companions and found themselves above the turn-off point.<\/li>\n<li style=\"text-align: justify\">The open or galactic clusters are much younger than the globular cluster populating the central bulge of the galaxy. Their ages vary from a few million to a few billion years.<\/li>\n<li style=\"text-align: justify\">The ages of globular clusters are in the range 12 \u2013 14 billion years, uncomfortably close the age of the universe itself.<\/li>\n<li style=\"text-align: justify\">Efforts are being made to determine the ages of clusters more precisely to avoid conflict with the age of the universe.<\/li>\n<\/ul>\n<div class=\"textLayer\">\n<p>&nbsp;<\/p>\n<p><strong>Know More<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The basic material is from Astronomy and Astrophysics with Elements of Cosmology, V. B. Bhatia, Narosa Publishing House, New Delhi, which has been substantially augmented by material from the following sources:<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">http:\/\/www.astronomy.ohio-state.edu\/~pogge\/Ast162\/Unit3\/tests.html<\/p>\n<p style=\"text-align: justify\">http:\/\/www.starobserver.eu\/openclusters\/m44.html<\/p>\n<p style=\"text-align: justify\">http:\/\/www.pnas.org\/content\/94\/13\/6579\/F2.expansion.html<\/p>\n<p style=\"text-align: justify\">https:\/\/en.wikipedia.org\/wiki\/Messier_67#\/media\/File:Open_cluster_HR_diagram_ages.gif<\/p>\n<p style=\"text-align: justify\">http:\/\/sci.esa.int\/education\/36828-stellar-processes-and-evolution\/?fbodylongid=1742<\/p>\n<p style=\"text-align: justify\">Australia Telescope Outreach and Education<\/p>\n<p style=\"text-align: justify\">https:\/\/www.wikiwand.com\/en\/Red-giant_branch<\/p>\n<p style=\"text-align: justify\">http:\/\/abyss.uoregon.edu\/~js\/ast122\/lectures\/lec15.html<\/p>\n<p style=\"text-align: justify\">https:\/\/ned.ipac.caltech.edu\/level5\/March03\/Vandenberg\/Vandenberg3.html<\/p>\n<p style=\"text-align: justify\">http:\/\/rml3.com\/a20p\/mainseqfitting.htm<\/p>\n<p style=\"text-align: justify\">http:\/\/www.astro.caltech.edu\/~george\/ay1\/lec_pdf\/Ay1_Lec09.pdf<\/p>\n<p style=\"text-align: justify\">http:\/\/burro.cwru.edu\/academics\/Astr221\/LifeCycle\/clusters.html<\/p>\n<p style=\"text-align: justify\">https:\/\/www.e-education.psu.edu\/astro801\/content\/l7_p6.html<\/p>\n<p style=\"text-align: justify\">http:\/\/applet-magic.com\/virialth.htm<\/p>\n<p style=\"text-align: justify\">http:\/\/coolcosmos.ipac.caltech.edu\/cosmic_classroom\/cosmic_reference\/molecular_clouds.html<\/p>\n<\/div>\n<div class=\"annotationLayer\"><\/div>\n","protected":false},"author":4,"menu_order":11,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-v-b-bhatia"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-191","chapter","type-chapter","status-publish","hentry","contributor-prof-v-b-bhatia"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/191","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/users\/4"}],"version-history":[{"count":4,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/191\/revisions"}],"predecessor-version":[{"id":209,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/191\/revisions\/209"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/191\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/media?parent=191"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapter-type?post=191"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/contributor?post=191"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/license?post=191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}