{"id":110,"date":"2018-11-16T11:22:05","date_gmt":"2018-11-16T11:22:05","guid":{"rendered":"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=110"},"modified":"2018-11-16T12:17:11","modified_gmt":"2018-11-16T12:17:11","slug":"stellar-spectra-and-stellar-classification-contd","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/chapter\/stellar-spectra-and-stellar-classification-contd\/","title":{"rendered":"Stellar Spectra and Stellar Classification (Contd)"},"content":{"raw":"<div>\r\n\r\n&nbsp;\r\n\r\n<strong>1.\u00a0 Learning 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>appreciate that there is great diversity in stellar spectra and all stars cannot be accommodated in the eight major classes O, B, A, F, G, K and M<\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">describe the new classes Q, P and W (Wolf-Rayet Stars) introduced before class O<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">state special features of Wolf-Rayet stars<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">name the suffixes and prefixes which are used to describe the characteristic features of some stars<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">explain the insertion of new classes like R, N and S classes after M stars<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">appreciate that R and N stars have bands of carbon compounds while the S stars have bands of ZrO<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">understand that the Harvard classification scheme is based on the decreasing surface temperature from class O to M<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">derive the expression for the fraction of hydrogen atoms in excited states<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n\r\n<span style=\"text-align: initial;font-size: 1em\"><strong>2.\u00a0\u00a0<\/strong> <\/span><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 module (Module 11) we introduced the spectral classification of stars. We explained the nature of the spectra as that containing mainly absorption lines. \u00a0We discussed the variety in the spectra of stars.\u00a0 Even within this variety it was possible to discern patterns.\u00a0 There are stars with a very few lines. On the other hand, there are stars with huge number of lines and molecular bands. On the basis of the increasing complexity in the stellar spectra, Annie Cannon was able to devise a simple classification scheme, known as Harvard Stellar Classification System. Seven major classes, O, B, A, F, G, K, and M were identified on the basis of their spectra.\u00a0 Each major class was subdivided into ten sub-classes. For example, class A9 is followed by F0, which, in turn, is followed by F2.\u00a0 It was pointed out that the stars belonging to the first three major classes, that is, classes O, B and A are called the early type stars, while the stars belonging to the last four major classes are referred to as late type stars. Stellar spectra are much more diverse than we have noticed so far. We now dwell upon this complexity. Later, following M. N. Saha, we will attempt to account for the classification scheme in terms of the decreasing stellar surface temperature.<\/span><\/p>\r\n\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>3.\u00a0 Diversity in Stellar Spectra\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The stellar spectra show more complexity and diversity than we took notice of in the last module. Therefore, the spectral classification outlined above is not adequate to describe all the observed spectra. Three major classes (to which decimal subdivision is not applicable) before class O, and many prefixes and suffixes are used in conjuction with the spectral classes to describe comprehensively the spectra of many stars.<\/p>\r\n&nbsp;\r\n\r\n<strong>3.1.\u00a0 Wolf-Rayet Stars\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The classes placed before O are Q, P and W, all hot stars showing emission lines.\u00a0 P stands for <strong>planetary nebula<\/strong>, believed to be the stage in the evoltion of a star just before it becomes a white dwarf star.\u00a0 W stars are <strong>Wolf-Rayet stars<\/strong>, named after two the French astronomers who studied them.\u00a0 The Wolf-Rayet stars show in their spectra broad and intense emission lines of ionized carbon, nitrogen and helium.<\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-125\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.1.png\" alt=\"\" width=\"715\" height=\"485\" \/>\r\n<p style=\"text-align: center\">Fig. 12.1.\u00a0 Spectra of Wolf Rayet star WR137.\u00a0 Notice the intense emission lines of ionized carbon. (Source: \u00a0Source: Wikipedia - Spectrum of Wolf-Rayet star WR137 by Gypaete )<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Wolf-Rayet stars are very hot stars, Their surface temperatures range from ~ 30000 K to ~ 50000 K.\u00a0 These stars are very luminous; the mean absolute magnitude is ~ -5.\u00a0 They are about 10 times as massive as the Sun.\u00a0 The stars of this mass tend to have very strong stellar winds.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">These winds blow away as much matter as 10-4 ?\u2a00 per year, leaving behind a thin atmosphere, through which we are able to observe the central region of the star. This region is rich in carbon\u00a0and nitrogen.\u00a0 It appears, therefore, that the Wolf-Rayet stars are helium burning stars (second stage after hydrogen burning), producing carbon and nitrogen whose lines we see in their spectra. The central temperatures may be of the order of 108 K.\u00a0 Clearly, Wolf-Rayet is a stage in the evolution of a star, lasting a few hundred thousand years.<\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-124\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.2.png\" alt=\"\" width=\"699\" height=\"401\" \/>\r\n<p style=\"text-align: center\">Fig. 12.2.\u00a0 After hydrogen burning in the core of the star is complete, the temperature rises to 108 K.\u00a0 At this temperature helium burning can commence to supply the energy need by the star to radiate from the surface.<\/p>\r\n&nbsp;\r\n\r\n<strong>3.2. Scheme of Prefixes and Suffixes to Denote Special Characteristics of Spectra\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">An example of a prefix attached to the spectral class of a star is <strong>c <\/strong>which denotes that most of the lines in the star\u2019s spectrum have narrow profiles, such as in the star \u03b1 \u2013 Cygni.\u00a0 Some of the other prefixes and suffixes used are the following:<\/p>\r\n&nbsp;\r\n\r\n<strong>n <\/strong>\u2013 denotes wide and diffuse lines;\r\n<p style=\"text-align: justify\"><strong>s <\/strong>\u2013 used in spectral classes B and A to denote lines of narrow profiles (but not as narrow as denoted by the prefix <strong>c<\/strong>);<\/p>\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">e <\/strong><span style=\"text-align: initial;font-size: 1em\">\u2013 denotes the appearance of emmission lines in the classes O to M where they are not normally expected.\u00a0 The prefix appearing in classes O and B means that Blamer lines of hydrogen are in emission;<\/span><\/p>\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">v <\/strong><span style=\"text-align: initial;font-size: 1em\">\u2013 denotes the variable spectrum and ev denotes the variable emission spectrum;<\/span><\/p>\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">k <\/strong><span style=\"text-align: initial;font-size: 1em\">\u2013 denotes the presence of H and K lines of Ca<\/span><strong style=\"text-align: initial;font-size: 1em\">+<\/strong><span style=\"text-align: initial;font-size: 1em\">;<\/span><\/p>\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">p <\/strong><span style=\"text-align: initial;font-size: 1em\">\u2013 denotes that the spectrum contains peculiarities not normally found in the spectral class in which the spectrum is classified. In certain stars of class A, for example, the tines of SiII and SrII are exceptionally strong.\u00a0 These stars are designated as Ap stars.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>3.3.\u00a0 Addition of Classes R, N and S to the Major Spectral Types\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Recall that the late type stars show characteristic bands of TiO molecules. However, a few late type stars are distinguished by the fact that they show strong bands of C, CH and CN, but not of TiO which are so prominent in class M. These stars are classified as <strong>R <\/strong>and <strong>N stars <\/strong>and are called <strong>carbon stars<\/strong>.\u00a0 On the other hand, there is a class of stars which show bands due to ZrO, LaO and YtO.\u00a0 These are called <strong>S stars<\/strong>.\u00a0 The bands of ZrO are the defining feature of these stars. The S stars are variable stars with long periods. They are also quite small in number. \u00a0With the addition of these classes, the complete classification is sometimes written as<\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-123\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.3.png\" alt=\"\" width=\"700\" height=\"205\" \/><img class=\"aligncenter size-full wp-image-122\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.4.png\" alt=\"\" width=\"441\" height=\"390\" \/>\r\n<p style=\"text-align: center\">Fig. 12.3.\u00a0 HST image of W Aquilae, a Mira variable star, showing the faint companion.\u00a0 (Source:\u00a0 Wikipedia; Hubble Legacy Archive image constructed from blue (F435W) and green\/red (F606W) exposures.)<\/p>\r\n<img class=\"aligncenter size-full wp-image-121\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.5.png\" alt=\"\" width=\"520\" height=\"375\" \/>\r\n<p style=\"text-align: center\">Fig. 12.4. Spectra of R, N and S stars along with the other major classes. (Source: http:\/\/prc.nao.ac.jp\/extra\/uos\/ja\/no04\/ )<\/p>\r\n<img class=\"aligncenter size-full wp-image-120\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.6.png\" alt=\"\" width=\"745\" height=\"533\" \/>\r\n\r\n<\/div>\r\n<p style=\"text-align: center\"><span style=\"text-align: initial;font-size: 1em\">Fig. 12.5. Spectra of two S-Type stars.\u00a0 Notice bands due to ZrO, the distinguishing feature of S stars.\u00a0 (Source: htt ps:\/\/ned.ipac.cal tech.edu\/level5\/Gray\/Gray31.html\u00a0 )<\/span><\/p>\r\n\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>4.\u00a0 Surface Temperature and Spectral Classification \u2013\u00a0 Saha\u2019s\u00a0 Theory\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">We have already noted that spectral sequence from simple to complex spectra is a temperature sequence. At the top of the sequence, the surface temperature of O stars is so high that most atoms are ionized. The exception is HeII, which is difficult to ionize a second time. So, these stars show only lines of HeII and a few other lines.\u00a0 As we progress to lower temperatures, first we encounter lines of hydrogen (class A) which has a high ionization potential, and then ionized metal atoms (classes F, G and K).\u00a0 At still lower surface temperatures, even metal atoms cannot\u00a0<span style=\"font-size: 1em;text-align: initial\">be ionized, so we have neutral metal atoms. In classes K and M, the surface temperatures are so low that even molecules cannot be dissociated.\u00a0 In the spectra of these classes we have molecular lines in addition to a host of neutral atom lines.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">M. N. Saha, grasped the true meaning of the spectral sequences. He pointed out that the ionization process is like a chemical reaction and is subject to the same conditions of equilibrium as is a chemical reaction. \u00a0This notion leads immediately to relative numbers of atoms in various stages of ionization existing in equilibrium at a given temperature.\u00a0 Since the intensity of an absorption line is proportional to the number of atoms which can absorb radiation corresponding to this line, and this number being a function of temperature, the intensity of various lines is obtained as a function of temperature. \u00a0This, then, allows us to understand the spectral classification as classification based on surface temperature of stars.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>4.1.\u00a0 LTE and Boltzmann Law of Population of Excited Atomic States\u00a0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Consider an assembly of various kinds of non-interacting or weakly interacting particles in statistical equilibrium at a certain temperature \ufffd.\u00a0 This implies that the assembly is in thermodynamic equilibrium (TE).\u00a0 TE implies thermal, mechanical and chemical equilibria.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">However, as we shall discuss later, these conditions are not generally satisfied in stars. The conditions may be very close to TE, and we may assume that TE exists. Such equilibrium is termed as <strong>local thermodynamic equilibrium <\/strong>(LTE), to be discussed later.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">The number of particles of a given kind in energy range ?and ?+ \ufffd?is given by the usual distribution law:<\/p>\r\n<img class=\"wp-image-119 alignnone\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.7.png\" alt=\"\" width=\"599\" height=\"75\" \/>\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Here d? is the <\/span><strong style=\"text-align: initial;font-size: 1em\">statistical weight <\/strong><span style=\"text-align: initial;font-size: 1em\">or the number of possible quantum states of a single typical\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">particle of the chosen kind between energies ?and ?+ d?. For a non-interacting system, the\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">kind assumed here, the quantum states of a particle of the chosen kind can be enumerated as if\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">the particles of other kinds were not present. The negative sign in the denominator of Equation\u00a0<\/span><\/p>\r\n\r\n<\/div>\r\n<img class=\"aligncenter wp-image-131\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.8.png\" alt=\"\" width=\"800\" height=\"1066\" \/>\r\n\r\n<img class=\"aligncenter wp-image-130\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.9.png\" alt=\"\" width=\"808\" height=\"1079\" \/>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-129\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.10.png\" alt=\"\" width=\"882\" height=\"1108\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-128\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.11.png\" alt=\"\" width=\"854\" height=\"1093\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-127\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.12.png\" alt=\"\" width=\"872\" height=\"523\" \/>\r\n\r\n<\/div>\r\n<div>\r\n\r\n&nbsp;\r\n\r\n<strong>Summary\u00a0<\/strong>\r\n<ul>\r\n \t<li>Because of very high diversity in stellar spectra, all spectra cannot be accommodated in the eight major classes of the Harvard System.<\/li>\r\n \t<li>Classes Q, P and W (Wolf-Rayet) are added before class O.<\/li>\r\n \t<li>Wolf-Rayet stars are very hot stars and contain broad and intense emission lines.<\/li>\r\n \t<li>The mass of these stars is ~ 10 <span style=\"text-align: initial;font-size: 1em\">?\u2a00<\/span>.\u00a0 These stars have very strong winds.<\/li>\r\n \t<li>It is possible that the Wolf-Rayet stars are helium burning stars and represent a\u00a0stage in the life of a star.<\/li>\r\n \t<li>There are several suffixes and prefixes which are used to denote the spectral characteristics of stars.<\/li>\r\n \t<li>A few late type stars are distinguished by strong bands of C, CH and CN, but not of TiO.\u00a0 These stars are classified as R and N stars and are called carbon stars.<\/li>\r\n \t<li>There are also stars which show bands of ZrO, LaO and YtO.\u00a0 These are called S stars<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/li>\r\n \t<li>S stars are generally variable stars with long periods.<\/li>\r\n \t<li>M. N. Saha pointed out that spectral sequence from simple to complex spectra is a temperature sequence<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/li>\r\n \t<li>Boltzmann law of population of excited atomic states is given by\u00a0<img class=\"size-full wp-image-132 alignnone\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.13.png\" alt=\"\" width=\"153\" height=\"53\" \/>.<\/li>\r\n \t<li>The fraction of excited atoms of hydrogen is a function of temperature.<\/li>\r\n \t<li>There is a rapid decrease in the fraction of excited hydrogen atoms with decreasing temperature.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<p style=\"text-align: justify\">The basic material is from Textbook of Astronomy and Astrophysicsby V. B. Bhatia, supplemented by diagrams and graphs from the following sources:<\/p>\r\n\r\n<ul>\r\n \t<li>http:\/\/www.star.ucl.ac.uk\/~pac\/spectral_classification.html<\/li>\r\n \t<li>https:\/\/en.wikipedia.org\/wiki\/Stellar_classification<\/li>\r\n \t<li>http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/starlog\/staspe.html<\/li>\r\n \t<li>http:\/\/www.atlasoftheuniverse.com\/startype.html<\/li>\r\n \t<li>https:\/\/www.cfa.harvard.edu\/~pberlind\/atlas\/htmls\/note.html<\/li>\r\n \t<li>https:\/\/en.wikipedia.org\/wiki\/S-type_starhttp:\/\/prc.nao.ac.jp\/extra\/uos\/ja\/no04\/<\/li>\r\n \t<li>https:\/\/ned.ipac.caltech.edu\/level5\/Gray\/Gray31.html<\/li>\r\n \t<li>https:\/\/en.wikipedia.org\/wiki\/Wolf%E2%80%93Rayet_star<\/li>\r\n \t<li>https:\/\/en.wikipedia.org\/wiki\/Atmospheric_refraction<\/li>\r\n \t<li>https:\/\/en.wikipedia.org\/wiki\/Astronomical_seeing<\/li>\r\n \t<li>http:\/\/spiff.rit.edu\/classes\/phys373\/lectures\/atmos\/atmos.html<\/li>\r\n<\/ul>","rendered":"<div>\n<p>&nbsp;<\/p>\n<p><strong>1.\u00a0 Learning Outcomes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>After studying this module, you should be able to<\/p>\n<ul>\n<li>appreciate that there is great diversity in stellar spectra and all stars cannot be accommodated in the eight major classes O, B, A, F, G, K and M<\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">describe the new classes Q, P and W (Wolf-Rayet Stars) introduced before class O<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">state special features of Wolf-Rayet stars<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">name the suffixes and prefixes which are used to describe the characteristic features of some stars<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">explain the insertion of new classes like R, N and S classes after M stars<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">appreciate that R and N stars have bands of carbon compounds while the S stars have bands of ZrO<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">understand that the Harvard classification scheme is based on the decreasing surface temperature from class O to M<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">derive the expression for the fraction of hydrogen atoms in excited states<\/span><\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<p><span style=\"text-align: initial;font-size: 1em\"><strong>2.\u00a0\u00a0<\/strong> <\/span><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 module (Module 11) we introduced the spectral classification of stars. We explained the nature of the spectra as that containing mainly absorption lines. \u00a0We discussed the variety in the spectra of stars.\u00a0 Even within this variety it was possible to discern patterns.\u00a0 There are stars with a very few lines. On the other hand, there are stars with huge number of lines and molecular bands. On the basis of the increasing complexity in the stellar spectra, Annie Cannon was able to devise a simple classification scheme, known as Harvard Stellar Classification System. Seven major classes, O, B, A, F, G, K, and M were identified on the basis of their spectra.\u00a0 Each major class was subdivided into ten sub-classes. For example, class A9 is followed by F0, which, in turn, is followed by F2.\u00a0 It was pointed out that the stars belonging to the first three major classes, that is, classes O, B and A are called the early type stars, while the stars belonging to the last four major classes are referred to as late type stars. Stellar spectra are much more diverse than we have noticed so far. We now dwell upon this complexity. Later, following M. N. Saha, we will attempt to account for the classification scheme in terms of the decreasing stellar surface temperature.<\/span><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>3.\u00a0 Diversity in Stellar Spectra\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The stellar spectra show more complexity and diversity than we took notice of in the last module. Therefore, the spectral classification outlined above is not adequate to describe all the observed spectra. Three major classes (to which decimal subdivision is not applicable) before class O, and many prefixes and suffixes are used in conjuction with the spectral classes to describe comprehensively the spectra of many stars.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>3.1.\u00a0 Wolf-Rayet Stars\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The classes placed before O are Q, P and W, all hot stars showing emission lines.\u00a0 P stands for <strong>planetary nebula<\/strong>, believed to be the stage in the evoltion of a star just before it becomes a white dwarf star.\u00a0 W stars are <strong>Wolf-Rayet stars<\/strong>, named after two the French astronomers who studied them.\u00a0 The Wolf-Rayet stars show in their spectra broad and intense emission lines of ionized carbon, nitrogen and helium.<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-125\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.1.png\" alt=\"\" width=\"715\" height=\"485\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.1.png 715w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.1-300x203.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.1-65x44.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.1-225x153.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.1-350x237.png 350w\" sizes=\"auto, (max-width: 715px) 100vw, 715px\" \/><\/p>\n<p style=\"text-align: center\">Fig. 12.1.\u00a0 Spectra of Wolf Rayet star WR137.\u00a0 Notice the intense emission lines of ionized carbon. (Source: \u00a0Source: Wikipedia &#8211; Spectrum of Wolf-Rayet star WR137 by Gypaete )<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Wolf-Rayet stars are very hot stars, Their surface temperatures range from ~ 30000 K to ~ 50000 K.\u00a0 These stars are very luminous; the mean absolute magnitude is ~ -5.\u00a0 They are about 10 times as massive as the Sun.\u00a0 The stars of this mass tend to have very strong stellar winds.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">These winds blow away as much matter as 10-4 ?\u2a00 per year, leaving behind a thin atmosphere, through which we are able to observe the central region of the star. This region is rich in carbon\u00a0and nitrogen.\u00a0 It appears, therefore, that the Wolf-Rayet stars are helium burning stars (second stage after hydrogen burning), producing carbon and nitrogen whose lines we see in their spectra. The central temperatures may be of the order of 108 K.\u00a0 Clearly, Wolf-Rayet is a stage in the evolution of a star, lasting a few hundred thousand years.<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-124\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.2.png\" alt=\"\" width=\"699\" height=\"401\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.2.png 699w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.2-300x172.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.2-65x37.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.2-225x129.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.2-350x201.png 350w\" sizes=\"auto, (max-width: 699px) 100vw, 699px\" \/><\/p>\n<p style=\"text-align: center\">Fig. 12.2.\u00a0 After hydrogen burning in the core of the star is complete, the temperature rises to 108 K.\u00a0 At this temperature helium burning can commence to supply the energy need by the star to radiate from the surface.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>3.2. Scheme of Prefixes and Suffixes to Denote Special Characteristics of Spectra\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">An example of a prefix attached to the spectral class of a star is <strong>c <\/strong>which denotes that most of the lines in the star\u2019s spectrum have narrow profiles, such as in the star \u03b1 \u2013 Cygni.\u00a0 Some of the other prefixes and suffixes used are the following:<\/p>\n<p>&nbsp;<\/p>\n<p><strong>n <\/strong>\u2013 denotes wide and diffuse lines;<\/p>\n<p style=\"text-align: justify\"><strong>s <\/strong>\u2013 used in spectral classes B and A to denote lines of narrow profiles (but not as narrow as denoted by the prefix <strong>c<\/strong>);<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">e <\/strong><span style=\"text-align: initial;font-size: 1em\">\u2013 denotes the appearance of emmission lines in the classes O to M where they are not normally expected.\u00a0 The prefix appearing in classes O and B means that Blamer lines of hydrogen are in emission;<\/span><\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">v <\/strong><span style=\"text-align: initial;font-size: 1em\">\u2013 denotes the variable spectrum and ev denotes the variable emission spectrum;<\/span><\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">k <\/strong><span style=\"text-align: initial;font-size: 1em\">\u2013 denotes the presence of H and K lines of Ca<\/span><strong style=\"text-align: initial;font-size: 1em\">+<\/strong><span style=\"text-align: initial;font-size: 1em\">;<\/span><\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">p <\/strong><span style=\"text-align: initial;font-size: 1em\">\u2013 denotes that the spectrum contains peculiarities not normally found in the spectral class in which the spectrum is classified. In certain stars of class A, for example, the tines of SiII and SrII are exceptionally strong.\u00a0 These stars are designated as Ap stars.<\/span><\/p>\n<\/div>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>3.3.\u00a0 Addition of Classes R, N and S to the Major Spectral Types\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Recall that the late type stars show characteristic bands of TiO molecules. However, a few late type stars are distinguished by the fact that they show strong bands of C, CH and CN, but not of TiO which are so prominent in class M. These stars are classified as <strong>R <\/strong>and <strong>N stars <\/strong>and are called <strong>carbon stars<\/strong>.\u00a0 On the other hand, there is a class of stars which show bands due to ZrO, LaO and YtO.\u00a0 These are called <strong>S stars<\/strong>.\u00a0 The bands of ZrO are the defining feature of these stars. The S stars are variable stars with long periods. They are also quite small in number. \u00a0With the addition of these classes, the complete classification is sometimes written as<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-123\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.3.png\" alt=\"\" width=\"700\" height=\"205\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.3.png 700w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.3-300x88.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.3-65x19.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.3-225x66.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.3-350x103.png 350w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-122\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.4.png\" alt=\"\" width=\"441\" height=\"390\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.4.png 441w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.4-300x265.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.4-65x57.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.4-225x199.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.4-350x310.png 350w\" sizes=\"auto, (max-width: 441px) 100vw, 441px\" \/><\/p>\n<p style=\"text-align: center\">Fig. 12.3.\u00a0 HST image of W Aquilae, a Mira variable star, showing the faint companion.\u00a0 (Source:\u00a0 Wikipedia; Hubble Legacy Archive image constructed from blue (F435W) and green\/red (F606W) exposures.)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-121\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.5.png\" alt=\"\" width=\"520\" height=\"375\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.5.png 520w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.5-300x216.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.5-65x47.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.5-225x162.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.5-350x252.png 350w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/p>\n<p style=\"text-align: center\">Fig. 12.4. Spectra of R, N and S stars along with the other major classes. (Source: http:\/\/prc.nao.ac.jp\/extra\/uos\/ja\/no04\/ )<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-120\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.6.png\" alt=\"\" width=\"745\" height=\"533\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.6.png 745w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.6-300x215.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.6-65x47.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.6-225x161.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.6-350x250.png 350w\" sizes=\"auto, (max-width: 745px) 100vw, 745px\" \/><\/p>\n<\/div>\n<p style=\"text-align: center\"><span style=\"text-align: initial;font-size: 1em\">Fig. 12.5. Spectra of two S-Type stars.\u00a0 Notice bands due to ZrO, the distinguishing feature of S stars.\u00a0 (Source: htt ps:\/\/ned.ipac.cal tech.edu\/level5\/Gray\/Gray31.html\u00a0 )<\/span><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>4.\u00a0 Surface Temperature and Spectral Classification \u2013\u00a0 Saha\u2019s\u00a0 Theory\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">We have already noted that spectral sequence from simple to complex spectra is a temperature sequence. At the top of the sequence, the surface temperature of O stars is so high that most atoms are ionized. The exception is HeII, which is difficult to ionize a second time. So, these stars show only lines of HeII and a few other lines.\u00a0 As we progress to lower temperatures, first we encounter lines of hydrogen (class A) which has a high ionization potential, and then ionized metal atoms (classes F, G and K).\u00a0 At still lower surface temperatures, even metal atoms cannot\u00a0<span style=\"font-size: 1em;text-align: initial\">be ionized, so we have neutral metal atoms. In classes K and M, the surface temperatures are so low that even molecules cannot be dissociated.\u00a0 In the spectra of these classes we have molecular lines in addition to a host of neutral atom lines.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">M. N. Saha, grasped the true meaning of the spectral sequences. He pointed out that the ionization process is like a chemical reaction and is subject to the same conditions of equilibrium as is a chemical reaction. \u00a0This notion leads immediately to relative numbers of atoms in various stages of ionization existing in equilibrium at a given temperature.\u00a0 Since the intensity of an absorption line is proportional to the number of atoms which can absorb radiation corresponding to this line, and this number being a function of temperature, the intensity of various lines is obtained as a function of temperature. \u00a0This, then, allows us to understand the spectral classification as classification based on surface temperature of stars.<\/span><\/p>\n<\/div>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>4.1.\u00a0 LTE and Boltzmann Law of Population of Excited Atomic States\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Consider an assembly of various kinds of non-interacting or weakly interacting particles in statistical equilibrium at a certain temperature \ufffd.\u00a0 This implies that the assembly is in thermodynamic equilibrium (TE).\u00a0 TE implies thermal, mechanical and chemical equilibria.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">However, as we shall discuss later, these conditions are not generally satisfied in stars. The conditions may be very close to TE, and we may assume that TE exists. Such equilibrium is termed as <strong>local thermodynamic equilibrium <\/strong>(LTE), to be discussed later.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The number of particles of a given kind in energy range ?and ?+ \ufffd?is given by the usual distribution law:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-119 alignnone\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.7.png\" alt=\"\" width=\"599\" height=\"75\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.7.png 759w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.7-300x38.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.7-65x8.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.7-225x28.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.7-350x44.png 350w\" sizes=\"auto, (max-width: 599px) 100vw, 599px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Here d? is the <\/span><strong style=\"text-align: initial;font-size: 1em\">statistical weight <\/strong><span style=\"text-align: initial;font-size: 1em\">or the number of possible quantum states of a single typical\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">particle of the chosen kind between energies ?and ?+ d?. For a non-interacting system, the\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">kind assumed here, the quantum states of a particle of the chosen kind can be enumerated as if\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">the particles of other kinds were not present. The negative sign in the denominator of Equation\u00a0<\/span><\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-131\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.8.png\" alt=\"\" width=\"800\" height=\"1066\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.8.png 1009w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.8-225x300.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.8-768x1024.png 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.8-65x87.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.8-350x467.png 350w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-130\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.9.png\" alt=\"\" width=\"808\" height=\"1079\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.9.png 862w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.9-225x300.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.9-768x1025.png 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.9-767x1024.png 767w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.9-65x87.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.9-350x467.png 350w\" sizes=\"auto, (max-width: 808px) 100vw, 808px\" \/><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-129\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.10.png\" alt=\"\" width=\"882\" height=\"1108\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.10.png 882w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.10-239x300.png 239w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.10-768x965.png 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.10-815x1024.png 815w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.10-65x82.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.10-225x283.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.10-350x440.png 350w\" sizes=\"auto, (max-width: 882px) 100vw, 882px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-128\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.11.png\" alt=\"\" width=\"854\" height=\"1093\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.11.png 854w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.11-234x300.png 234w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.11-768x983.png 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.11-800x1024.png 800w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.11-65x83.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.11-225x288.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.11-350x448.png 350w\" sizes=\"auto, (max-width: 854px) 100vw, 854px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-127\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.12.png\" alt=\"\" width=\"872\" height=\"523\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.12.png 872w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.12-300x180.png 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.12-768x461.png 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.12-65x39.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.12-225x135.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.12-350x210.png 350w\" sizes=\"auto, (max-width: 872px) 100vw, 872px\" \/><\/p>\n<\/div>\n<div>\n<p>&nbsp;<\/p>\n<p><strong>Summary\u00a0<\/strong><\/p>\n<ul>\n<li>Because of very high diversity in stellar spectra, all spectra cannot be accommodated in the eight major classes of the Harvard System.<\/li>\n<li>Classes Q, P and W (Wolf-Rayet) are added before class O.<\/li>\n<li>Wolf-Rayet stars are very hot stars and contain broad and intense emission lines.<\/li>\n<li>The mass of these stars is ~ 10 <span style=\"text-align: initial;font-size: 1em\">?\u2a00<\/span>.\u00a0 These stars have very strong winds.<\/li>\n<li>It is possible that the Wolf-Rayet stars are helium burning stars and represent a\u00a0stage in the life of a star.<\/li>\n<li>There are several suffixes and prefixes which are used to denote the spectral characteristics of stars.<\/li>\n<li>A few late type stars are distinguished by strong bands of C, CH and CN, but not of TiO.\u00a0 These stars are classified as R and N stars and are called carbon stars.<\/li>\n<li>There are also stars which show bands of ZrO, LaO and YtO.\u00a0 These are called S stars<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/li>\n<li>S stars are generally variable stars with long periods.<\/li>\n<li>M. N. Saha pointed out that spectral sequence from simple to complex spectra is a temperature sequence<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/li>\n<li>Boltzmann law of population of excited atomic states is given by\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-132 alignnone\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.13.png\" alt=\"\" width=\"153\" height=\"53\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.13.png 153w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.13-150x53.png 150w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/6.7.13-65x23.png 65w\" sizes=\"auto, (max-width: 153px) 100vw, 153px\" \/>.<\/li>\n<li>The fraction of excited atoms of hydrogen is a function of temperature.<\/li>\n<li>There is a rapid decrease in the fraction of excited hydrogen atoms with decreasing temperature.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The basic material is from Textbook of Astronomy and Astrophysicsby V. B. Bhatia, supplemented by diagrams and graphs from the following sources:<\/p>\n<ul>\n<li>http:\/\/www.star.ucl.ac.uk\/~pac\/spectral_classification.html<\/li>\n<li>https:\/\/en.wikipedia.org\/wiki\/Stellar_classification<\/li>\n<li>http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/starlog\/staspe.html<\/li>\n<li>http:\/\/www.atlasoftheuniverse.com\/startype.html<\/li>\n<li>https:\/\/www.cfa.harvard.edu\/~pberlind\/atlas\/htmls\/note.html<\/li>\n<li>https:\/\/en.wikipedia.org\/wiki\/S-type_starhttp:\/\/prc.nao.ac.jp\/extra\/uos\/ja\/no04\/<\/li>\n<li>https:\/\/ned.ipac.caltech.edu\/level5\/Gray\/Gray31.html<\/li>\n<li>https:\/\/en.wikipedia.org\/wiki\/Wolf%E2%80%93Rayet_star<\/li>\n<li>https:\/\/en.wikipedia.org\/wiki\/Atmospheric_refraction<\/li>\n<li>https:\/\/en.wikipedia.org\/wiki\/Astronomical_seeing<\/li>\n<li>http:\/\/spiff.rit.edu\/classes\/phys373\/lectures\/atmos\/atmos.html<\/li>\n<\/ul>\n","protected":false},"author":4,"menu_order":7,"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-110","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\/110","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":6,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/110\/revisions"}],"predecessor-version":[{"id":134,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/110\/revisions\/134"}],"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\/110\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/media?parent=110"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapter-type?post=110"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/contributor?post=110"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/license?post=110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}