{"id":225,"date":"2018-11-19T06:57:37","date_gmt":"2018-11-19T06:57:37","guid":{"rendered":"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=225"},"modified":"2018-11-19T07:10:56","modified_gmt":"2018-11-19T07:10:56","slug":"masses-of-stars-contd","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/chapter\/masses-of-stars-contd\/","title":{"rendered":"Masses of Stars (Contd.)"},"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<p style=\"text-align: justify\">After studying this module, you should be able to<\/p>\r\n\r\n<ul style=\"text-align: justify\">\r\n \t<li>describe how masses of both the components of a spectroscopic binary system may be found<\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">explain the meaning of mass function of a binary group<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">describe the nature of an eclipsing binary group<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">understand the variety of light curves<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">explain how the masses and radii of stars of an eclipsing binary group can be extracted from their light curves<\/span><\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\n<strong>2.\u00a0 Introduction<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">In Module 17 we started discussing the determination of stellar masses. Recall that the mass of a star is an important attribute because it determines the way the star will evolve. Recall also that\u00a0<span style=\"text-align: initial;font-size: 1em\">the source of information of stellar masses is the study of binary stars. A binary system may be a visual binary system, a spectroscopic binary system or an eclipsing binary system. \u00a0Usually the information we get is about the mass of either the more massive component or the combined mass of the two components.\u00a0 However, by a lucky chance, if a system is a visual binary as well as a spectroscopic or an eclipsing binary system, then it is possible to get information about the masses of both the components of the system.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In the last module, we dealt with the visual binaries. We also learnt how the velocity curve of a spectroscopic binary system may be extracted from the data collected about the system and orbital elements of the system may be found, leading to an upper limit on the combined mass of the system.\u00a0 In this module, we learn how, under favourable circumstances, the masses of both the components of a spectroscopic binary group may be gleaned from the observational data.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">We also describe the variety of light curves of eclipsing binary systems and explain how the light curves may be used to estimate sizes and masses of the stars belonging to these groups.<\/span><\/p>\r\n\r\n<\/div>\r\n<img class=\"aligncenter wp-image-237 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_02-e1542611333831.jpg\" alt=\"\" width=\"2005\" height=\"1469\" \/> <img class=\"aligncenter wp-image-236 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_03-e1542610539398.jpg\" alt=\"\" width=\"1947\" height=\"2582\" \/> <img class=\"aligncenter wp-image-235 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_04-e1542610821823.jpg\" alt=\"\" width=\"1897\" height=\"2640\" \/> <img class=\"aligncenter wp-image-234 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_05-e1542610848934.jpg\" alt=\"\" width=\"2037\" height=\"2598\" \/> <img class=\"aligncenter wp-image-233 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_06-e1542610867436.jpg\" alt=\"\" width=\"2037\" height=\"2739\" \/> <img class=\"aligncenter wp-image-232 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_07-e1542610890552.jpg\" alt=\"\" width=\"2004\" height=\"2252\" \/> <img class=\"aligncenter wp-image-231 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_08-e1542610917769.jpg\" alt=\"\" width=\"2103\" height=\"2697\" \/> <img class=\"aligncenter wp-image-230 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_09-e1542610943721.jpg\" alt=\"\" width=\"2062\" height=\"2483\" \/> <img class=\"aligncenter wp-image-229 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_10-e1542610968673.jpg\" alt=\"\" width=\"2004\" height=\"2623\" \/> <img class=\"aligncenter wp-image-228 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_11-e1542610998793.jpg\" alt=\"\" width=\"2054\" height=\"2549\" \/> <img class=\"aligncenter wp-image-227 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_12-e1542611025465.jpg\" alt=\"\" width=\"1988\" height=\"2491\" \/>\r\n\r\n&nbsp;\r\n\r\n<strong>5.\u00a0 Summary<\/strong>\r\n<ul>\r\n \t<li style=\"text-align: justify\">When velocity curves of both the components of the spectroscopic binary group can be deciphered, masses of both the components can be estimated.<\/li>\r\n \t<li style=\"text-align: justify\">Since the inclination of the orbit to the plane of the sky is an unknown quantity, we calculate only the mass function of the binary system.<\/li>\r\n \t<li style=\"text-align: justify\">From the eclipses caused by the two components to each other, we get the light curve of an eclipsing binary system.<\/li>\r\n \t<li style=\"text-align: justify\">Light curves show a lot of variety depending on the luminosities of the two components, the sizes of the two components, distances of the two components from the CM and the inclination of their orbits to the plane of the sky.<\/li>\r\n \t<li style=\"text-align: justify\">Analyses of light curves lead to information on sizes, luminosities, separation and masses of the components of the eclipsing binary system.<\/li>\r\n \t<li style=\"text-align: justify\">If the eclipsing binary system is also a spectroscopic binary system, we can get the inclination of the orbit and hence individual masses of the components, rather than the mass function.<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\n<strong>Suggested Readings<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The basic material for this module is taken from Textbook of Astronomy and Astrophysics with Elements of Cosmology by V. B. Bhatia. This material has been supplemented by the following web sources:<\/span><\/p>\r\n\r\n<div class=\"textLayer\">\r\n<ul>\r\n \t<li>http:\/\/www.eso.org\/public\/images\/eso1311a\/<\/li>\r\n \t<li>http:\/\/www.astro.caltech.edu\/~george\/ay20\/Ay20-Lec4x.pdf<\/li>\r\n \t<li>http:\/\/spiff.rit.edu\/classes\/phys230\/lectures\/mass\/mass.html<\/li>\r\n \t<li>http:\/\/www.astro.sunysb.edu\/metchev\/PHY521\/lecture26.pdf<\/li>\r\n \t<li>www.astro.umass.edu\/~snell\/lectures228\/lecture7.odp<\/li>\r\n \t<li>http:\/\/astronomy.nju.edu.cn\/~lixd\/GA\/AT4\/AT417\/HTML\/AT41708.htm<\/li>\r\n<\/ul>\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 style=\"text-align: justify\">After studying this module, you should be able to<\/p>\n<ul style=\"text-align: justify\">\n<li>describe how masses of both the components of a spectroscopic binary system may be found<\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">explain the meaning of mass function of a binary group<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">describe the nature of an eclipsing binary group<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">understand the variety of light curves<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">explain how the masses and radii of stars of an eclipsing binary group can be extracted from their light curves<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>2.\u00a0 Introduction<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">In Module 17 we started discussing the determination of stellar masses. Recall that the mass of a star is an important attribute because it determines the way the star will evolve. Recall also that\u00a0<span style=\"text-align: initial;font-size: 1em\">the source of information of stellar masses is the study of binary stars. A binary system may be a visual binary system, a spectroscopic binary system or an eclipsing binary system. \u00a0Usually the information we get is about the mass of either the more massive component or the combined mass of the two components.\u00a0 However, by a lucky chance, if a system is a visual binary as well as a spectroscopic or an eclipsing binary system, then it is possible to get information about the masses of both the components of the system.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In the last module, we dealt with the visual binaries. We also learnt how the velocity curve of a spectroscopic binary system may be extracted from the data collected about the system and orbital elements of the system may be found, leading to an upper limit on the combined mass of the system.\u00a0 In this module, we learn how, under favourable circumstances, the masses of both the components of a spectroscopic binary group may be gleaned from the observational data.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">We also describe the variety of light curves of eclipsing binary systems and explain how the light curves may be used to estimate sizes and masses of the stars belonging to these groups.<\/span><\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-237 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_02-e1542611333831.jpg\" alt=\"\" width=\"2005\" height=\"1469\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_02-e1542611333831.jpg 2005w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_02-e1542611333831-300x220.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_02-e1542611333831-768x563.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_02-e1542611333831-1024x750.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_02-e1542611333831-65x48.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_02-e1542611333831-225x165.jpg 225w, 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https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_11-e1542610998793-825x1024.jpg 825w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_11-e1542610998793-65x81.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_11-e1542610998793-225x279.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_11-e1542610998793-350x434.jpg 350w\" sizes=\"auto, (max-width: 2054px) 100vw, 2054px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-227 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_12-e1542611025465.jpg\" alt=\"\" width=\"1988\" height=\"2491\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_12-e1542611025465.jpg 1988w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_12-e1542611025465-239x300.jpg 239w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_12-e1542611025465-768x962.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_12-e1542611025465-817x1024.jpg 817w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_12-e1542611025465-65x81.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_12-e1542611025465-225x282.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530654Module18Text_Page_12-e1542611025465-350x439.jpg 350w\" sizes=\"auto, (max-width: 1988px) 100vw, 1988px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>5.\u00a0 Summary<\/strong><\/p>\n<ul>\n<li style=\"text-align: justify\">When velocity curves of both the components of the spectroscopic binary group can be deciphered, masses of both the components can be estimated.<\/li>\n<li style=\"text-align: justify\">Since the inclination of the orbit to the plane of the sky is an unknown quantity, we calculate only the mass function of the binary system.<\/li>\n<li style=\"text-align: justify\">From the eclipses caused by the two components to each other, we get the light curve of an eclipsing binary system.<\/li>\n<li style=\"text-align: justify\">Light curves show a lot of variety depending on the luminosities of the two components, the sizes of the two components, distances of the two components from the CM and the inclination of their orbits to the plane of the sky.<\/li>\n<li style=\"text-align: justify\">Analyses of light curves lead to information on sizes, luminosities, separation and masses of the components of the eclipsing binary system.<\/li>\n<li style=\"text-align: justify\">If the eclipsing binary system is also a spectroscopic binary system, we can get the inclination of the orbit and hence individual masses of the components, rather than the mass function.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>Suggested Readings<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The basic material for this module is taken from Textbook of Astronomy and Astrophysics with Elements of Cosmology by V. B. Bhatia. This material has been supplemented by the following web sources:<\/span><\/p>\n<div class=\"textLayer\">\n<ul>\n<li>http:\/\/www.eso.org\/public\/images\/eso1311a\/<\/li>\n<li>http:\/\/www.astro.caltech.edu\/~george\/ay20\/Ay20-Lec4x.pdf<\/li>\n<li>http:\/\/spiff.rit.edu\/classes\/phys230\/lectures\/mass\/mass.html<\/li>\n<li>http:\/\/www.astro.sunysb.edu\/metchev\/PHY521\/lecture26.pdf<\/li>\n<li>www.astro.umass.edu\/~snell\/lectures228\/lecture7.odp<\/li>\n<li>http:\/\/astronomy.nju.edu.cn\/~lixd\/GA\/AT4\/AT417\/HTML\/AT41708.htm<\/li>\n<\/ul>\n<\/div>\n<div class=\"annotationLayer\"><\/div>\n","protected":false},"author":4,"menu_order":13,"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-225","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\/225","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\/225\/revisions"}],"predecessor-version":[{"id":239,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/225\/revisions\/239"}],"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\/225\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/media?parent=225"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapter-type?post=225"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/contributor?post=225"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/license?post=225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}