{"id":242,"date":"2018-11-19T07:21:38","date_gmt":"2018-11-19T07:21:38","guid":{"rendered":"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=242"},"modified":"2018-11-19T08:34:30","modified_gmt":"2018-11-19T08:34:30","slug":"close-binaries-mass-luminosity-relation-of-stars","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/chapter\/close-binaries-mass-luminosity-relation-of-stars\/","title":{"rendered":"Close Binaries, Mass-Luminosity Relation of Stars"},"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>sketch the equipotentials of effective gravitational field around the close binary system<\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">locate the Lagrangian points in the equipotentials<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">define detached, semi-detached and contact binary systems<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">explain how matter is exchanged between the two components of the binary system<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">understand how an accretion disc is formed<\/span><\/li>\r\n \t<li>define cataclysmic variable systems and recurrent novae<\/li>\r\n \t<li>describe the nature of supernovae 1a<\/li>\r\n \t<li>explain the formation of extra-galactic x-ray sources such as Hercules X-1 and Cygnus X-1<\/li>\r\n \t<li>describe mass-luminosity relation<\/li>\r\n \t<li>explain how dynamical parallaxes are determined<\/li>\r\n<\/ul>\r\n<\/div>\r\n<img class=\"aligncenter wp-image-255 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_02-e1542612320315.jpg\" alt=\"\" width=\"1988\" height=\"1914\" \/> <img class=\"aligncenter wp-image-254 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_03-e1542612342157.jpg\" alt=\"\" width=\"2013\" height=\"2722\" \/> <img class=\"aligncenter wp-image-253 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_04-e1542612369415.jpg\" alt=\"\" width=\"2070\" height=\"2648\" \/> <img class=\"aligncenter wp-image-252 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_05-e1542612389706.jpg\" alt=\"\" width=\"1963\" height=\"2640\" \/> <img class=\"aligncenter wp-image-251 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_06-e1542612421109.jpg\" alt=\"\" width=\"2021\" height=\"2656\" \/> <img class=\"aligncenter wp-image-250 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_07-e1542612449478.jpg\" alt=\"\" width=\"1988\" height=\"2730\" \/> <img class=\"aligncenter wp-image-249 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_08-e1542612476414.jpg\" alt=\"\" width=\"1971\" height=\"2813\" \/> <img class=\"aligncenter wp-image-248 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_09-e1542612494151.jpg\" alt=\"\" width=\"1996\" height=\"2153\" \/> <img class=\"aligncenter wp-image-247 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_10-e1542612516530.jpg\" alt=\"\" width=\"2029\" height=\"2409\" \/> <img class=\"aligncenter wp-image-246 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_11-e1542612549713.jpg\" alt=\"\" width=\"2037\" height=\"2689\" \/> <img class=\"aligncenter wp-image-245 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_12-e1542612597260.jpg\" alt=\"\" width=\"2021\" height=\"2739\" \/> <img class=\"aligncenter wp-image-244 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_13-e1542612626686.jpg\" alt=\"\" width=\"2004\" height=\"2343\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<strong>7.\u00a0 Summary<\/strong>\r\n<ul>\r\n \t<li style=\"text-align: justify\">A close binary system has five Lagrangian points where the effective gravitational field vanishes.<\/li>\r\n \t<li style=\"text-align: justify\">The inner Lagrangian point separates the two Roche lobes forming the figure of eight.<\/li>\r\n \t<li style=\"text-align: justify\">When both the Roche lobes are unfilled, the system is said to be detached.<\/li>\r\n \t<li style=\"text-align: justify\">When one Roche lobe is filled but the other is unfilled, the system is said to be semi- detached.<\/li>\r\n \t<li style=\"text-align: justify\">When both the Roche lobes are filled, the system is called a contact binary system.<\/li>\r\n \t<li style=\"text-align: justify\">If a contact binary system consists of a compact object and a normal star, matter can push past the inner Lagrangian point and can fall in the gravitational field of the compact object.<\/li>\r\n \t<li style=\"text-align: justify\">As it falls in the gravitational field, the matter gains kinetic energy.<\/li>\r\n \t<li style=\"text-align: justify\">When matter hits the surface of the compact object, kinetic energy gets converted into heat energy of the matter.<\/li>\r\n \t<li style=\"text-align: justify\">Since matter carries angular momentum, it does not fall on the surface of the compact object but forms an accretion disc around it.<\/li>\r\n \t<li style=\"text-align: justify\">When the compact object is a white dwarf star, the radiation from the accretion disc can explain recurrent novae.<\/li>\r\n \t<li style=\"text-align: justify\">By gaining matter from its companion, the white dwarf star can have mass exceeding Chandrasekhar limiting mass, which can lead to supernova explosion.<\/li>\r\n \t<li style=\"text-align: justify\">These supernovae are assigned class 1a. Since the exploding star has always mass equal to 1.4 solar mass, supernovae 1a always reach the same maximum brightness.<\/li>\r\n \t<li style=\"text-align: justify\">These supernovae can be used as standard candles for measuring cosmic distances.<\/li>\r\n \t<li style=\"text-align: justify\">When the compact object in the system is a neutron star, the matter in the accretion disc is so hot that it emits x-rays. This is a possible for model for x-ray sources of Hercules X-1 type.<\/li>\r\n \t<li style=\"text-align: justify\">When the compact object is a black hole, the source of x-rays can be modelled like Cygnus X-1.<\/li>\r\n \t<li style=\"text-align: justify\">Masses of stars determined by binary systems are used to establish a mass-luminosity relation, enabling the masses of stars to be estimated indirectly.<\/li>\r\n<\/ul>\r\n<div class=\"textLayer\">\r\n\r\n&nbsp;\r\n\r\n<strong>Suggested Readings<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Major sources for the matter covered in this module are: Textbook of Astronomy and Astrophysics with Elements of Cosmology by V. B. Bhatia.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">https:\/\/en.wikipedia.org\/wiki\/Lagrangian_point<\/p>\r\n<p style=\"text-align: justify\">https:\/\/www.space.com\/30302-lagrange-points.html<\/p>\r\n<p style=\"text-align: justify\">https:\/\/imagine.gsfc.nasa.gov\/science\/objects\/cataclysmic_variables.html<\/p>\r\n<p style=\"text-align: justify\">Oroszet.al. Ap, J., 2011<\/p>\r\n<p style=\"text-align: justify\">http:\/\/www.agnld.uni-potsdam.de\/~shw\/TSA\/Application\/X-Ray\/Internet.html.<\/p>\r\n<p style=\"text-align: justify\">http:\/\/www.isthe.com\/chongo\/tech\/astro\/HR-temp-mass-table-bymass.html<\/p>\r\n<p style=\"text-align: justify\">https:\/\/www.nasa.gov\/sites\/default\/files\/images\/138785main_image_feature_460_ys_full.jpg<\/p>\r\n<p style=\"text-align: justify\">https:\/\/en.wikipedia.org\/wiki\/Hercules_X-1<\/p>\r\n<p style=\"text-align: justify\">Discovery of a Periodic Pulsating Binary X-Ray Source in Hercules from UHURU: Tananbaum, H.; Gursky, H.; Kellogg, E.M.; Levinson, R.; Schreier, E.; Giacconi, R, 1972 ApJ...174L.143T<\/p>\r\n<p style=\"text-align: justify\">https:\/\/en.wikipedia.org\/wiki\/Cygnus_X-1<\/p>\r\n<p style=\"text-align: justify\">http:\/\/www.constellation-guide.com\/cygnus-x-1\/<\/p>\r\n<p style=\"text-align: justify\">http:\/\/www2.astro.psu.edu\/users\/rbc\/a534\/lec18.pdf<\/p>\r\n\r\n<\/div>\r\n<div class=\"annotationLayer\"><\/div>","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>sketch the equipotentials of effective gravitational field around the close binary system<\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">locate the Lagrangian points in the equipotentials<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">define detached, semi-detached and contact binary systems<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">explain how matter is exchanged between the two components of the binary system<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">understand how an accretion disc is formed<\/span><\/li>\n<li>define cataclysmic variable systems and recurrent novae<\/li>\n<li>describe the nature of supernovae 1a<\/li>\n<li>explain the formation of extra-galactic x-ray sources such as Hercules X-1 and Cygnus X-1<\/li>\n<li>describe mass-luminosity relation<\/li>\n<li>explain how dynamical parallaxes are determined<\/li>\n<\/ul>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-255 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_02-e1542612320315.jpg\" alt=\"\" width=\"1988\" height=\"1914\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_02-e1542612320315.jpg 1988w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_02-e1542612320315-300x289.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_02-e1542612320315-768x739.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_02-e1542612320315-1024x986.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_02-e1542612320315-65x63.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_02-e1542612320315-225x217.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_02-e1542612320315-350x337.jpg 350w\" sizes=\"auto, (max-width: 1988px) 100vw, 1988px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-254 size-full\" src=\"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_03-e1542612342157.jpg\" alt=\"\" width=\"2013\" height=\"2722\" 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srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_13-e1542612626686.jpg 2004w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_13-e1542612626686-257x300.jpg 257w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_13-e1542612626686-768x898.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_13-e1542612626686-876x1024.jpg 876w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_13-e1542612626686-65x76.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_13-e1542612626686-225x263.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-content\/uploads\/sites\/97\/2018\/11\/1523530675Module19Text_Page_13-e1542612626686-350x409.jpg 350w\" sizes=\"auto, (max-width: 2004px) 100vw, 2004px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>7.\u00a0 Summary<\/strong><\/p>\n<ul>\n<li style=\"text-align: justify\">A close binary system has five Lagrangian points where the effective gravitational field vanishes.<\/li>\n<li style=\"text-align: justify\">The inner Lagrangian point separates the two Roche lobes forming the figure of eight.<\/li>\n<li style=\"text-align: justify\">When both the Roche lobes are unfilled, the system is said to be detached.<\/li>\n<li style=\"text-align: justify\">When one Roche lobe is filled but the other is unfilled, the system is said to be semi- detached.<\/li>\n<li style=\"text-align: justify\">When both the Roche lobes are filled, the system is called a contact binary system.<\/li>\n<li style=\"text-align: justify\">If a contact binary system consists of a compact object and a normal star, matter can push past the inner Lagrangian point and can fall in the gravitational field of the compact object.<\/li>\n<li style=\"text-align: justify\">As it falls in the gravitational field, the matter gains kinetic energy.<\/li>\n<li style=\"text-align: justify\">When matter hits the surface of the compact object, kinetic energy gets converted into heat energy of the matter.<\/li>\n<li style=\"text-align: justify\">Since matter carries angular momentum, it does not fall on the surface of the compact object but forms an accretion disc around it.<\/li>\n<li style=\"text-align: justify\">When the compact object is a white dwarf star, the radiation from the accretion disc can explain recurrent novae.<\/li>\n<li style=\"text-align: justify\">By gaining matter from its companion, the white dwarf star can have mass exceeding Chandrasekhar limiting mass, which can lead to supernova explosion.<\/li>\n<li style=\"text-align: justify\">These supernovae are assigned class 1a. Since the exploding star has always mass equal to 1.4 solar mass, supernovae 1a always reach the same maximum brightness.<\/li>\n<li style=\"text-align: justify\">These supernovae can be used as standard candles for measuring cosmic distances.<\/li>\n<li style=\"text-align: justify\">When the compact object in the system is a neutron star, the matter in the accretion disc is so hot that it emits x-rays. This is a possible for model for x-ray sources of Hercules X-1 type.<\/li>\n<li style=\"text-align: justify\">When the compact object is a black hole, the source of x-rays can be modelled like Cygnus X-1.<\/li>\n<li style=\"text-align: justify\">Masses of stars determined by binary systems are used to establish a mass-luminosity relation, enabling the masses of stars to be estimated indirectly.<\/li>\n<\/ul>\n<div class=\"textLayer\">\n<p>&nbsp;<\/p>\n<p><strong>Suggested Readings<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Major sources for the matter covered in this module are: Textbook of Astronomy and Astrophysics with Elements of Cosmology by V. B. Bhatia.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">https:\/\/en.wikipedia.org\/wiki\/Lagrangian_point<\/p>\n<p style=\"text-align: justify\">https:\/\/www.space.com\/30302-lagrange-points.html<\/p>\n<p style=\"text-align: justify\">https:\/\/imagine.gsfc.nasa.gov\/science\/objects\/cataclysmic_variables.html<\/p>\n<p style=\"text-align: justify\">Oroszet.al. Ap, J., 2011<\/p>\n<p style=\"text-align: justify\">http:\/\/www.agnld.uni-potsdam.de\/~shw\/TSA\/Application\/X-Ray\/Internet.html.<\/p>\n<p style=\"text-align: justify\">http:\/\/www.isthe.com\/chongo\/tech\/astro\/HR-temp-mass-table-bymass.html<\/p>\n<p style=\"text-align: justify\">https:\/\/www.nasa.gov\/sites\/default\/files\/images\/138785main_image_feature_460_ys_full.jpg<\/p>\n<p style=\"text-align: justify\">https:\/\/en.wikipedia.org\/wiki\/Hercules_X-1<\/p>\n<p style=\"text-align: justify\">Discovery of a Periodic Pulsating Binary X-Ray Source in Hercules from UHURU: Tananbaum, H.; Gursky, H.; Kellogg, E.M.; Levinson, R.; Schreier, E.; Giacconi, R, 1972 ApJ&#8230;174L.143T<\/p>\n<p style=\"text-align: justify\">https:\/\/en.wikipedia.org\/wiki\/Cygnus_X-1<\/p>\n<p style=\"text-align: justify\">http:\/\/www.constellation-guide.com\/cygnus-x-1\/<\/p>\n<p style=\"text-align: justify\">http:\/\/www2.astro.psu.edu\/users\/rbc\/a534\/lec18.pdf<\/p>\n<\/div>\n<div class=\"annotationLayer\"><\/div>\n","protected":false},"author":4,"menu_order":14,"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-242","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\/242","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\/242\/revisions"}],"predecessor-version":[{"id":258,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/242\/revisions\/258"}],"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\/242\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/media?parent=242"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapter-type?post=242"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/contributor?post=242"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/license?post=242"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}