{"id":1221,"date":"2021-04-02T13:55:30","date_gmt":"2021-04-02T13:55:30","guid":{"rendered":"http:\/\/www.astrobulletin.univ.kiev.ua\/?p=1221"},"modified":"2025-01-30T13:03:41","modified_gmt":"2025-01-30T13:03:41","slug":"62_zhdanov","status":"publish","type":"post","link":"https:\/\/astrobulletin.knu.ua\/ua\/62_zhdanov\/","title":{"rendered":"62_Zhdanov"},"content":{"rendered":"<p>&nbsp;<\/p>\n<p><strong>Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 62, p. 6<span lang=\"en-US\">-9\u00a0<\/span>(2020)<br \/>\n<\/strong><\/p>\n<p><span style=\"font-size: 18pt;\"><strong><span style=\"color: #333399;\">Effect of the sourse ellipticity on light curves in extragalactic gravitational lens systems<\/span><\/strong><\/span><\/p>\n<p><strong>V. Zhdanov, Dr Hab., Prof.<\/strong><br \/>\n<strong>A. Alexandrov, PhD, Senior Res.<\/strong><\/p>\n<p><strong>Taras Shevchenko National University of Kyiv\u00a0<\/strong><\/p>\n<p><!--more--><br \/>\n<strong>Abstract<\/strong><\/p>\n<p style=\"text-align: justify;\">In extragalactic gravitational lens system (GLS) several macro-images of a remote source (quasar) are observed. Gravitational microlensing leads to uncorrelated brightness variations of the macro-images. These variations can be separated from proper brightness changes of the source, which are repeated in each image with some relative delay. In most papers the gravitational microlensing effects in extragalactic GLS typically deal with centrally symmetric sources, though the real form of the source can be more complicated. In this paper we consider statistical signals of the source ellipticity in light curves of microlensed objects, which arise as a result of observations of many high amplification events. As a first step, we consider a qualitative version of the problem, when an elliptic source with Gaussian brightness distribution is crossed by a number of simple (fold) caustics with different orientations. Also we assume that the caustic network is isotropic, that is all orientations of the caustics and directions of their velocities are equally possible. We use the linear fold caustic approximation for the amplification of a small point source, when two critical images appear\/disappear after the caustic crossing. For a rough estimate, the strength and velocity of the caustic are fixed by certain characteristic values. We estimate the averaged light curve after many caustic crossing events and compare maxima of brightness on the light curves for different eccentricities of the source. The ellipticity signal in the light curves is noticeable for a considerable oblateness of the source. Though we expect that the effect will be smeared out after taking into account the distribution of the caustic velocities and caustic strengths. Possible complications of the problem are indicated due to interplay of effects due to velocity distribution of stars in the lensing galaxy and bulk motion of the lensing galaxy as a whole.<\/p>\n<p><strong>Key words<br \/>\n<\/strong>Gravitational lenses, fold-caustic, microlensing, elliptical source, light curves.<\/p>\n<p style=\"text-align: justify;\"><strong>References<br \/>\n<\/strong>Schneider P. Gravitational Lenses \/ P. Schneider, J. Ehlers, E.E. Falco. \u2013 Berlin: Springer, 1992.<br \/>\nZhdanov V.I. Qualitative problems in gravitational microlensing \/ V.I. Zhdanov, A.N. Alexandrov, E.V. Fedorova, V.M. Sliusar \/\/ Dark Matter. V. 2.<br \/>\nAstrophysical Aspects of the Problem. \u2013 Kyiv: Akademperiodyka, 2014. \u2013 P. 84-130.<br \/>\nZhdanov V.I. Analytical methods in gravitational microlensing \/ V.I. Zhdanov, A.N. Alexandrov , E.V. Fedorova, V.M. Sliusar \/\/ ISRN Astron. Astrophys. \u2013 2012. \u2013 Article ID 906951. \u2013 21 p. doi:10.5402\/2012\/906951.<br \/>\nPoindexter S. Microlensing Evidence that a Type 1 Quasar is Viewed Face-On \/ S. Poindexter, C.S. Kochanek \/\/ Astrophys. J. \u2013 2010. \u2013 Vol. 712, Is.1. \u2013 P. 668-673.<br \/>\nHeyrovsk\u0443 D. Microlensing of an elliptical source by a point mass \/ D. Heyrovsk\u0443, A. Loeb \/\/ Astrophys. J., 1997. \u2013 Vol. 490. \u2013 P. 38\u201350.<br \/>\nGaudi B.S. Microlensing of elliptical sources by fold caustics \/ B.S. Gaudi, Z. Haiman \/\/ arXiv:astro-ph\/0401035.<br \/>\nAlexandrov A.N. Gravitational microlensing of an elliptical source near a fold caustic \/ A.N. Alexandrov, V.I. Zhdanov, A.V. Kuybarov (in Ukr. \u0413\u0440\u0430\u0432\u0456\u0442\u0430\u0446\u0456\u0439\u043d\u0435 \u043c\u0456\u043a\u0440\u043e\u043b\u0456\u043d\u0437\u0443\u0432\u0430\u043d\u043d\u044f \u0435\u043b\u0456\u043f\u0442\u0438\u0447\u043d\u043e\u0433\u043e \u0434\u0436\u0435\u0440\u0435\u043b\u0430 \u043f\u043e\u0431\u043b\u0438\u0437\u0443 \u043a\u0430\u0443\u0441\u0442\u0438\u043a\u0438-\u0441\u043a\u043b\u0430\u0434\u043a\u0438) \/\/ Bull. Taras Shevchenko Nat. Univ. of Kyiv, Astronomy. \u2013 2018. \u2116. 57. \u2013 P. 10-15.<br \/>\nVernardos G. Quasar microlensing light curve analysis using deep machine learning \/ G.Vernardos, G.Tsagkatakis \/\/ Mon. Not. Roy. Astron. Soc. \u2013 2019.\u2013 Vol. 486, Is.2. \u2013 P. 1944-1952.<br \/>\nMinakov A.A. Statistical analysis of gravitational microlensing \/ A. A. Minakov and V. G. Vakulik (in Rus. \u0421\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0430\u043d\u0430\u043b\u0438\u0437 \u0433\u0440\u0430\u0432\u0438\u0442\u0430\u0446\u0438\u043e\u043d\u043d\u043e\u0433\u043e \u043c\u0438\u043a\u0440\u043e\u043b\u0438\u043d\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f). \u2013 \u041a.: \u041d\u0430\u0443\u043a\u043e\u0432\u0430 \u0414\u0443\u043c\u043a\u0430. \u2013 2010.<br \/>\nAlexandrov A.N. Asymptotic formulas for the magnification of a gravitational lens system near a fold caustic \/ A.N. Alexandrov, V.I. Zhdanov, \u0415.V. Fedorova \/\/ Astron. Lett. \u2013 2010. \u2013 Vol. 36, \u21165. \u2013 P. 329-337.<br \/>\nAlexandrov A.N. Asymptotic expansions and amplification of a gravitational lens near a fold caustic \/ A.N. Alexandrov, V.I. Zhdanov \/\/ Mon. Not. Roy. Astron. Soc. \u2013 2011. \u2013 Vol. 417. \u2013 P. 541\u2013554.<\/p>\n<p><a href=\"http:\/\/www.astrobulletin.knu.ua\/wp-content\/uploads\/file\/62\/BTSNUA_62-6-9.pdf\">Full text PDF<\/a><\/p>\n<p>DOI:\u00a0<a href=\"https:\/\/doi.org\/10.17721\/BTSNUA.2020.62.6-9\">https:\/\/doi.org\/10.17721\/BTSNUA.2020.62.6-9<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>\u0412\u0438\u0431\u0430\u0447\u0442\u0435 \u0446\u0435\u0439 \u0442\u0435\u043a\u0441\u0442 \u0434\u043e\u0441\u0442\u0443\u043f\u043d\u0438\u0439 \u0442\u0456\u043b\u044c\u043a\u0438 \u0432 &ldquo;English&rdquo;.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26],"tags":[],"class_list":["post-1221","post","type-post","status-publish","format-standard","hentry","category-number_62"],"_links":{"self":[{"href":"https:\/\/astrobulletin.knu.ua\/ua\/wp-json\/wp\/v2\/posts\/1221","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/astrobulletin.knu.ua\/ua\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/astrobulletin.knu.ua\/ua\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/astrobulletin.knu.ua\/ua\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/astrobulletin.knu.ua\/ua\/wp-json\/wp\/v2\/comments?post=1221"}],"version-history":[{"count":7,"href":"https:\/\/astrobulletin.knu.ua\/ua\/wp-json\/wp\/v2\/posts\/1221\/revisions"}],"predecessor-version":[{"id":1598,"href":"https:\/\/astrobulletin.knu.ua\/ua\/wp-json\/wp\/v2\/posts\/1221\/revisions\/1598"}],"wp:attachment":[{"href":"https:\/\/astrobulletin.knu.ua\/ua\/wp-json\/wp\/v2\/media?parent=1221"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/astrobulletin.knu.ua\/ua\/wp-json\/wp\/v2\/categories?post=1221"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/astrobulletin.knu.ua\/ua\/wp-json\/wp\/v2\/tags?post=1221"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}