Physics Journal
Articles Information
Physics Journal, Vol.2, No.2, Mar. 2016, Pub. Date: Jan. 21, 2016
Phemenological Modelling of a Group of Eclipsing Binary Stars
Pages: 140-150 Views: 1018 Downloads: 932
Authors
[01] Ivan L. Andronov, Department “High and Applied Mathematics”, Odessa National Maritime University, Odessa, Ukraine.
[02] Mariia G. Tkachenko, Department “High and Applied Mathematics”, Odessa National Maritime University, Odessa, Ukraine.
[03] Lidia L. Chinarova, Astronomical Observatory, Odessa National University, Odessa, Ukraine.
Abstract
Phenomenological modeling of variable stars allows determination of a set of the parameters, which are needed for classification in the “General Catalogue of Variable Stars” and similar catalogs. We apply a recent method NAV (“New Algol Variable”) to eclipsing binary stars of different types. Although all periodic functions may be represented as Fourier series with an infinite number of coefficients, this is impossible for a finite number of the observations. Thus one may use a restricted Fourier series, i.e. a trigonometric polynomial (TP) of order s either for fitting the light curve, or to make a periodogram analysis. However, the number of parameters needed drastically increases with decreasing width of minimum. In the NAV algorithm, the special shape of minimum is used, so the number of parameters is limited to 10 (if the period and initial epoch are fixed) or 12 (not fixed). We illustrate the NAV method by application to a recently discovered Algol-type eclipsing variable 2MASS J11080308-6145589 (in the field of previously known variable star RS Car) and compare results to that obtained using the TP fits. For this system, the statistically optimal number of parameters is 44, but the fit is still worse than that of the NAV fit. Application to the system GSC 3692-00624 argues that the NAV fit is better than the TP one even for the case of EW-type stars with much wider eclipses. Model parameters are listed.
Keywords
Astronomy, Stellar Astrophysics, Variable Stars, Eclipsing Binaries, Time Series Analysis, Data Reduction
References
[01] Anderson, T. W, (2003). An Introduction to Multivariate Statistical Analysis. New York. John Wiley & Sons, p. 721.
[02] Andronov, I.L, (1991). Structure and Evolution of Stars. Odessa Inst. Adv. Teachers, p.84.
[03] Andronov, I.L, (1994). (Multi-) Frequency Variations of Stars. Some Methods and Results. Odessa Astronomical Publications, vol. 7, pp. 49-54.
[04] Andronov, I.L, (2003). Multiperiodic versus Noise Variations: Mathematical Methods, ASP Conf. Ser., vol. 292, pp. 391-400.
[05] Andronov, I.L. (2010). Mathematical Modeling of the Light Curves Using the "New Algol Variables" (NAV) Algorithm. Int. Conf. KOLOS-2010 Abstract Booklet, pp. 1-2.
[06] Andronov, I.L. (2012). Phenomenological Modeling of the Light Curves of Algol-Type Eclipsing Binary Stars. Astrophys., vol. 55, pp. 536-550.
[07] Andronov, I.L., Antoniuk, K.A., Baklanov, A.V., Breus, V.V., Burwitz, V., Chinarova, L.L., Chochol, D., Dubovsky, P.A., Han, W., Hegedus, T., Henden, A., Hric, L., Chun-Hwey, Kim,Yonggi, Kim, Kolesnikov, S.V., Kudzej, I., Liakos, A., Niarchos, P.G., Oksanen, A., Patkos, L., Petrik, K., Pit', N.V., Shakhovskoy, N.M., Virnina, N.A., Yoon, J., Zola, S.(2010) Inter-Longitude Astronomy (ILA) Project: Current Highlights And Perspectives. I. Magnetic vs. Non-Magnetic Interacting Binary Stars. Odessa Astronomical Publications, vol. 23, pp. 8-10.
[08] Patkos,L., Petrik, K., Pit,' N.V., Shakhovskoy, N.M., Virnina, N.A., Yoon, J. and Zola S. (2010). Inter-Longitude Astronomy (ILA) Project: Current Highlights and Perspectives. I. Magnetic vs. Non-Magnetic Interacting Binary Stars. Odessa Astron. Publ., vol. 23, pp. 8-12.
[09] Andronov I.L. and Baklanov A.V. 2004, Astronomy School Reports, vol. 5, pp.264-270.
[10] Andronov, I.L., Kim, Yonggi, Kim, Young-Hee, Yoon, Joh-Na, Chinarova, L.L. and Tkachenko, M.G. (2015) Phenomenological Modeling of Newly Discovered Eclipsing Binary 2MASS J18024395 + 4003309 = VSX J180243.9+400331. Journal of Astronomy and Space Science, Vol. 32, p. 127-136.
[11] Andronov, I.L. and Tkachenko, M.G. (2013). Comparative Analysis of Numerical Methods of Determination of Parameters of Binary Stars. Case of Spherical Components. Odessa Astronomical Publications, vol. 26, pp. 204-206.
[12] Bradstreet, D.H. (2005). Fundamentals of Solving Eclipsing Binary Light Curves Using Binary Maker 3. SASS, vol. 24, pp 23-37.
[13] Bradstreet, D.H., Steelman, D.P. (2002). Binary Maker 3.0 - An Interactive Graphics-Based Light Curve Synthesis Program Written in Java. Bulletin of the American Astronomical Society, vol. 34, p. 1224.
[14] Cherepashchuk, A.M. (1993). Parametric Models in Inverse Problems of Astrophysics. Astronomicheskii Zhurnal, vol. 70, pp. 1157-1176.
[15] Devlen, A. (2015). A New Variable Star in Perseus: GSC 3692-00624. Open European Journal on Variable Stars 171: 1-6.
[16] Kallrath, J. and Milone, E.F. (2009). Eclipsing Binary Stars: Modeling and Analysis, Springer-Verlag New York, p. 444.
[17] Kopal, Z. (1959). Close Binary Systems. Chapman & Hall, London, pp. 558.
[18] Korn, G.A. and Korn, Th.M. (1968). Mathematical Handbook for Scientists and Engineers. Definitions, Theorems, and Formulas for Reference and Review. New York: McGraw-Hill, pp. 1130.
[19] Kudashkina, L. S., Andronov, I. L. (1996) Fourier Coefficients for the Light Curves of 62 Mira-Type Stars. Odessa Astronomical Publications 9: 108-111.
[20] Malkov, Yu., Oblak, E., Avvakumova, E.A. and Torra J. (2007) A procedure for the classification of eclipsing binaries, Astron. Astrophys., vol. 465, pp. 549-556.
[21] Mikulášek, Z. (2015) Phenomenological modelling of eclipsing system light curves. Astronomy and Astrophysics, vol. 584, A8: pp. 1-13.
[22] Mikulášek, Z., Zejda, M. and Janík J. (2011). Period Analyses Without O-C Diagrams, Proceedings IAU Symposium, vol. 282, pp. 391-394.
[23] Mikulášek, Z., Zejda, M., Pribulla, T., Vaňko, M., Qian, S.-B. and Zhu, L.-Y. (2015) The Concept of Few-Parameter Modeling of Eclipsing Binary and Exoplanet Transit Light Curves. Astron. Soc. Pacif. Conf. Ser., Vol. 496, p.176-180.
[24] Nicholson, M. P. (2009). Five new variable stars in the field of the old nova RS Car. Open European Journal on Variable Stars, Vol. 102, pp. 1-4.
[25] Paczyński, B., Szczygieł, D. M., Pilecki, B. and Pojmański, G. (2006) Eclipsing binaries in the All Sky Automated Survey catalogue. MNRAS, Vol. 368, pp. 1311-1318.
[26] Papageorgiou, A., Kleftogiannis, G. and Christopoulou, P.-E. (2014). An Automated Search of O'Connell Effect from Surveys of Eclipsing Binaries, Contrib. Astron. Obs. Skalnate Pleso, vol.43, pp. 470-472.
[27] Parenago, P.P. and Kukarkin, B.V. (1936). The Shapes of Light Curves of Long Period Cepheids. Zeitschrift für Astrophysik, vol. 11, pp. 337-355.
[28] Pickering, E. (1881). Variable Stars of Short Period. Proc. Amer. Acad. Arts and Sciences, vol. 16, pp. 257-278.
[29] Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (2007). Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, pp. 1193.
[30] Prsa, A., Matijevic, G., Latkovic, O., Vilardell, F. and Wils P. (2011). PHOEBE: Physics Of Eclipsing Binaries. Astrophysics Source Code Library, (record ascl: 1106.002, 2011ascl.soft06002P).
[31] Prsa, A., Guinan, E.F., Devinney, E.J., Degroote, P., Bloemen, S. and Matijevic, G. (2012). Advances in Modeling Eclipsing Binary Stars in the Era of Large All-Sky Surveys with EBAI and PHOEBE. IAUS, vol. 282, pp. 271-278.
[32] Rucinski, S.M. (1973). The W UMa-type Systems as Contact Binaries. I. Two Methods of Geometrical Elements Determination. Degree of Contact. Acta Astronomica, vol. 23, pp. 79-118.
[33] Rucinski, S. (2010). Contact Binaries: The Current State. AIP Conf. Proc., vol. 1314, pp. 29-36.
[34] Samus, N.N., Durlevich, O.V., Kazarovets, E.V., Kireeva, N.N.and Pastukhova, E.N., General Catalog of Variable Stars (2014) CDS/ADC Collection of Electronic Catalogues, 1, 2025, code 2009yCat....1.2025S, electronically available at http://www.sai.msu.su/gcvs/gcvs/
[35] Shul'berg, A.M. (1971). Close Binary Systems with Spherical Components. Moscow, Nauka, 246 pp.
[36] Tsessevich, V.P., ed. (1971). Eclipsing Variable Stars. Moscow, Nauka, 350 pp.
[37] Vavilova, I.B., Pakulyak, L.K., Shlyapnikov, A.A., Protsyuk, Y.I., Savanevich, V.E., Andronov, I.L., Andruk, V.N., Kondrashova, N.N., Baklanov, A.V., Golovin, A.V., Fedorov, P.N., Akhmetov, V.S., Isak, I.I., Mazhaev, A.E., Golovnya, V.V., Virun, N.V., Zolotukhina, A.V., Kazantseva, L.V., Virnina, N.A., Breus, V.V., Kashuba, S.G., Chinarova, L.L., Kudashkina, L.S. and Epishev, V.P. (2012). Astroinformation Resource of the Ukrainian Virtual Observatory: Joint Observational Data Archive, Scientific Tasks, and Software. Kinem. Phys. Celest. Bodies, vol. 28, pp. 85-102.
[38] Wilson, R.E. (1979). Eccentric Orbit Generalization and Simultaneous Solution of Binary Star Light and Velocity Curves. ApJ, vol. 234, pp. 1054-1066.
[39] Wilson, R.E. (1994). Binary-star light Curve Models. PASP, vol.106, pp. 921-941.
[40] Wilson, R.E., Devinney, E.J. and Edward J. (1971). Realization of Accurate Close-Binary Light Curves: Application to MR Cygni. ApJ, vol.166, pp. 605-619.
[41] Wilson, R.E. (1993). Documentation of Eclipsing Binary Computer Model. University of Florida.
[42] Zoła, S., Kolonko, M. and Szczech, M. (1997). Analysis of a Photoelectric Light Curve of the W UMa-Type Binary ST Ind. A&A, vol. 324, pp. 1010-1012.
[43] Zoła, S., Gazeas, K., Kreiner, J.M., Ogloza, W., Siwak, M., Koziel-Wierzbowska, D. and Winiarski, M. (2010). Physical Parameters of Components in Close Binary Systems – VII. MNRAS, vol. 408, pp. 464-474.
600 ATLANTIC AVE, BOSTON,
MA 02210, USA
+001-6179630233
AIS is an academia-oriented and non-commercial institute aiming at providing users with a way to quickly and easily get the academic and scientific information.
Copyright © 2014 - American Institute of Science except certain content provided by third parties.