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The gravity-darkening of highly distorted stars in close binary systems

V. Practical analysis of the contact components of W ursae majoris-type systems

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Abstract

From a quantitative analysis of the photometric ellipticity effect, values of the exponent of gravity-darkening α have been empirically deduced for the components of sixteen W UMa systems with accurate cross-correlation spectroscopic mass ratios. In the analysis, the exponents for both components of a W UMa system are assumed to be the same. In view of the generally unstable nature of their light curves and the consequent difficulty to find an unique set of the fractional radii of both components, α-values have been derived for various equipotential surfaces with boundary cases set at the inner and outer Roche lobes.

The results indicate that if the fill-out factors are less than 0.5 (as is so for most of the actual cases), the deduced α-values are all greater than Lucy's conventional value of 0.32. The empirical α-values as a whole are found to increase with the mean effective temperature of the components and, furthermore, they show a tendency to decrease with increasing mass ratio, particularly for A-type systems. Thus, a W UMa system consisting of two components of quite different masses has a large empirical α-value. These observational evidences indicate that the structure of the photosphere of contact components of W UMa systems is significantly different from that of normal Main-Sequence stars of similar spectral type and may provide a clue to solve puzzles of W UMa stars.

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References

  • Adams, W. S. and Joy, A. H.: 1919,Astrophys. J. 49, 186.

    Google Scholar 

  • Al-Naimiy, H. M. K.: 1978a,Astrophys. Space Sci. 53, 181.

    Google Scholar 

  • Al-Naimiy, H. M. K.: 1978b,Astrophys. Space Sci. 56, 219.

    Google Scholar 

  • Al-Naimiy, H. M. K.: 1982,Astron. J. 87, 1041.

    Google Scholar 

  • Awadalla, N. S. and Yamasaki, A.: 1984,Astrophys. Space Sci. 107, 347.

    Google Scholar 

  • Barden, S. C.: 1987,Astrophys. J. 317, 333.

    Google Scholar 

  • Batten, A. H., Fletcher, J. M., and Mann, P. J.: 1978,Publ. Dominion Astrophys. Obs. 15, 121.

    Google Scholar 

  • Berthier, E.: 1975,Astron. Astrophys. 40, 237.

    Google Scholar 

  • Binnendijk, L.: 1959,Astron. J. 64, 65.

    Google Scholar 

  • Binnendijk, L.: 1960,Astron. J. 65, 88.

    Google Scholar 

  • Binnendijk, L.: 1965,Astron. J. 70, 209.

    Google Scholar 

  • Binnendijk, L., 1966,Astron. J. 71, 340.

    Google Scholar 

  • Binnendijk, L.: 1967,Publ. Dominion Astrophys. Obs. 13, No. 3.

  • Binnendijk, L.: 1969a,Astron. J. 74, 211.

    Google Scholar 

  • Binnendijk, L.: 1969b,Astron. J. 74, 218.

    Google Scholar 

  • Binnendijk, L.: 1970,Vistas Astron. 12, 217.

    Google Scholar 

  • Binnendijk, L.: 1971,Astron. J. 76, 923.

    Google Scholar 

  • Binnendijk, L.: 1977,Vistas Astron. 21, 359.

    Google Scholar 

  • Bookmyer, B. B.: 1968,Astron. J. 73, 26.

    Google Scholar 

  • Bookmyer, B. B.: 1969,Astron. J. 74, 1197.

    Google Scholar 

  • Bookmyer, B. B.: 1976,Publ. Astron. Soc. Pacific 88, 473.

    Google Scholar 

  • Bradstreet, D. H.: 1981,Astron. J. 86, 98.

    Google Scholar 

  • Bradstreet, D. H.: 1985,Astrophys. J. Suppl. 58, 413.

    Google Scholar 

  • Breinhorst, R. A.: 1971,Astrophys. Space Sci. 10, 411.

    Google Scholar 

  • Breinhorst, R. A. and Hoffmann, M.: 1982,Astrophys. Space Sci. 86, 107.

    Google Scholar 

  • Broglia, P.: 1960,Contr. Obs. Milano-Merate, No. 165.

  • Carr, R. B.: 1971,Publ. Goodsell Obs., No. 16.

  • Cester, B. and Gridelli, L.: 1967,Publ. Trieste Astron. Obs., No. 165.

  • Chambliss, C. R.: 1971,Astron. J. 76, 64.

    Google Scholar 

  • Chang, Y. C.: 1948,Astrophys. J. 107, 101.

    Google Scholar 

  • Cillié, G. G.: 1951,Harvard Bull., No. 920, p. 41.

    Google Scholar 

  • Devinney, E. J. and Twigg, L. W.: 1974,Bull. Am. Astron. Soc. 6, 335.

    Google Scholar 

  • Eaton, J. A.: 1986,Acta Astron. 36, 79.

    Google Scholar 

  • Eggen, O. J.: 1967,Mem. Roy. Astron. Soc. 70, 111.

    Google Scholar 

  • Giuricin, G., Mardirossian, F., and Mezzetti, M.: 1982,Astron. Astrophys. Suppl. 49, 89.

    Google Scholar 

  • Heard, J. F.: 1965,J. Roy. Astron. Soc. Canada 59, 258.

    Google Scholar 

  • Hilditch, R. W.: 1981,Monthly Notices Roy. Astron. Soc. 196, 305.

    Google Scholar 

  • Hill, G.: 1979,Publ. Dominion Astrophys. Obs. 15, 297.

    Google Scholar 

  • Hill, G., Hilditch, R. W., Younger, F., and Fisher, W. A.: 1975,Mem. Roy. Astron. Soc. 79, 131.

    Google Scholar 

  • Hinderer, F.: 1960,J. Obs. 43, 161.

    Google Scholar 

  • Hoffmann, M.: 1978,Astron. Astrophys. Suppl. 33, 63.

    Google Scholar 

  • Hoffmann, M.: 1980,Astron. Astrophys. Suppl. 40, 263.

    Google Scholar 

  • Hrivnak, B. J.: 1982,Astrophys. J. 260, 744.

    Google Scholar 

  • Hrivnak, B. J.: 1985,Astrophys. J. 290, 696.

    Google Scholar 

  • Hrivnak, B. J., Milone, E. F., Hill, G., and Fisher, W. A.: 1984,Astrophys. J. 285, 683.

    Google Scholar 

  • Huruhata, M., Dambara, T., and Kitamura, M.: 1953,Ann. Tokyo Astron. Obs,, 2nd Ser. 3, 227.

    Google Scholar 

  • Huruhata, M., Kitamura, M., and Nakamura, T.: 1957,Ann. Tokyo Astron. Obs., 2nd Ser. 5, 31.

    Google Scholar 

  • Hutchings, J. B.: 1973,Astrophys. J. 180, 501.

    Google Scholar 

  • Hutchings, J. B. and Hill, G.: 1973a,Astrophys. J. 179, 539.

    Google Scholar 

  • Hutchings, J. B. and Hill, G.: 1973b,Astrophys. J. 180, 501.

    Google Scholar 

  • Kaluzny, J.: 1984,Acta Astron. 34, 217.

    Google Scholar 

  • Kaluzny, J. and Pojmanski, G.: 1983,Acta Astron. 33, 277.

    Google Scholar 

  • King, D. J. and Hilditch, R. W.: 1984,Monthly Notices Roy. Astron. Soc. 209, 645.

    Google Scholar 

  • Kitamura, M.: 1965,Adv. Astron, Astrophys. 3, 27.

    Google Scholar 

  • Kitamura, M. and Nakamura, Y.: 1983,Ann. Tokyo Astron. Obs., 2nd Ser. 19, 413 (Part I).

    Google Scholar 

  • Kitamura, M. and Nakamura, Y.: 1986,Ann. Tokyo Astron. Obs., 2nd Ser. 21, 229 (Part II).

    Google Scholar 

  • Kitamura, M. and Nakamura, Y.: 1987a,Ann. Tokyo Astron. Obs., 2nd Ser. 21, 311 (Part III).

    Google Scholar 

  • Kitamura, M. and Nakamura, Y.: 1987b,Ann. Tokyo Astron. Obs., 2nd Ser. 21, 387 (Part IV).

    Google Scholar 

  • Kitamura, M. and Yamasaki, A.: 1971,Tokyo Astron. Obs. Bull., 2nd Ser, No. 209.

  • Knipe, G. F.: 1965,Astrophys. J. 142, 1068.

    Google Scholar 

  • Koch, R. H.: 1960,Astron. J. 65, 374.

    Google Scholar 

  • Koch, R. H. and Shanus, C. R.: 1978,Astron. J. 83, 1452.

    Google Scholar 

  • Kopal, Z.: 1959,Close Binary Systems, Chapman-Hall, London, Ch. III.

    Google Scholar 

  • Kopal, Z.: 1968a,Astrophys. Space Sci. 2, 23.

    Google Scholar 

  • Kopal, Z.: 1968b,Astrophys. Space Sci. 2, 166.

    Google Scholar 

  • Kopal, Z.: 1978,Dynamics of Close Binary Systems, D. Reidel Publ. Co., Dordrecht, Holland, Ch. VI.

    Google Scholar 

  • Kopal, Z. and Shapley, M. B.: 1956,Jodrell Bank Ann. 1, 141.

    Google Scholar 

  • La Fara, R.: 1951,Astrophys. J. 115, 14.

    Google Scholar 

  • Lafta, S. J. and Grainger, J. F.: 1985,Astrophys. Space Sci. 114, 23.

    Google Scholar 

  • Lavrov, M. I. and Zhukov, G. V.: 1975,Astron. Circ., No. 873.

  • Lenouvel, F. and Daguillon, J.: 1956,J. Obs. 39, 1.

    Google Scholar 

  • Linnaluoto, S. and Piirola, V.: 1979,Astron. Astrophys. Suppl. 36, 33.

    Google Scholar 

  • Linnell, A. P.: 1985,Astrophys. J. Suppl. 57, 611.

    Google Scholar 

  • Linnell, A. P.: 1986,Astrophys. J. 300, 304.

    Google Scholar 

  • Linnell, A. P.: 1987,Astrophys. J. 316, 389.

    Google Scholar 

  • Liu, Q.-Y. and Zhang, J.-T.: 1982,Chinese Astron. Astrophys. 6, 167.

    Google Scholar 

  • Lu, W.: 1985,Publ. Astron. Soc. Pacific 97, 1086.

    Google Scholar 

  • Lucy, L. B.: 1967,Z. Astrophys. 65, 89.

    Google Scholar 

  • Lucy, L. B.: 1968,Astrophys. J. 151, 1123.

    Google Scholar 

  • Lucy, L. B.: 1973,Astrophys. Space Sci. 22, 381.

    Google Scholar 

  • Maceroni, C.: 1986,Astron. Astrophys. 170, 43.

    Google Scholar 

  • Maceroni, C., Milone, L., and Russo, G.: 1982,Astron. Astrophys. Suppl. 49, 123.

    Google Scholar 

  • Mauder, H.: 1975,Astrophys. Space Sci. 34, 297.

    Google Scholar 

  • McDonald, D. D.: 1964,Publ. McCormick Obs. 12, 51.

    Google Scholar 

  • McLean, B. J.: 1981,Monthly Notices Roy. Astron. Soc. 195, 931.

    Google Scholar 

  • McLean, B. J.: 1983,Monthly Notices Roy. Astron. Soc. 204, 817.

    Google Scholar 

  • McLean, B. J. and Hilditch, R. W.: 1983,Monthly Notices Roy. Astron. Soc. 203, 1.

    Google Scholar 

  • Milone, E. F., Chia, T. T., Castle, K. G., Robb, R. M. and Merrill, J. E.: 1980,Astrophys. J. Suppl. 43, 339.

    Google Scholar 

  • Milone, E. F., Hrivnak, B. J., and Fisher, W. A.: 1985a,Astron. J. 90, 354.

    Google Scholar 

  • Milone, E. F., Hrivnak, B. J., Hill, G., and Fisher, W. A.: 1985b,Astron. J. 90, 109.

    Google Scholar 

  • Milone, E. F., Wilson, R. E., and Hrivnak, B. J.: 1987,Astrophys. J. 319, 325.

    Google Scholar 

  • Mochnacki, S. W.: 1972,Bull. Amer. Astron. Soc. 4, 399.

    Google Scholar 

  • Mochnacki, S. W. and Doughty, N. A.: 1972a,Monthly Notices Roy. Astron. Soc. 156, 51.

    Google Scholar 

  • Mochnacki, S. W. and Doughty, N. A.: 1972b,Monthly Notices Roy. Astron. Soc. 156, 243.

    Google Scholar 

  • Nagy, T. A.: 1974, Ph.D. Thesis, Univ. of Pennsylvania.

  • Nagy, T. A.: 1977,Publ. Astron. Soc. Pacific 89, 366.

    Google Scholar 

  • Nesci, R., Maceroni, C., Milone, L., and Russo, G.: 1986,Astron. Astrophys. 159, 142.

    Google Scholar 

  • Paczynski, B.: 1964,Astron. J. 69, 124.

    Google Scholar 

  • Popper, D. M.: 1948,Astrophys. J. 108, 490.

    Google Scholar 

  • Popper, D. M.: 1950,Publ. Astron. Soc. Pacific 62, 115.

    Google Scholar 

  • Popper, D. M.: 1966,Astron. J. 71, 175.

    Google Scholar 

  • Popper, D. M.: 1980,Ann. Rev. Astron. Astrophys. 18, 115.

    Google Scholar 

  • Purgathofer, A.: 1960,Mitt. Sternw. Wien 10, 195.

    Google Scholar 

  • Purgathofer, A. and Widorn, T.: 1959,Mitt. Sternw. Wien 10, 119.

    Google Scholar 

  • Rensing, M. J., Mochnacki, S. W., and Bolton, C. T.: 1985,Astron. J. 90, 767.

    Google Scholar 

  • Rigterink, P. V.: 1972,Astron. J. 77, 319.

    Google Scholar 

  • Rovithis, P. and Rovithis-Livaniou, H.: 1982,Astrophys. Space Sci. 87, 287.

    Google Scholar 

  • Rovithis, P. and Rovithis-Livaniou, H.: 1984,Astron. Astrophys. Suppl. 58, 679.

    Google Scholar 

  • Rucinski, S. M.: 1974,Acta Astron. 24, 119.

    Google Scholar 

  • Rucinski, S. M.: 1976,Publ. Astron. Soc. Pacific 88, 777.

    Google Scholar 

  • Rucinski, S. M., Whelan, J. A. J., and Worden, S. P.: 1977,Publ. Astron. Soc. Pacific 89, 684.

    Google Scholar 

  • Saito, K.: 1971,Tokyo Astron. Obs. Bull., 2nd Ser., No. 211.

  • Schmidt, H. and Schrick, K. W.: 1956,Z. Astrophys. 41, 1.

    Google Scholar 

  • Struve, O.: 1974,Astrophys. J. 106, 92.

    Google Scholar 

  • Struve, O.: 1950,Astrophys. J. 111, 658.

    Google Scholar 

  • Struve, O. and Gratton, L.: 1948,Astrophys. J. 108, 497.

    Google Scholar 

  • Struve, O. and Horak, H. G.: 1950,Astrophys. J. 112, 178.

    Google Scholar 

  • Struve, O. and Zebergs, V.: 1959,Astrophys. J. 130, 137.

    Google Scholar 

  • Struve, O., Horak, H. G., Canavaggia, R., Kourganoff, V., and Colacevich, A.: 1950,Astrophys. J. 111, 658.

    Google Scholar 

  • Tanabe, H. and Nakamura, T.: 1957,Ann. Tokyo Astron. Obs., 2nd Ser. 5, 15.

    Google Scholar 

  • Tempesti, P. and de Carlo, R.: 1968,Teramo Note Comm., No. 45.

  • Twigg, L. W.: 1979,Monthly Notices Roy. Astron. Soc. 189, 907.

    Google Scholar 

  • Wade, R. A. and Rucinski, S. M.: 1985,Astron. Astrophys. Suppl. 60, 471.

    Google Scholar 

  • Wentzel, W.: 1967,Mitt. Veränd. Sterne, Sonneberg 4, 60.

    Google Scholar 

  • Whelan, J. A. J., Worden, S. P. and Mochnacki, S. W.: 1973,Astrophys. J. 183, 133.

    Google Scholar 

  • Wilson, R. E.: 1967,Astron. J. 72, 1028.

    Google Scholar 

  • Wilson, R. E. and Devinney, E. J.: 1973,Astrophys. J. 182, 539.

    Google Scholar 

  • Winkler, L.: 1977,Astron. J. 82, 648.

    Google Scholar 

  • Wolfschmidt, G., Rahe, J., and Schöffel, E.: 1979,Mitt. Astron. Ges. 45, 49.

    Google Scholar 

  • Wood, F. B., Oliver, J. P., Florkowski, D. R., and Koch, R. H.: 1980,Finding List for Observers of Interacting Binaries, Univ. Pennsylvania Press, Pennsylvania.

    Google Scholar 

  • Woodward, E. J., Koch, R., and Eisenhardt, P. R.: 1980,Astron. J. 85, 50.

    Google Scholar 

  • Worden, S. P. and Whelan, J.: 1973,Monthly Notices Roy. Astron. Soc. 163, 391.

    Google Scholar 

  • Yamasaki, A.: 1982,Astrophys. Space Sci. 85, 43.

    Google Scholar 

  • Yamasaki, A. and Kitamura, M.: 1972,Publ. Astron. Soc. Japan 24, 213.

    Google Scholar 

  • Zhai, D., Leung, K.-C., and Zhang, R.: 1984,Astron. Astrophys. Suppl. 57, 487.

    Google Scholar 

  • Zhai, D., Lu, W., and Zhang, X.: 1987, private communication.

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  1. Yasuhisa Nakamura

    Present address: Department of Science Education, Fukushima University, Fukushima, Japan

Authors and Affiliations

  1. Tokyo Astronomical Observatory, Mitaka, Tokyo, Japan

    Masatoshi Kitamura

  2. Komaba Senior High School, Ohashi, Meguro-ku, Tokyo, Japan

    Yasuhisa Nakamura

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Kitamura, M., Nakamura, Y. The gravity-darkening of highly distorted stars in close binary systems. Astrophys Space Sci 145, 117–156 (1988). https://doi.org/10.1007/BF00645696

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