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Rotation and tide are two important factors which have an influence on the stellar structure and evolution. They cannot be neglected. According to the observation data of the massive binary system V478 Cyg, we test the theoretical model including the deformation which is induced by rotation and tide (our model). We compare our model with Kähler-Eggleton (KE) model, and the distorted model is more consistent with observations than the traditional model (KE model). Besides, it is found that great deformation occurs in the outer envelope, where its density is lower than the mean density. Rotation and tide can cause the gravity at the two polar points to increase and the gravity in the equatorial plane to decrease. Therefore, the radiative flux, which depends on the local effective gravity, is not constant on the equipotentials any more. The poles which become hotter, experience a high mass loss than the equator, which becomes cooler. Furthermore, the two components in our model have bigger radii, equatorial velocities and central compactness and low H-energy production rate. The bigger mean radius of the distorted star produces a smaller temperature gradient inside the star, resulting in a lower energy transport. The lower energy generation rate inside the distorted model will widen the main sequence and increase the stellar lifetime. Stellar temperature and luminosity of the distorted model are shifted toward lower value. The tidal distortion inside the secondary star plays a most important role in the rate of the apsidal motion because of lower compactness. The apsidal motion derived from rotation is larger than the one derived from the general relativity.
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Keywords:
- stellar structure and evolution /
- rotation /
- tide /
- apsidal motion
[1] Huang R Q 2006 Stellar Physics (1st Ed.) (Beijing: China Science and Technology Press) p313 (in Chinese) [黄润乾 2006 恒星物理 (第1版) (北京: 中国科学技术出版社)第313页]
[2] Paczynski B 1971 Annu. Rev. Astron. Astrophys. 9 183
[3] Kippenhahn R, Thomas H C 1970 Proceedings of IAU Colloq.4 Columbus, USA, September 8-11, 1969 p20
[4] Endal A S, Sofia S 1976 Astrophys. J. 210 184
[5] Pinsonneault M H, Kawaler S D, Sofia S, Demarqure P 1989 Astrophys. J. 338 424
[6] Pinsonneault M H, Kawaler S D, Demarqure P 1990 Astrophys. J. Suppl. Ser. 74 501
[7] Pinsonneault M H, Deliyannis C P, Demarqure P 1991 Astrophys. J. 367 239
[8] Song H F, Zhang B, Zhang J, Wu H B, Peng Q H 2003 Chin. Phys. Lett. 20 2084
[9] Wang X M, Zhou X G, Tao Z Y, Yu X D 2013 Acta Phys. Sin. 62 029201 (in Chinese) [王秀明, 周小刚, 陶祖钰, 俞小鼎 2013 62 029201]
[10] Xu Y, Xu W, Ma Y G, Cai X Z, Chen J G, Fan G T, Fan G W, Guo W, Luo W, Pan Q Y, Shen W Q, Yang L F 2009 Chin. Phys. B 18 1421
[11] Liu H L, Liu M Q, Lai X J, Luo Z Q 2007 Chin. Phys. B 16 1637
[12] Huang R Q 2004 Astron. Astrophys. 425 591
[13] Huang R Q 2004 Astron. Astrophys. 422 981
[14] Song H F, Wang J Z, Li Y 2013 Acta Phy. Sin. 62 059701 (in Chinese) [宋汉峰, 王靖洲, 李云 2013 62 059701]
[15] Kopal Z 1959 Close Binary Systems (1st Ed.) (New York: Wiley) p30
[16] Landin N R, Mendes L T S, Vaz P R 2009 Astron. Astrophys. 494 209
[17] Hartkopf W I, Guinan E F, Harmanec P 2006 Proceedings of IAU Symposium Prague, Czech Republic, August 22-25, 2006 p5
[18] Claret A, Giménez A 2010 Astron. Astrophys. 519 A57
[19] Claret A, Giménez A, Wolf M 2010 Astron. Astrophys. 515 A4
[20] Giménez A 1985 Astrophys. J. 297 405
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[1] Huang R Q 2006 Stellar Physics (1st Ed.) (Beijing: China Science and Technology Press) p313 (in Chinese) [黄润乾 2006 恒星物理 (第1版) (北京: 中国科学技术出版社)第313页]
[2] Paczynski B 1971 Annu. Rev. Astron. Astrophys. 9 183
[3] Kippenhahn R, Thomas H C 1970 Proceedings of IAU Colloq.4 Columbus, USA, September 8-11, 1969 p20
[4] Endal A S, Sofia S 1976 Astrophys. J. 210 184
[5] Pinsonneault M H, Kawaler S D, Sofia S, Demarqure P 1989 Astrophys. J. 338 424
[6] Pinsonneault M H, Kawaler S D, Demarqure P 1990 Astrophys. J. Suppl. Ser. 74 501
[7] Pinsonneault M H, Deliyannis C P, Demarqure P 1991 Astrophys. J. 367 239
[8] Song H F, Zhang B, Zhang J, Wu H B, Peng Q H 2003 Chin. Phys. Lett. 20 2084
[9] Wang X M, Zhou X G, Tao Z Y, Yu X D 2013 Acta Phys. Sin. 62 029201 (in Chinese) [王秀明, 周小刚, 陶祖钰, 俞小鼎 2013 62 029201]
[10] Xu Y, Xu W, Ma Y G, Cai X Z, Chen J G, Fan G T, Fan G W, Guo W, Luo W, Pan Q Y, Shen W Q, Yang L F 2009 Chin. Phys. B 18 1421
[11] Liu H L, Liu M Q, Lai X J, Luo Z Q 2007 Chin. Phys. B 16 1637
[12] Huang R Q 2004 Astron. Astrophys. 425 591
[13] Huang R Q 2004 Astron. Astrophys. 422 981
[14] Song H F, Wang J Z, Li Y 2013 Acta Phy. Sin. 62 059701 (in Chinese) [宋汉峰, 王靖洲, 李云 2013 62 059701]
[15] Kopal Z 1959 Close Binary Systems (1st Ed.) (New York: Wiley) p30
[16] Landin N R, Mendes L T S, Vaz P R 2009 Astron. Astrophys. 494 209
[17] Hartkopf W I, Guinan E F, Harmanec P 2006 Proceedings of IAU Symposium Prague, Czech Republic, August 22-25, 2006 p5
[18] Claret A, Giménez A 2010 Astron. Astrophys. 519 A57
[19] Claret A, Giménez A, Wolf M 2010 Astron. Astrophys. 515 A4
[20] Giménez A 1985 Astrophys. J. 297 405
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