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The tide is a very important physical factor which can significantly affect the structure and evolution of stars. The physical factors which can affect tidal synchronization and orbital circularization are explored in this paper. For stars with radiative envelopes, radiative damping mechanism is required to explain the observed synchronization and circularization of close binaries. A star can experience a range of oscillations that arise from, and are driven by, the tidal field:the dynamical tides. The dynamical tide is the dynamical response to the tidal force exerted by the companion; it takes into account the elastic properties of the star, and the possibilities of resonances with its free modes of oscillation. The dissipation mechanism acting on this kind of tide is the deviation from adiabaticity of the forced oscillation, due to the radiative damping. Several physical factors can have an influence on the process of radiative damping which is scaled with thermal timescale. These physical factors include stellar mass, initial velocity, orbital period, metallicity, overshooting, etc. According to the equations for angular momentum transfer and chemical elements diffusion, we can obtain how these physical factors affect the evolution of rotating binaries and the mixing of chemical elements in two rotating components. The results indicates that the binaries with massive stars, smaller initial spin velocities, smaller overshooting parameters, and shorter orbital periods can attain the equilibrium speed and orbital circularization early. At synchronous states, the tidal torque is zero and stellar winds continue to brake the star. Therefore, two components cannot keep the synchronous state for a long time. At the equilibrium state, the tidal torque is counteracted by wind torques. Therefore, the equilibrium speed is less than the synchronous one. The system with smaller initial spin velocities reaches the equilibrium speed and orbital circularization early because angular momentum transformation between spin and the orbit can shorten the orbital distance and increase the tidal torques. Nitrogen enrichment in binaries is weaker than the one in single stars due to tidal braking. The results reveal that the system with massive components, higher metallicities, larger overshooting parameters, and shorter orbital periods can display high nitrogen enrichment. Stellar radius is small in the star with lower mass, lower metallicities, slower spin speeds and larger overshooting parameters whereas the star with lower metallicities have higher surface effective temperature. Rapid rotating stars evolve towards low temperature and luminosity in the HR diagram.
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Keywords:
- close binaries /
- evolution /
- rotation /
- tide
[1] Huang R Q 2006 Stellar Physics (2nd Ed.) (Beijing:Science and Technology of China Press) pp378-384 (in Chinese) [黄润乾 2006 恒星物理 (第二版) (北京:中国科学技术出版社) 第378384页]
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[4] Endal A S, Sofia S 1976 Astrophys. J. 210 184
[5] Pinsonneault M H, Kawaler S D, Sofia S, Demarque P 1989 Astrophys. J. 338 424
[6] Pinsonneault M H, Kawaler S D, Demarque P 1990 Astrophys. J. Suppl. Ser. 74 501
[7] Pinsonneault M H, Deliyannis C P, Demarque P 1991 Astrophys. J. 367 239
[8] Huang R Q 2004 Astron. Astrophys. 422 981
[9] Huang R Q 2004 Astron. Astrophys. 425 591
[10] Song H F, Wang J Z, Li Y 2013 Acta Phys. Sin. 62 059701 (in Chinese) [宋汉峰, 王靖洲, 李云 2013 物理学报 62 059701]
[11] Song H F, Wang J Z, Song F, Song F, Wang J T 2017 Astron. Astrophys. 600 A42
[12] Zhan Q, Song H F, Tai L T, Wang J T 2015 Acta Phys. Sin. 64 089701 (in Chinese) [詹琼, 宋汉峰, 邰丽婷, 王江涛 2015 物理学报 64 089701]
[13] Tai L T, Song H F, Wang J T 2016 Acta Phys. Sin. 65 049701 (in Chinese) [邰丽婷, 宋汉峰, 王江涛 2016 物理学报 65 049701]
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[18] Song H F, Meynet G, Maeder A, Ekstrom S, Eggenberger P, Georgy C, Qin Y, Fragos T, Soerensen M, Barblan F, Wade G A 2018 Astron. Astrophys. 609 A3
[19] Wang J T, Song H F 2016 Chin. Phys. Lett. 33 099702
[20] Li Z, Song H F, Peng W G 2018 Chin. Phys. Lett. 35 079701
[21] Toledano O, Moreno E, Koenigsberger G, Detmers R, Langer N 2007 Astron. Astrophys. 461 1057
[22] Zahn J P 1989 Astron. Astrophys. 220 112
[23] Endal A S, Sofia S 1978 Astrophys. J. 220 279
[24] Kippenhahn R 1974 Late Stages of Stellar Evolution (Warsaw:D Reidel Publishing Co) p20
[25] Heger A, Langer N, Woosley S E 2000 Astrophys. J. 528 368
[26] Paxton B, Bildsten L, Dotter A, Herwig F, Lesaffre P, Timmes F 2011 Astrophys. J. Suppl. 192 3P
[27] Paxton B, Cantiello M, Arras P, Bildsten L, Brown E F, Dotter A, Mankovich C, Montgomery M H, Stello D, Timmes F X, Townsend R 2013 Astrophys. J. Suppl. 208 4P
[28] Paxton B, Marchant P, Schwab J, Bauer E B, Bildsten L, Cantiello M, Dessart L, Farmer R, Hu H, Langer N, Townsend R H D, Townsley D M, Timmes F X 2015 Astrophys. J. Suppl. 220 15P
[29] Vink J S, de Koter A, Lamers H J G L M 2001 Astron. Astrophys. 369 574
[30] Maeder A, Meynet G 2012 Rev. Mod. Phys. 84 25
[31] von Zeipel H 1924 Mon. Not. R. Astron. Soc. 84 665
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[1] Huang R Q 2006 Stellar Physics (2nd Ed.) (Beijing:Science and Technology of China Press) pp378-384 (in Chinese) [黄润乾 2006 恒星物理 (第二版) (北京:中国科学技术出版社) 第378384页]
[2] Paczynski B 1971 Annu. Rev. Astron. Astrophys. 9 183
[3] Kippenhahn R, Thomas H C 1969 Mitt. A. G. 27 168
[4] Endal A S, Sofia S 1976 Astrophys. J. 210 184
[5] Pinsonneault M H, Kawaler S D, Sofia S, Demarque P 1989 Astrophys. J. 338 424
[6] Pinsonneault M H, Kawaler S D, Demarque P 1990 Astrophys. J. Suppl. Ser. 74 501
[7] Pinsonneault M H, Deliyannis C P, Demarque P 1991 Astrophys. J. 367 239
[8] Huang R Q 2004 Astron. Astrophys. 422 981
[9] Huang R Q 2004 Astron. Astrophys. 425 591
[10] Song H F, Wang J Z, Li Y 2013 Acta Phys. Sin. 62 059701 (in Chinese) [宋汉峰, 王靖洲, 李云 2013 物理学报 62 059701]
[11] Song H F, Wang J Z, Song F, Song F, Wang J T 2017 Astron. Astrophys. 600 A42
[12] Zhan Q, Song H F, Tai L T, Wang J T 2015 Acta Phys. Sin. 64 089701 (in Chinese) [詹琼, 宋汉峰, 邰丽婷, 王江涛 2015 物理学报 64 089701]
[13] Tai L T, Song H F, Wang J T 2016 Acta Phys. Sin. 65 049701 (in Chinese) [邰丽婷, 宋汉峰, 王江涛 2016 物理学报 65 049701]
[14] Zahn J P 1975 Astron. Astrophys. 41 329
[15] Zahn J P 1977 Astron. Astrophys. 57 383
[16] Song H F, Maeder A, Meynet G, Huang R Q, Ekstrom S, Granada A 2013 Astron. Astrophys. 556 A100
[17] Song H F, Meynet G, Maeder A, Ekstrom S, Eggenberger P 2016 Astron. Astrophys. 585 A120
[18] Song H F, Meynet G, Maeder A, Ekstrom S, Eggenberger P, Georgy C, Qin Y, Fragos T, Soerensen M, Barblan F, Wade G A 2018 Astron. Astrophys. 609 A3
[19] Wang J T, Song H F 2016 Chin. Phys. Lett. 33 099702
[20] Li Z, Song H F, Peng W G 2018 Chin. Phys. Lett. 35 079701
[21] Toledano O, Moreno E, Koenigsberger G, Detmers R, Langer N 2007 Astron. Astrophys. 461 1057
[22] Zahn J P 1989 Astron. Astrophys. 220 112
[23] Endal A S, Sofia S 1978 Astrophys. J. 220 279
[24] Kippenhahn R 1974 Late Stages of Stellar Evolution (Warsaw:D Reidel Publishing Co) p20
[25] Heger A, Langer N, Woosley S E 2000 Astrophys. J. 528 368
[26] Paxton B, Bildsten L, Dotter A, Herwig F, Lesaffre P, Timmes F 2011 Astrophys. J. Suppl. 192 3P
[27] Paxton B, Cantiello M, Arras P, Bildsten L, Brown E F, Dotter A, Mankovich C, Montgomery M H, Stello D, Timmes F X, Townsend R 2013 Astrophys. J. Suppl. 208 4P
[28] Paxton B, Marchant P, Schwab J, Bauer E B, Bildsten L, Cantiello M, Dessart L, Farmer R, Hu H, Langer N, Townsend R H D, Townsley D M, Timmes F X 2015 Astrophys. J. Suppl. 220 15P
[29] Vink J S, de Koter A, Lamers H J G L M 2001 Astron. Astrophys. 369 574
[30] Maeder A, Meynet G 2012 Rev. Mod. Phys. 84 25
[31] von Zeipel H 1924 Mon. Not. R. Astron. Soc. 84 665
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