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The effects of rotation on the evolution of Population Ⅲ (Pop Ⅲ) stars in the burning stages of core H and He are investigated. Due to their zero-metallicity nature, these stars are initially unable to burn hydrogen through the CNO cycle (Here, C, N, and O stand for carbon, nitrogen, and oxygen, respectively). And without this crucial energy supply, they experience a contraction phase during the early main sequence (MS). The lack of CNO elements not only affects the central region of the star but also leads to energy increase (due to triggering of the CNO cycle) in the stellar envelope due to the outward diffusion of He-burning products. Therefore, rotational mixing has a unique effect on these stars. Rotation significantly affects the observable properties of Pop Ⅲ stars through two main effects. One is that rotational mixing brings additional fuel into the nuclear burning core, which increases the luminosity as well as the stellar lifetimes, and the other is that rotational mixing brings He-burning products from the core to the H-burning shell during later evolutionary phases. This will change the temperature distribution, and may lead to significant expansion in some models, depending on the relative core size. The relative core size is crucial here, because the contribution of the outer shell and the core to the total energy produced tells us about the structure of the star and dominant factors in the evolution of the surface properties. Despite weaker meridional currents in Pop Ⅲ stars, angular momentum can accumulate at the surface in fast-rotating massive models because of their negligible mass loss through radiative winds. This spin-up causes the models with an initial mass of 40M⊙, an initial velocity of υini = 400 km/s, and a metallicity of Z = 10–4 to reach critical rotation during the MS, resulting in increased mass loss. Rotational mixing strongly affects metal enrichment, but unlike stars with high metallicity, it cannot consistently enhance metal production. Rotation leads to an early enhancement of CNO in the H shell during He burning, which may hinder metal enrichment. This effect also occurs during the core He-burning phase. In these cases, the convection caused by the CNO enhancement in the H shell will lead to the retraction of the He-burning core. As the core grows, the speed at which the H shell moves outwards is faster than the speed at which the He-burning products can be expelled from the core through rotational mixing, therefore hindering the interaction of these products with the H-burning shell, which is necessary for metal enrichment. H-He shell interactions after core He burning play a crucial role in metal production, where the rotation may enhance enrichment. This highlights the complexity in the metal enrichment processes of these models. A detailed understanding of the interior structure is therefore required to accurately predict metal yields. -
Keywords:
- stellar structure and evolution /
- rotation /
- Population Ⅲ /
- metallicity
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图 1 (a) 初始转速为$ {v_{{\text{ini}}}} $= 0, 200, 400 km/s的不同金属丰度的40M⊙恒星模型的角速度比率$ \varOmega /{\varOmega _{{\text{crit}}}} $演化情况, 绿色虚线表示模型达到临界转速的位置; (b) 初始转速$ {v_{{\text{ini}}}} $= 0, 200, 400 km/s的不同金属丰度的40M⊙恒星模型的表面赤道速度的演化情况; (c) 金属丰度Z = 10–4的40M⊙恒星的子午环流的垂直速度在中心氢燃烧阶段的分布轮廓图
Figure 1. (a) The evolution of $ \varOmega /{\varOmega _{{\text{crit}}}} $ for 40M⊙ stellar models with different metallicities, and initial rotation speeds of 0, 200, and 400 km/s, the green dashed line in the figure indicates the position where the model reaches the critical rotation speed; (b) the evolution of surface equatorial velocities for 40M⊙ stellar models with different metallicities and initial rotation speeds of 0, 200, and 400 km/s; (c) the profile for the vertical components of meridional circulation in a 40M⊙ star with metallicity Z = 10–4 during the central H burning.
图 2 (a) 金属丰度Z = 0, 40M⊙恒星在不同初始转动速度下的星风损失随时间演化; (b) 金属丰度Z = 10–4, 40M⊙恒星在不同初始转动速度下的星风损失随时间演化
Figure 2. (a) The evolution of stellar wind mass loss with time for 40M⊙ with Z = 0 metallicity under different initial rotation speeds; (b) the evolution of stellar wind mass loss with time for 40M⊙ with Z = 10–4 metallicity under different initial rotation speeds.
图 3 (a) 无转动情况下金属丰度Z = 0和Z = 10–4的大质量恒星在赫罗图中的演化; (b) 40M⊙恒星在不同转动速度和不同金属丰度下的赫罗图的演化
Figure 3. (a) The evolution of massive stars with Z = 0 and Z = 10–4 metallicities in the HR diagram under non-rotation conditions; (b) the evolution of HR diagrams for 40M⊙ stars under different rotation speeds and metallicities.
图 4 (a) 金属丰度Z = 0, 40M⊙恒星在不同初始转动速度下的对流核随时间演化; (b) 金属丰度Z = 10–4, 40M⊙恒星在不同初始转动速度下的对流核随时间演化
Figure 4. (a) The evolution of convection cores with time for 40M⊙ with 0 metallicity under different initial rotation speeds; (b) the evolution of convection cores with time for 40M⊙ with 10–4 metallicity under different initial rotation speeds.
图 5 (a) 金属丰度Z = 0的40M⊙恒星在不同初始转动速度下表面14N随时间的演化; (b) 金属丰度Z = 10–4的40M⊙恒星在不同初始转动速度下表面14N随时间的演化
Figure 5. (a) The evolution of surface N-14 abundance with time for 40M⊙ with 0 metallicity under different initial rotation speeds; (b) the evolution of surface 14N abundance with time for 40M⊙ with 10–4 metallicity under different initial rotation speeds.
图 6 (a) 40M⊙恒星在不同初始转动速度和金属丰度下中心温度随时间的演化; (b) 40M⊙恒星在不同初始转动速度和金属丰度下中心密度随时间的演化
Figure 6. (a) The evolution of central temperature with time for 40M⊙ stars under different initial rotation and metallicities; (b) the evolution of central density with time for 40M⊙ stars under different initial rotation and metallicities.
图 7 40M☉的转动恒星金属丰度分别为Z = 0和Z = 10–4的模型在氦燃烧阶段3个不同时刻(以中心氦含量Yc为标识)的能量产生率分布图, 图中绿色(黑色)实线分别代表氦(氢)燃烧产生的能量, 红色虚线表示对应光度对总光度的贡献比例(数值标注于右侧纵轴), 对流区域用灰色阴影区域表示 (a1), (a2) Yc = 0.8; (b1), (b2) Yc = 0.5; (c1), (c2) Yc = 0.2
Figure 7. Energy production capacity distribution diagrams at three different moments during the He-burning core phase for rotating 40M☉ stellar models with metallicities of 0 and 10–4, the green (or black) solid line represent the energy generated by He (or H) burning, respectively, the red dashed line indicates the contribution ratio of the corresponding luminosity to the total luminosity(the numerical values are labeled on the right vertical axis), convective regions are indicated by the grey shaded areas: (a1), (a2) Yc = 0.8; (b1), (b2) Yc = 0.5; (c1), (c2) Yc = 0.2.
图 8 初始转动速度为400 km/s的40M☉恒星模型在金属丰度为Z = 0和Z = 10–4下氦燃烧阶段3个不同时刻(以中心氦含量Yc为标识)的元素丰度分布, 丰度曲线展示了恒星从中心到表面的化学元素分布, 对流区域用灰色阴影区域表示 (a1), (a2) Yc = 0.8; (b1), (b2) Yc = 0.5; (c1), (c2) Yc = 0.2
Figure 8. Elemental abundance distributions at three different moments during the He-burning phase for 40M☉ stellar models with an initial rotation speed of 400 km/s, under two metallicities cases Z = 0 and Z = 10–4, the curves in the figure show the chemical element distribution from the center to the surface of the star, convective regions are indicated by the grey shaded areas: (a1), (a2) Yc = 0.8; (b1), (b2) Yc = 0.5; (c1), (c2) Yc = 0.2.
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[1] Savage B D, Sembach K R 1996 Annu. Rev. Astron. Astrophys. 34 279
Google Scholar
[2] Draine B T 2003 Annu. Rev. Astron. Astrophys. 41 241
Google Scholar
[3] Jenkins E B 2009 Astrophys. J. 700 1299
Google Scholar
[4] Meynet G, Georgy C, Hirschi R, Maeder A, Massey P, Przybilla N, Nieva M F 2011 Bull. R. Soc. Sci. Liège. 80 266
Google Scholar
[5] Cui Z, Wang Z J, Zhu C H 2018 Publ. Astron. Soc. Pac. 130 084202
Google Scholar
[6] 彭卫国, 宋汉锋, 詹琼, 吴兴华, 景江红 2019 物理学报 68 219701
Google Scholar
Peng W G, Song H F, Zhan Q, Wu X H, Jing J H 2019 Acta Phys. Sin. 68 219701
Google Scholar
[7] Wu F W, Song H F, Li Q L, He Y, Qu X Y, Han Z 2024 Chin. Phys. Lett. 41 089701
Google Scholar
[8] Marigo P, Chiosi C, Kudritzki R P 2003 Astron. Astrophys. 399 617
Google Scholar
[9] Marigo P, Girardi L, Chiosi C, Wood P R 2001 Astron. Astrophys. 371 152
Google Scholar
[10] Ekström S, Meynet G, Chiappini C, Hirschi R, Maeder A 2008 Astron. Astrophys. 489 685
Google Scholar
[11] Yoon S C, Dierks A, Langer N 2012 Astron. Astrophys. 542 A113
Google Scholar
[12] Ekström S, Georgy C, Eggenberger P, Meynet G, Mowlavi N, Wyttenbach A, Granada A, Decressin T, Hirschi R, Frischknecht U, Charbonnel C, Maeder A 2012 Astron. Astrophys. 537 A146
Google Scholar
[13] Georgy C, Ekström S, Eggenberger P, Meynet G, Haemmerlé L, Maeder A, Granada A, Groh J H, Hirschi R, Mowlavi N, Yusof N, Charbonnel C, Decressin T, Barblan F 2013 Astron. Astrophys. 558 A103
Google Scholar
[14] Groh J H, Ekström S, Georgy C, Meynet G, Choplin A, Eggenberger P, Hirschi R, Maeder A, Murphy L J, Boian I, Farrell E J 2019 Astron. Astrophys. 627 A24
Google Scholar
[15] Bromm V, Kudritzki R P, Loeb A 2001 Astrophys. J. 552 464
Google Scholar
[16] Abel T, Bryan G L, Norman M L 2002 Sci. 295 93
Google Scholar
[17] Heger A, Woosley S E 2002 Astrophys. J. 567 532
Google Scholar
[18] Brott I, de Mink S E, Cantiello M, Langer N, de Koter A, Evans C J, Hunter I, Trundle C, Vink J S 2011 Astron. Astrophys. 530 A115
Google Scholar
[19] Stacy A, Bromm V, Loeb A 2011 Mon. Not. R. Astron. Soc. 413 543
Google Scholar
[20] Stacy A, Greif T H, Klessen R S, Bromm V, Loeb A 2013 Mon. Not. R. Astron. Soc. 431 1470
Google Scholar
[21] Hirano S, Bromm V 2018 Mon. Not. R. Astron. Soc. 476 3964
Google Scholar
[22] Murphy L J, Groh J H, Ekström S, Meynet G, Pezzotti C, Georgy C, Choplin A, Eggenberger P, Farrell E, Haemmerlé L, Hirschi R, Maeder A, Martinet S 2021 Mon. Not. R. Astron. Soc. 501 2745
Google Scholar
[23] Sibony Y, Liu B, Simmonds C, Meynet G, Bromm V 2022 Astron. Astrophys. 666 A199
Google Scholar
[24] Aryan A, Pandey S B, Gupta R, Ror A K 2023 Mon. Not. R. Astron. Soc. 521 L17
Google Scholar
[25] Tsiatsiou S, Sibony Y, Nandal D, Sciarini L, Hirai Y, Ekström S, Farrell E, Murphy L, Choplin A, Hirschi R, Chiappini C, Liu B, Bromm V, Groh J, Meynet G 2024 Astron. Astrophys. 687 A307
Google Scholar
[26] Zahn J P 1992 Astron. Astrophys. 265 115
Google Scholar
[27] Maeder A, Zahn J P 1998 Astron. Astrophys. 334 1000
Google Scholar
[28] Kippenhahn R, Thomas H C 1969 Mitt. Astron. Ges. 27 168
Google Scholar
[29] Maeder A, Meynet G 2004 Proceedings of IAU Symposium Cancun, Yucatan, Mexico, November 11-15, 2002 p500
[30] Kaehler H 1986 Astron. Astrophys. 157 329
Google Scholar
[31] Maeder A, Meynet G 2012 Reviews of Modern Physics. 84 25
Google Scholar
[32] Heger A, Langer N, Woosley S E 2000 Astrophys. J. 528 368
Google Scholar
[33] Maeder A 1995 Astron. Astrophys. 299 84
Google Scholar
[34] Maeder A 1997 Astron. Astrophys. 321 134
Google Scholar
[35] Vink J S, de Koter A, Lamers H J G L M 2001 Astron. Astrophys. 369 574
Google Scholar
[36] Iglesias C A, Rogers F J 1996 Astrophys. J. 464 943
Google Scholar
[37] Ferguson J W, Alexander D R, Allard F, Hauschildt P H 2001 Astrophys. J. 557 798
Google Scholar
[38] Asplund M, Grevesse N, Sauval A J 2005 Astronomical Society of the Pacific Conference Series Austin, Texas, June 17-19, 2004 p25
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