Author Affiliations
1College of Physics, Guizhou University, Guiyang 550025, China2Yunnan Astronomical Observatory, Chinese Academy of Sciences, Kunming 650011, China3School of Space Science and Physics, Shandong University, Weihai 556011, China4Department of Astronomy, University of Geneva, Geneva 1290, Switzerlandshow less
Fig. 1. (a) Variations of equatorial velocity in single star models; (b) variations of equatorial velocity in binary star models. Hollow diamonds denote the end of main sequence; hollow circles stand for the beginning of helium burning; solid circles denote the end of helium burning; hollow squares represent the beginning of carbon burning; solid squares represent the end of carbon burning(a)单星模型赤道转动速度随时间的变化; (b)双星模型赤道转动速度随时间的变化; 其中, 空心菱形为主序结束, 空心圆圈为中心氦开始燃烧, 实心圆圈为中心氦燃烧结束, 空心正方形为中心碳开始燃烧, 实心正方形是中心碳燃烧结束
Fig. 2. (a) Stellar mass and its mass of convective core vary with evolutionary time for the models of single star; (b) stellar mass and its mass of convective core vary with evolutionary time for the models of binary star(a) 各种单星模型的质量(实线)和其对应的对流核的质量(划线)随时间的变化; (b) 各种双星模型的质量(实线)和其对应的对流核的质量(划线)随时间的变化
Fig. 3. (a) Surface nitrogen abundance vary with evolutionary time for the models of single star; (b) surface nitrogen abundance vary with evolutionary time for the models of binary star; (c) surface helium abundance vary with central helium for the models of single stars and binary star(a)单星模型中恒星表面氮丰度随时间的演化; (b)双星模型中两子星表面氮丰度随时间的演化; (c) 主序阶段, 单星和双星模型的表面氦质量丰度随中心氦质量丰度的变化
Fig. 4. (a) Evolution as a function of the actual mass of the abundances (in mass fraction) of different elements at the surface of a non-rotating single model S1; (b) evolution as a function of the actual mass of the abundances (in mass fraction) of different elements at the surface of a rotating single model S6; (c) evolution as a function of the actual mass of the abundances (in mass fraction) of different elements at the surface of the primary star of model B1; (d) evolution as a function of the actual mass of the abundances (in mass fraction) of different elements at the surface of the primary star of model B2(a) 单星非转动S1模型表面各种元素的质量丰度的对数值随时间的演化; (b) 单星转动S6模型表面各种元素的质量丰度的对数值随时间的演化; (c) 双星非转动B1模型中的主星表面各种元素的质量丰度的对数值随时间的演化; (d) 双星转动模型B2中的主星表面各种元素的质量丰度的对数值随时间的演化
Fig. 5. Rate of mass transfer during Roche lobe overflow vary with evolutionary time for the models of binary star双星模型洛希瓣物质交换率随时间的演化
Fig. 6. (a) Evolutionary tracks in HR diagram for single stars; (b) evolutionary tracks in HR diagram for binaries(a) 单星模型在赫罗图中演化; (b) 双星模型中的主星在赫罗图中的演化; 双星模型的初始偏心率为0
Fig. 7. (a) Surface mass fraction of hydrogen varies with central helium mass fraction in models of single star; (b) surface effective temperature varies with central helium mass fraction in models of single star; (c) surface mass fraction of hydrogen varies with central helium mass fraction in models of binary star; (d) surface effective temperature varies with central helium mass fraction in models of of binary star(a) 单星模型表面氢的质量丰度随中心氦质量丰度的变化; (b) 单星模型表面有效温度随中心氦质量丰度的变化; (c) 双星模型表面氢的质量丰度随中心氦质量丰度的变化; (d) 双星模型表面有效温度随中心氦质量丰度的变化
| 0.45 WR星的类型 | 判定依据 | 注:
$T_{\rm eff}$![]() ![]() 是恒星的有效温度;
${X_{i} }/{X_{j} }$![]() ![]() 为恒星元素的质量丰度之比;
$\rm ({C+O})/{He}$![]() ![]() 为数丰度之比.
| | O型星 | $\log (T_{\rm eff})>4.5$![]() ![]() | | WNL型星 | $\log (T_{\rm eff})>4.0$![]() ![]() 和
$X_{\rm H} <0.3$![]() ![]() | | WNE型星 | $X_{\rm H} <10^{-5}$![]() ![]() 和
$X_{\rm C}![]() ![]() | | WNC型星 | $\dfrac{X_{\rm C}}{X_{\rm N}}>0.1$![]() ![]() 和
$\dfrac{X_{\rm C}}{X_{\rm N}}<10$![]() ![]() | | WC型星 | $X_{\rm C}>X_{\rm N}$![]() ![]() 和
$\rm \dfrac{C+O}{He}<1$![]() ![]() | | WO型星 | $X_{\rm C}>X_{\rm N}$![]() ![]() 和
$\rm \dfrac{C+O}{He}>1$![]() ![]() |
|
Table 1. Criteria for classification of WR stars
| Models | $M_1/M_\odot$![]() ![]() | $M_2/M_\odot$![]() ![]() | $Z$![]() ![]() | $\alpha$![]() ![]() | $P_{\rm orb, ini}$![]() ![]() /d
| $V_{\rm ini, 1}$![]() ![]() /km·s–1 | $V_{\rm ini, 2}$![]() ![]() /km·s–1 | 注: B为双星系统, S为单星;
$M_1$![]() ![]() ,
$M_2$![]() ![]() 分别为主星和次星的质量(以太阳质量
$M_{\odot}$![]() ![]() 为单位); Z为金属丰度;
$\alpha$![]() ![]() 为对流超射系数;
$P_{\rm orb, ini}$![]() ![]() 为双星初始轨道周期;
$V_{\rm ini, 1}$![]() ![]() ,
$V_{\rm ini, 2}$![]() ![]() 分别为主星和次星的初始自转赤道速度.
| | S1 | 60 | — | 0.014 | 0.0385 | — | 0 | — | | S2 | 60 | — | 0.014 | 0.0385 | — | 300 | — | | S3 | 60 | — | 0.014 | 0.0385 | — | 600 | — | | S4 | 40 | — | 0.014 | 0.0385 | — | 300 | — | | S5 | 60 | — | 0.0021 | 0.0385 | — | 300 | — | | S6 | 60 | — | 0.0021 | 0.0385 | — | 600 | — | | B1 | 60 | 40 | 0.014 | 0.0385 | 3.0 | 0 | 0 | | B2 | 60 | 40 | 0.014 | 0.0385 | 3.0 | 300 | 300 | | B3 | 60 | 40 | 0.014 | 0.0385 | 3.0 | 600 | 600 | | B4 | 60 | 40 | 0.014 | 0.0385 | 40.0 | 300 | 300 | | B5 | 60 | 40 | 0.0021 | 0.0385 | 3.0 | 300 | 300 |
|
Table 2. Initial parameters for single stars and binaries
| Sequence | Age/Myr | $M/M_{\odot}$![]() ![]() | $\log T_{\rm eff}$![]() ![]() | $\log ({L_{1}}/{L_{\odot}})$![]() ![]() | $\rm [N/H]$![]() ![]() | $V_{\rm eq}$![]() ![]() /km·s–1 | $\log T_{\rm c}$![]() ![]() | $\log \rho_{\rm c}$![]() ![]() | | 注: ZAMS为零龄主序; TAMS表示主序结束; BCHEB为中心氦核开始燃烧; ECHEB为中心氦核结束燃烧; BCCB 为中心碳核开始燃烧; CCB为中心碳核结束燃烧. | | ZAMS | | | | | | | | | | S1 | 0.0000 | 60.00 | 4.68 | 5.72 | 7.84 | 0.00 | 7.60 | 0.31 | | S2 | 0.0000 | 60.00 | 4.66 | 5.70 | 7.84 | 300.00 | 7.59 | 0.29 | | S3 | 0.0000 | 60.00 | 4.63 | 5.64 | 7.84 | 600.00 | 7.58 | 0.26 | | S4 | 0.0000 | 40.00 | 4.62 | 5.34 | 7.84 | 300.00 | 7.57 | 0.40 | | S5 | 0.0000 | 60.00 | 4.67 | 5.74 | 6.99 | 300.00 | 7.57 | 0.24 | | S6 | 0.0000 | 60.00 | 4.65 | 5.70 | 6.99 | 600.00 | 7.56 | 0.21 | | TAMS | | | | | | | | | | S1 | 3.9511 | 42.02 | 4.42 | 5.98 | 9.01 | 0.00 | 7.81 | 0.91 | | S2 | 4.1537 | 44.42 | 4.46 | 6.00 | 8.96 | 18.07 | 7.81 | 0.90 | | S3 | 4.5124 | 37.75 | 4.69 | 5.98 | 9.29 | 18.66 | 7.81 | 0.92 | | S4 | 5.3408 | 31.87 | 4.22 | 5.70 | 8.63 | 1.42 | 7.79 | 1.00 | | S5 | 4.3346 | 54.56 | 4.29 | 6.05 | 7.96 | 7.21 | 7.87 | 1.05 | | S6 | 5.0531 | 34.52 | 4.88 | 5.99 | 8.96 | 25.65 | 7.86 | 1.10 | | BCHEB | | | | | | | | | | S1 | 3.9550 | 42.01 | 4.46 | 6.00 | 9.01 | 0.00 | 7.98 | 1.43 | | S2 | 4.1574 | 44.40 | 4.51 | 6.02 | 8.98 | 19.75 | 7.98 | 1.42 | | S3 | 4.5162 | 37.62 | 4.77 | 6.01 | 9.30 | 25.72 | 7.98 | 1.45 | | S4 | 5.3453 | 31.83 | 4.25 | 5.72 | 8.63 | 1.37 | 7.96 | 1.51 | | S5 | 4.3383 | 54.53 | 4.31 | 6.06 | 7.96 | 7.28 | 8.03 | 1.55 | | S6 | 5.0570 | 34.44 | 4.96 | 6.02 | 8.97 | 36.78 | 8.03 | 1.60 | | ECHEB | | | | | | | | | | S1 | 4.3054 | 25.27 | 5.21 | 5.99 | 23.45 | 0.00 | 8.53 | 3.13 | | S2 | 4.5120 | 25.94 | 5.21 | 6.00 | 23.02 | 158.64 | 8.53 | 3.13 | | S3 | 4.8924 | 16.90 | 5.20 | 5.74 | 24.64 | 76.49 | 8.51 | 3.22 | | S4 | 5.7771 | 15.57 | 5.35 | 5.79 | 25.17 | 327.58 | 8.88 | 4.59 | | S5 | 4.6825 | 39.56 | 4.45 | 6.19 | 8.45 | 5.98 | 8.54 | 3.07 | | S6 | 5.4231 | 18.20 | 5.21 | 5.79 | 28.82 | 49.92 | 8.52 | 3.21 | | BCCB | | | | | | | | | | S1 | 4.3099 | 25.16 | 5.33 | 6.06 | 16.72 | 0.00 | 8.83 | 4.14 | | S2 | 4.5167 | 25.81 | 5.34 | 6.07 | 19.18 | 286.44 | 8.85 | 4.24 | | S3 | 4.8980 | 16.80 | 5.34 | 5.83 | 20.60 | 149.13 | 8.86 | 4.45 | | S4 | 5.7772 | 15.57 | 5.36 | 5.79 | 25.28 | 334.92 | 8.92 | 4.78 | | S5 | 4.6870 | 39.45 | 4.46 | 6.25 | 8.57 | 37.32 | 8.84 | 4.12 | | S6 | 5.4284 | 18.10 | 5.34 | 5.87 | 20.66 | 94.78 | 8.85 | 4.35 | | ECCB | | | | | | | | | | S1 | 4.3100 | 25.15 | 5.42 | 6.09 | 18.59 | 0.00 | 9.07 | 5.25 | | S2 | 4.5167 | 25.81 | 5.42 | 6.10 | 18.47 | 313.57 | 9.06 | 5.19 | | S3 | 4.8981 | 16.80 | 5.41 | 5.86 | 20.55 | 157.94 | 9.06 | 5.40 | | S4 | 5.7772 | 15.57 | 5.40 | 5.81 | 25.43 | 367.73 | 9.03 | 5.33 | | S5 | — | — | — | — | — | — | — | — | | S6 | 5.4285 | 18.10 | 5.41 | 5.90 | 20.90 | 97.57 | 9.05 | 5.34 |
|
Table 3. Parameters for single star at different evolutionary stages
| Sequence | Age
/Myr
| $P_{\rm orb}$![]() ![]() /d
| $M_{1}/M_{\odot}$![]() ![]() | $M_{2}/M_{\odot}$![]() ![]() | $\log(T_{\rm eff, 1})$![]() ![]() /K
| $\log \Big(\dfrac{L_{1}}{L_{\odot} }\Big)$![]() ![]() | $\log(T_{\rm eff, 2})$![]() ![]() /K
| $\log \Big(\dfrac{L_{2}}{L_{\odot} }\Big)$![]() ![]() | >
$\Big[\rm \dfrac{N_{1}}{H}\Big]$![]() ![]() | >
$\Big[\rm \dfrac{N_{2}}{H}\Big]$![]() ![]() | $V_{\rm eq1}$![]() ![]() /
km·s–1 | $V_{\rm eq2}$![]() ![]() /
km·s–1 | $\log T_{\rm c}$![]() ![]() /
K
| $\log \rho_{\rm c}$![]() ![]() /
g·cm–3 | | ZAMS | | | | | | | | | | | | | | | | B1 | 0.0000 | 3.00 | 60.00 | 40.00 | 4.68 | 5.71 | 4.64 | 5.36 | 7.84 | 7.84 | 0.00 | 0.00 | 7.62 | 0.37 | | B2 | 0.0000 | 3.00 | 60.00 | 40.00 | 4.67 | 5.70 | 4.63 | 5.34 | 7.84 | 7.84 | 288.35 | 294.86 | 7.61 | 0.35 | | B3 | 0.0000 | 3.00 | 60.00 | 40.00 | 4.64 | 5.65 | 4.59 | 5.27 | 7.84 | 7.84 | 566.93 | 581.75 | 7.60 | 0.32 | | B4 | 0.0000 | 40.00 | 60.00 | 40.00 | 4.67 | 5.70 | 4.63 | 5.34 | 7.84 | 7.84 | 288.35 | 294.86 | 7.61 | 0.35 | | B5 | 0.0000 | 3.00 | 60.00 | 40.00 | 4.69 | 5.66 | 4.65 | 5.29 | 6.99 | 6.99 | 306.83 | 301.14 | 7.66 | 0.50 | | BTM1 | | | | | | | | | | | | | | | | B1 | 2.6862 | 3.60 | 53.01 | 38.15 | 4.59 | 5.84 | 4.59 | 5.48 | 7.84 | 7.84 | 0.00 | 0.00 | 7.64 | 0.39 | | B2 | 2.6314 | 3.63 | 51.90 | 38.00 | 4.59 | 5.82 | 4.59 | 5.47 | 8.25 | 7.94 | 250.24 | 162.73 | 7.63 | 0.39 | | B3 | 2.7810 | 4.12 | 51.34 | 37.86 | 4.57 | 5.83 | 4.59 | 5.48 | 8.22 | 7.96 | 238.80 | 146.79 | 7.64 | 0.40 | | B4 | 4.1328 | 63.17 | 43.82 | 35.94 | 4.23 | 6.02 | 4.49 | 5.56 | 9.05 | 8.69 | 35.18 | 120.39 | 8.24 | 2.26 | | B5 | 2.9131 | 3.25 | 57.69 | 39.46 | 4.60 | 5.86 | 4.61 | 5.47 | 7.34 | 7.07 | 270.95 | 164.95 | 7.68 | 0.52 | | ETM1 | | | | | | | | | | | | | | | | B1 | 3.8956 | 4.25 | 36.84 | 43.77 | 4.62 | 5.90 | 4.57 | 5.67 | 9.20 | 8.18 | 0.00 | 0.00 | 7.70 | 0.61 | | B2 | 2.7305 | 3.41 | 45.44 | 43.82 | 4.60 | 5.78 | 4.61 | 5.57 | 8.66 | 8.26 | 239.26 | 177.55 | 7.63 | 0.42 | | B3 | 2.9777 | 3.92 | 44.57 | 43.27 | 4.59 | 5.81 | 4.60 | 5.58 | 8.83 | 8.25 | 226.58 | 161.96 | 7.64 | 0.44 | | B4 | 4.1426 | 65.47 | 36.94 | 36.00 | 4.27 | 6.10 | 4.49 | 5.56 | 9.26 | 8.67 | 73.07 | 330.19 | 8.31 | 2.47 | | B5 | 3.9817 | 3.61 | 38.02 | 51.22 | 4.63 | 5.87 | 4.65 | 5.73 | 8.27 | 7.82 | 217.02 | 168.84 | 7.72 | 0.69 | | TAMS | | | | | | | | | | | | | | | | B1 | 4.0397 | 4.65 | 33.60 | 43.48 | 4.68 | 5.91 | 4.56 | 5.68 | 9.30 | 8.18 | 0.00 | 0.00 | 7.81 | 0.95 | | B2 | 4.1254 | 5.13 | 25.57 | 43.47 | 4.83 | 5.79 | 4.53 | 5.69 | 9.86 | 8.41 | 20.52 | 193.13 | 7.80 | 0.99 | | B3 | 4.0832 | 5.43 | 27.93 | 43.40 | 4.81 | 5.84 | 4.54 | 5.68 | 9.66 | 8.44 | 19.99 | 174.17 | 7.80 | 0.97 | | B4 | 4.0693 | 62.61 | 44.06 | 36.03 | 4.41 | 5.97 | 4.54 | 5.56 | 8.82 | 8.63 | 6.63 | 68.60 | 7.72 | 0.65 | | B5 | 4.3382 | 3.81 | 34.79 | 50.91 | 4.68 | 5.92 | 4.63 | 5.75 | 8.44 | 7.81 | 169.76 | 181.54 | 7.86 | 1.10 | | BCHEB | | | | | | | | | | | | | | | | B1 | 4.0409 | 4.65 | 33.57 | 43.48 | 4.69 | 5.91 | 4.56 | 5.68 | 9.30 | 8.18 | 0.00 | 0.00 | 7.82 | 0.99 | | B2 | 4.1297 | 5.15 | 25.44 | 43.46 | 4.92 | 5.82 | 4.53 | 5.69 | 9.87 | 8.41 | 30.07 | 192.49 | 7.97 | 1.52 | | B3 | 4.0874 | 5.45 | 27.80 | 43.39 | 4.90 | 5.87 | 4.54 | 5.68 | 9.68 | 8.44 | 29.48 | 173.40 | 7.98 | 1.50 | | B4 | 4.1281 | 63.03 | 43.88 | 35.95 | 4.48 | 5.99 | 4.53 | 5.56 | 9.04 | 8.63 | 4.75 | 60.68 | 7.91 | 1.21 | | B5 | 4.3422 | 3.82 | 34.74 | 50.91 | 4.75 | 5.94 | 4.63 | 5.76 | 8.44 | 7.81 | 149.04 | 181.17 | 8.02 | 1.60 | | BMT2 | | | | | | | | | | | | | | | | B1 | 4.0474 | 4.67 | 33.39 | 43.47 | 4.63 | 6.00 | 4.58 | 5.69 | 9.30 | 9.30 | 0.00 | 0.00 | 8.24 | 2.29 | | B2 | 3.1581 | 3.55 | 43.04 | 43.10 | 4.61 | 5.81 | 4.59 | 5.59 | 8.99 | 8.19 | 231.13 | 191.20 | 7.64 | 0.45 | | B3 | 3.1290 | 3.97 | 43.65 | 43.04 | 4.59 | 5.82 | 4.59 | 5.58 | 8.93 | 8.23 | 223.55 | 166.73 | 7.64 | 0.45 | | B4 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | | B5 | 4.3460 | 3.84 | 34.70 | 50.90 | 4.66 | 5.99 | 4.63 | 5.76 | 8.44 | 7.81 | 187.54 | 180.93 | 8.26 | 2.34 | | EMT2 | | | | | | | | | | | | | | | | B1 | 4.0562 | 5.13 | 30.44 | 45.39 | 4.65 | 6.06 | 4.62 | 5.72 | 9.48 | 8.74 | 0.00 | 0.00 | 8.31 | 2.49 | | B2 | 3.5409 | 3.78 | 37.67 | 44.95 | 4.61 | 5.82 | 4.59 | 5.65 | 9.06 | 8.42 | 212.81 | 195.54 | 7.66 | 0.51 | | B3 | 3.6151 | 4.27 | 37.66 | 44.50 | 4.60 | 5.84 | 4.58 | 5.65 | 9.07 | 8.44 | 203.84 | 175.46 | 7.66 | 0.52 | | B4 | — | — | — | — | — | — | — | — | — | — | — | — | — | — | | B5 | 4.3517 | 4.25 | 31.33 | 51.54 | 4.67 | 6.05 | 4.64 | 5.77 | 8.60 | 7.91 | 174.27 | 292.23 | 8.31 | 2.49 | | ECHEB | | | | | | | | | | | | | | | | B1 | 4.4454 | 8.50 | 14.60 | 44.32 | 5.30 | 5.71 | 4.57 | 5.75 | 25.43 | 8.65 | 0.00 | 0.00 | 8.74 | 3.96 | | B2 | 4.5716 | 8.31 | 11.27 | 42.40 | 5.27 | 5.52 | 4.45 | 5.73 | 24.26 | 8.41 | 58.94 | 181.80 | 8.70 | 3.93 | | B3 | 4.5155 | 9.20 | 12.05 | 42.46 | 5.27 | 5.56 | 4.47 | 5.71 | 24.15 | 8.44 | 52.74 | 142.55 | 8.68 | 3.83 | | B4 | 4.3645 | 94.44 | 25.01 | 35.66 | 5.14 | 5.92 | 4.50 | 5.58 | 24.02 | 8.65 | 0.32 | 127.17 | 8.37 | 2.68 | | B5 | 4.6953 | 5.16 | 24.36 | 51.19 | 5.18 | 5.95 | 4.61 | 5.80 | 27.78 | 7.85 | 6.01 | 149.71 | 8.48 | 2.99 | | BCCB | | | | | | | | | | | | | | | | B1 | 4.4468 | 8.51 | 14.58 | 44.31 | 5.35 | 5.75 | 4.57 | 5.75 | 24.91 | 8.65 | 0.00 | 0.00 | 8.89 | 4.66 | | B2 | 4.5741 | 8.32 | 11.24 | 42.40 | 5.33 | 5.58 | 4.45 | 5.73 | 23.39 | 8.41 | 67.64 | 179.57 | 8.85 | 4.60 | | B3 | 4.5184 | 9.22 | 12.02 | 42.45 | 5.34 | 5.62 | 4.47 | 5.71 | 24.42 | 8.44 | 62.74 | 140.22 | 8.88 | 4.71 | | B4 | 4.4963 | 110.76 | 20.53 | 35.48 | 5.36 | 5.95 | 4.48 | 5.59 | 24.89 | 8.65 | 0.56 | 99.94 | 8.90 | 4.56 | | B5 | 4.7078 | 5.25 | 23.75 | 51.18 | 5.37 | 6.03 | 4.61 | 5.80 | 23.51 | 7.85 | 10.68 | 146.97 | 8.92 | 4.63 | | ECCB | | | | | | | | | | | | | | | | B1 | 4.4469 | 8.51 | 14.58 | 44.31 | 5.41 | 5.77 | 4.57 | 5.75 | 24.88 | 8.65 | 0.00 | 0.00 | 9.04 | 5.38 | | B2 | 4.5743 | 8.32 | 11.24 | 42.40 | 5.37 | 5.60 | 4.45 | 5.73 | 22.95 | 8.41 | 66.77 | 173.97 | 9.01 | 5.44 | | B3 | 4.5185 | 9.22 | 12.01 | 42.45 | 5.38 | 5.64 | 4.47 | 5.71 | 24.41 | 8.44 | 63.39 | 136.75 | 9.01 | 5.41 | | B4 | 4.4963 | 110.77 | 20.53 | 35.48 | 5.42 | 5.97 | 4.48 | 5.59 | 24.88 | 8.65 | 0.67 | 98.21 | 9.05 | 5.22 | | B5 | 4.7078 | 5.25 | 23.75 | 51.18 | 5.42 | 6.04 | 4.61 | 5.80 | 23.50 | 7.85 | 12.57 | 144.92 | 9.05 | 5.18 |
|
Table 4. Evolutionary parameters for binary star at different stages.
| Sequence | Age/Myr | $M_1/M_{\odot}$![]() ![]() | log(
$X_{\rm ^{1}H}$![]() ![]() )
| log(
$X_{\rm ^{4}He}$![]() ![]() )
| log(
$X_{\rm ^{12}C}$![]() ![]() )
| log(
$X_{\rm ^{14}N}$![]() ![]() )
| log(
$X_{\rm ^{16}O}$![]() ![]() )
| log(
$X_{\rm ^{19}F}$![]() ![]() )
| log(
$X_{\rm ^{20}Ne}$![]() ![]() )
| log(
$X_{\rm ^{22}Ne}$![]() ![]() )
| $X_{\rm ^{26}Al}$![]() ![]() | | ZAMS | | | | | | | | | | | | | S1 | 0.0000 | 60.00 | –0.14 | –0.58 | –2.62 | –3.15 | –2.18 | –6.46 | –2.87 | –3.96 | 0 | | S2 | 0.0000 | 60.00 | –0.14 | –0.58 | –2.62 | –3.15 | –2.18 | –6.46 | –2.87 | –3.96 | 0 | | S6 | 0.0000 | 60.00 | –0.12 | –0.63 | –3.45 | –3.98 | –3.01 | –7.28 | –3.69 | –4.78 | 0 | | TAMS | | | | | | | | | | | | | S1 | 3.9511 | 42.02 | –0.23 | –0.40 | –3.91 | –2.08 | –3.07 | –9.23 | –2.87 | –6.77 | 9.77 × 10–6 | | S2 | 4.1537 | 44.42 | –0.22 | –0.42 | –3.70 | –2.11 | –2.86 | –7.86 | –2.87 | –5.37 | 4.57 × 10–6 | | S6 | 5.0531 | 34.52 | –0.99 | –0.05 | –4.56 | –2.88 | –4.60 | –10.46 | –3.83 | –7.51 | 4.36 × 10–6 | | BCHEB | | | | | | | | | | | | | S1 | 3.9550 | 42.01 | –0.23 | –0.40 | –3.91 | –2.08 | –3.07 | –9.23 | –2.87 | –6.77 | 9.77 × 10–6 | | S2 | 4.1574 | 44.40 | –0.22 | –0.41 | –3.77 | –2.10 | –2.91 | –8.07 | –2.87 | –5.58 | 4.89 × 10–6 | | S6 | 5.0570 | 34.44 | –0.99 | –0.05 | –4.56 | –2.88 | –4.60 | –10.46 | –3.83 | –7.51 | 4.36 × 10–6 | | WNL | | | | | | | | | | | | | S1 | 4.1147 | 34.94 | –0.58 | –0.14 | –3.87 | –2.06 | –3.63 | –9.72 | –2.88 | –6.53 | 4.16 × 10–5 | | S2 | 4.3343 | 36.29 | –0.57 | –0.14 | –3.82 | –2.06 | –3.59 | –9.67 | –2.88 | –6.45 | 3.54 × 10–5 | | S6 | 4.1796 | 48.34 | –0.52 | –0.16 | –4.60 | –2.88 | –4.55 | –10.50 | –3.79 | –7.50 | 4.46 × 10–6 | | WNE | | | | | | | | | | | | | S1 | 4.1801 | 31.26 | –5.02 | –0.01 | –3.73 | –2.05 | –3.77 | –9.61 | –2.89 | –6.56 | 5.62 × 10–5 | | S2 | — | — | — | — | — | — | — | — | — | — | — | | S6 | — | — | — | — | — | — | — | — | — | — | — | | WC | | | | | | | | | | | | | S1 | 4.2217 | 28.36 | –21.87 | –0.51 | –0.34 | –17.12 | –0.68 | –4.71 | –2.80 | –1.88 | 1.12 × 10–15 | | S2 | 4.4173 | 30.79 | –5.22 | –0.02 | –1.50 | –2.06 | –2.05 | –5.72 | –2.89 | –2.91 | 4.67 × 10–5 | | S6 | 5.2107 | 29.81 | –5.80 | –0.02 | –1.37 | –2.89 | –2.52 | –6.15 | –3.84 | –3.38 | 3.80 × 10–6 | | WO | | | | | | | | | | | | | S1 | 4.2569 | 26.70 | –21.35 | –0.65 | –0.34 | –16.95 | –0.52 | –4.72 | –2.70 | –1.89 | 2.57 × 10–15 | | S2 | 4.4302 | 28.58 | –17.68 | –0.71 | –0.36 | –5.17 | –0.45 | –4.72 | –2.63 | –1.91 | 4.16 × 10–8 | | S6 | 5.3898 | 18.84 | –29.68 | –0.64 | –0.32 | –17.99 | –0.55 | –5.48 | –3.51 | –2.71 | 8.51 × 10–17 | | ECHEB | | | | | | | | | | | | | S1 | 4.3054 | 25.27 | –29.41 | –0.77 | –0.37 | –16.81 | –0.41 | –4.72 | –2.59 | –1.91 | 5.01 × 10–15 | | S2 | 4.5120 | 25.94 | –28.78 | –0.82 | –0.39 | –16.61 | –0.38 | –4.72 | –2.54 | –1.93 | 7.07 × 10–15 | | S6 | 5.4231 | 18.20 | –35.90 | –0.71 | –0.33 | –17.93 | –0.48 | –5.48 | –3.43 | –2.72 | 1.14 × 10–16 | | BCCB | | | | | | | | | | | | | S1 | 4.3099 | 25.16 | –22.67 | –0.79 | –0.37 | –16.80 | –0.40 | –4.73 | –2.58 | –1.92 | 5.37 × 10–15 | | S2 | 4.5167 | 25.81 | –24.97 | –0.83 | –0.40 | –16.64 | –0.37 | –4.72 | –2.52 | –1.93 | 7.58 × 10–15 | | S6 | 5.4284 | 18.10 | –27.74 | –0.72 | –0.33 | –17.93 | –0.47 | –5.48 | –3.41 | –2.72 | 1.54 × 10–16 | | ECCB | | | | | | | | | | | | | S1 | 4.3100 | 25.15 | –24.54 | –0.79 | –0.37 | –16.80 | –0.40 | –4.73 | –2.58 | –1.92 | 5.37 × 10–15 | | S2 | 4.5167 | 25.81 | –24.26 | –0.83 | –0.40 | –16.64 | –0.37 | –4.72 | –2.52 | –1.93 | 7.76 × 10–15 | | S6 | 5.4285 | 18.10 | –27.99 | –0.72 | –0.33 | –17.93 | –0.47 | –5.48 | –3.41 | –2.72 | 1.54 × 10–16 |
|
Table 5. Mass fraction of various chemical elements at stellar surfaces at different stages in models S1, S2, and S6
| Sequence | Age/Myr | $M_1/M_{\odot}$![]() ![]() | log(
$X_{\rm ^{1}H}$![]() ![]() )
| log(
$X_{\rm ^{4}He}$![]() ![]() )
| log(
$X_{\rm ^{12}C}$![]() ![]() )
| log(
$X_{\rm ^{14}N}$![]() ![]() )
| log(
$X_{\rm ^{16}O}$![]() ![]() )
| log(
$X_{\rm ^{19}F}$![]() ![]() )
| log(
$X_{\rm ^{20}Ne}$![]() ![]() )
| log(
$X_{\rm ^{22}Ne}$![]() ![]() )
| $X_{\rm ^{26}Al}$![]() ![]() | | ZAMS | | | | | | | | | | | | | B1 | 0.0000 | 60.00 | –0.14 | –0.58 | –2.62 | –3.15 | –2.18 | –6.46 | –2.87 | –3.96 | 0 | | B2 | 0.0000 | 60.00 | –0.14 | –0.58 | –2.62 | –3.15 | –2.18 | –6.46 | –2.87 | –3.96 | 0 | | BTM1 | | | | | | | | | | | | | B1 | 2.6862 | 53.01 | –0.14 | –0.58 | –2.62 | –3.15 | –2.18 | –6.54 | –2.95 | –4.04 | 3.31 × 1021 | | B2 | 2.6314 | 51.90 | –0.14 | –0.58 | –2.76 | –2.74 | –2.21 | –6.66 | –2.95 | –4.16 | 3.38 × 10–7 | | ETM1 | | | | | | | | | | | | | B1 | 3.8956 | 36.84 | –0.40 | –0.23 | –3.87 | –2.06 | –3.56 | –9.69 | –2.96 | –6.62 | 1.81 × 10–5 | | B2 | 2.7305 | 45.44 | –0.16 | –0.53 | –3.02 | –2.36 | –2.38 | –6.94 | –2.95 | –4.45 | 3.89 × 10–6 | | ECHB | | | | | | | | | | | | | B1 | 4.0397 | 33.60 | –0.50 | –0.18 | –3.85 | –2.05 | –3.61 | –9.72 | –2.96 | –6.61 | 2.45 × 10–5 | | B2 | 4.1254 | 25.57 | –1.06 | –0.05 | –3.80 | –2.05 | –3.67 | –9.68 | –2.96 | –6.63 | 4.16 × 10–5 | | BCHEB | | | | | | | | | | | | | B1 | 4.0409 | 33.57 | –0.50 | –0.18 | –3.85 | –2.05 | –3.61 | –9.72 | –2.96 | –6.61 | 2.45 × 10–5 | | B2 | 4.1297 | 25.44 | –1.07 | –0.05 | –3.80 | –2.05 | –3.67 | –9.68 | –2.96 | –6.63 | 4.16 × 10–5 | | BMT2 | | | | | | | | | | | | | B1 | 4.0474 | 33.39 | –0.50 | –0.18 | –3.85 | –2.05 | –3.61 | –9.72 | –2.96 | –6.61 | 2.51 × 10–5 | | B2 | 3.1581 | 43.04 | –0.24 | –0.39 | –3.80 | –2.09 | –2.95 | –8.24 | –2.95 | –5.76 | 1.31 × 10–5 | | WNL | | | | | | | | | | | | | B1 | 4.0480 | 32.78 | –0.52 | –0.16 | –3.85 | –2.05 | –3.61 | –9.73 | –2.96 | –6.62 | 2.81 × 10–5 | | B2 | 3.8633 | 32.25 | –0.52 | –0.16 | –3.85 | –2.05 | –3.61 | –9.72 | –2.96 | –6.60 | 2.95 × 10–5 | | EMT2 | | | | | | | | | | | | | B1 | 4.0562 | 30.44 | –0.68 | –0.11 | –3.84 | –2.05 | –3.64 | –9.72 | –2.96 | –6.60 | 3.89 × 10–5 | | B2 | 3.5409 | 37.67 | –0.28 | –0.34 | –3.86 | –2.07 | –3.16 | –8.72 | –2.95 | –6.19 | 1.41 × 10–5 | | WNE | | | | | | | | | | | | | B1 | 4.1344 | 26.76 | –5.00 | –0.01 | –3.73 | –2.05 | –3.76 | –9.59 | –2.97 | –6.65 | 4.78 × 10–5 | | B2 | 4.2129 | 22.30 | –5.18 | –0.01 | –3.68 | –2.06 | –3.74 | –9.45 | –2.97 | –6.52 | 4.78 × 10–5 | | WC | | | | | | | | | | | | | B1 | 4.1976 | 23.92 | –28.45 | –0.09 | –0.80 | –14.82 | –2.17 | –4.58 | –2.97 | –1.87 | 6.45 × 10–17 | | B2 | 4.2498 | 21.01 | –10.94 | –0.01 | –2.05 | –2.10 | –3.40 | –5.62 | –2.97 | –2.91 | 4.36 × 10–5 | | WO | | | | | | | | | | | | | B1 | 4.4339 | 14.75 | –31.67 | –0.64 | –0.31 | –17.28 | –0.58 | –4.59 | –2.85 | –1.88 | 5.62 × 10–5 | | B2 | — | — | — | — | — | — | — | — | — | — | — | | ECHEB | | | | | | | | | | | | | B1 | 4.4454 | 14.60 | –31.77 | –0.70 | –0.31 | –17.19 | –0.53 | –4.59 | –2.82 | –1.89 | 7.76 × 10–16 | | B2 | 4.5716 | 11.27 | –30.86 | –0.60 | –0.30 | –17.45 | –0.65 | –4.58 | –2.90 | –1.88 | 2.45 × 10–16 | | BCCB | | | | | | | | | | | | | B1 | 4.4468 | 14.58 | –31.25 | –0.70 | –0.31 | –17.19 | –0.53 | –4.59 | –2.82 | –1.89 | 7.76 × 10–16 | | B2 | 4.5741 | 11.24 | –29.98 | –0.61 | –0.30 | –17.44 | –0.64 | –4.58 | –2.90 | –1.88 | 2.51 × 10–16 | | ECCB | | | | | | | | | | | | | B1 | 4.4469 | 14.58 | –31.22 | –0.70 | –0.31 | –17.19 | –0.53 | –4.59 | –2.82 | –1.89 | 7.76 × 10–16 | | B2 | 4.5743 | 11.24 | –29.54 | –0.61 | –0.30 | –17.44 | –0.64 | –4.58 | –2.90 | –1.88 | 2.51 × 10–16 |
|
Table 6. Mass fraction of various chemical elements at the surfaces of the primary star at different stages in models B1 and B2
