Table 1.
Properties of the Z = 0.0004 stellar models at the end of the H-, He-, and C-burning phases.
| End of H-burning | End of He-burning | End of C-burning | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mini | υrot/υcrit | Veq |
 |
τH | M | Veq | Veq/Vcrit | Ysurf | N/C | N/O | τHe | M | Veq | Prot | ΩC/ΩS | Ysurf | N/C | N/O | τC | M | Veq | Prot | ΩC/ΩS | Ysurf | N/C | N/O |
| M⊙ | km s−1 | Myr | M⊙ | km s−1 | mass fract. | Myr | M⊙ | km s−1 | day | mass fract. | kyr | M⊙ | km s−1 | day | mass fract. | |||||||||||
| 120.00 | 0.00 | 0 | – | 2.606 | 118.25 | – | – | 0.2489 | 0.2885 | 0.1152 | 0.269 | 92.52 | – | – | – | 0.6585 | 69.3650 | 59.8911 | 0.021 | 87.49 | – | – | – | 0.7042 | 66.2987 | 116.4622 |
| 120.00 | 0.40 | 463 | 501 | 3.050 | 115.92 | 156 | 0.231 | 0.4238 | 5.5363 | 2.1020 | 0.270 | 93.20 | 0 | 6.158 × 1008 | 2.854 × 1009 | 0.7973 | 58.4043 | 53.1908 | 0.002 | 92.51 | 0 | 1.351 × 1006 | 1.087 × 1008 | 0.8012 | 59.4490 | 58.2812 |
| 85.00 | 0.00 | 0 | – | 2.975 | 83.96 | – | – | 0.2489 | 0.2885 | 0.1152 | 0.297 | 66.15 | – | – | – | 0.6156 | 44.5292 | 15.2587 | 0.040 | 66.04 | – | – | – | 0.6208 | 49.8008 | 16.8616 |
| 85.00 | 0.40 | 469 | 470 | 3.464 | 82.86 | 233 | 0.394 | 0.3482 | 3.4577 | 1.2026 | 0.306 | 61.30 | 2 | 2.783 × 1004 | 5.702 × 1004 | 0.7391 | 43.5172 | 19.3621 | 0.002 | 57.81 | 0 | 4.534 × 1013 | 1.931 × 1015 | 0.7785 | 63.5034 | 47.5795 |
| 60.00 | 0.00 | 0 | – | 3.507 | 59.43 | – | – | 0.2489 | 0.2885 | 0.1152 | 0.337 | 47.36 | – | – | – | 0.4738 | 14.0549 | 3.6620 | 0.016 | 45.70 | – | – | – | 0.5412 | 26.0034 | 7.1750 |
| 60.00 | 0.40 | 435 | 427 | 4.046 | 59.01 | 195 | 0.328 | 0.3226 | 3.5990 | 1.0319 | 0.343 | 51.54 | 5 | 4.588 × 1003 | 6.297 × 1004 | 0.5369 | 14.0556 | 3.4987 | 0.011 | 49.91 | 1 | 6.666 × 1004 | 3.753 × 1007 | 0.5567 | 15.8821 | 4.0306 |
| 40.00 | 0.00 | 0 | – | 4.468 | 39.76 | – | – | 0.2489 | 0.2885 | 0.1152 | 0.416 | 39.46 | – | – | – | 0.2489 | 0.2885 | 0.1152 | 0.072 | 37.83 | – | – | – | 0.2489 | 0.2892 | 0.1153 |
| 40.00 | 0.40 | 393 | 328 | 5.144 | 39.66 | 482 | 0.889 | 0.3158 | 6.2331 | 1.1025 | 0.446 | 37.03 | 1 | 8.406 × 1004 | 2.269 × 1006 | 0.3265 | 6.8653 | 1.1755 | 0.061 | 34.58 | 0 | 3.120 × 1006 | 3.292 × 1009 | 0.3392 | 7.4605 | 1.2540 |
| 32.00 | 0.00 | 0 | – | 5.264 | 31.87 | – | – | 0.2489 | 0.2885 | 0.1152 | 0.501 | 31.78 | – | – | – | 0.2489 | 0.2885 | 0.1152 | 0.144 | 31.77 | – | – | – | 0.2489 | 0.2885 | 0.1152 |
| 32.00 | 0.40 | 366 | 306 | 6.174 | 31.80 | 371 | 0.606 | 0.3130 | 9.1039 | 1.1439 | 0.542 | 31.61 | 2 | 1.073 × 1004 | 3.142 × 1005 | 0.3148 | 9.2551 | 1.1550 | 0.124 | 30.52 | 1 | 8.788 × 1004 | 1.381 × 1008 | 0.3241 | 10.0297 | 1.2113 |
| 25.00 | 0.00 | 0 | – | 6.481 | 24.94 | – | – | 0.2489 | 0.2885 | 0.1152 | 0.637 | 24.91 | – | – | – | 0.2489 | 0.2885 | 0.1152 | 0.380 | 24.91 | – | – | – | 0.2489 | 0.2885 | 0.1152 |
| 25.00 | 0.40 | 343 | 280 | 7.683 | 24.90 | 310 | 0.565 | 0.3096 | 12.8248 | 1.1727 | 0.650 | 24.79 | 6 | 2.850 × 1003 | 8.852 × 1004 | 0.3108 | 13.0079 | 1.1805 | 0.242 | 23.97 | 1 | 3.325 × 1004 | 6.561 × 1007 | 0.3241 | 14.9144 | 1.2619 |
| 20.00 | 0.00 | 0 | – | 7.900 | 19.97 | – | – | 0.2489 | 0.2885 | 0.1152 | 0.858 | 19.96 | – | – | – | 0.2489 | 0.2885 | 0.1152 | 0.743 | 19.96 | – | – | – | 0.2489 | 0.2885 | 0.1152 |
| 20.00 | 0.40 | 314 | 269 | 10.216 | 19.95 | 322 | 0.568 | 0.3280 | 22.0435 | 1.3151 | 0.841 | 19.90 | 11 | 4.497 × 1002 | 1.514 × 1004 | 0.3296 | 22.4326 | 1.3239 | 0.455 | 19.90 | 0 | 3.636 × 1015 | 9.760 × 1018 | 0.3304 | 22.6263 | 1.3283 |
| 15.00 | 0.00 | 0 | – | 10.949 | 14.96 | – | – | 0.2489 | 0.2885 | 0.1152 | 1.276 | 14.94 | – | – | – | 0.2489 | 0.2885 | 0.1152 | 3.191 | 14.92 | – | – | – | 0.3123 | 3.5286 | 0.7647 |
| 15.00 | 0.40 | 319 | 242 | 13.171 | 14.95 | 200 | 0.375 | 0.2838 | 14.4660 | 1.0445 | 1.411 | 14.90 | 25 | 1.012 × 1002 | 4.312 × 1003 | 0.2846 | 14.7696 | 1.0515 | 1.828 | 14.90 | 3 | 2.090 × 1003 | 8.209 × 1006 | 0.2857 | 15.1674 | 1.0605 |
| 12.00 | 0.00 | 0 | – | 14.964 | 11.98 | – | – | 0.2489 | 0.2885 | 0.1152 | 1.744 | 11.97 | – | – | – | 0.2489 | 0.2885 | 0.1152 | 6.527 | 11.93 | – | – | – | 0.2797 | 2.9684 | 0.6025 |
| 12.00 | 0.40 | 285 | 230 | 17.822 | 11.98 | 235 | 0.450 | 0.2800 | 14.6114 | 1.0281 | 1.886 | 11.96 | 9 | 5.753 × 1002 | 2.483 × 1004 | 0.2808 | 14.9383 | 1.0353 | 5.890 | 11.91 | 2 | 1.389 × 1004 | 7.678 × 1007 | 0.3403 | 36.2088 | 1.4780 |
| 9.00 | 0.00 | 0 | – | 24.985 | 9.00 | – | – | 0.2489 | 0.2885 | 0.1152 | 2.796 | 8.99 | – | – | – | 0.2489 | 0.2885 | 0.1152 | 4.760 | 8.96 | – | – | – | 0.2603 | 2.7311 | 0.5473 |
| 9.00 | 0.40 | 270 | 215 | 29.563 | 9.00 | 217 | 0.431 | 0.2755 | 14.7022 | 1.0121 | 3.204 | 8.99 | 34 | 4.728 × 1001 | 2.391 × 1003 | 0.2761 | 14.9728 | 1.0177 | 3.569 | 8.96 | 3 | 4.759 × 1003 | 4.213 × 1007 | 0.3129 | 34.7414 | 1.3241 |
| 7.00 | 0.00 | 0 | – | 38.682 | 7.00 | – | – | 0.2489 | 0.2885 | 0.1152 | 5.030 | 7.00 | – | – | – | 0.2489 | 0.2885 | 0.1152 | ||||||||
| 7.00 | 0.40 | 275 | 205 | 45.281 | 7.00 | 204 | 0.421 | 0.2706 | 11.6227 | 0.9457 | 5.231 | 7.00 | 34 | 3.854 × 1001 | 2.203 × 1003 | 0.2711 | 11.8618 | 0.9519 | ||||||||
| 5.00 | 0.00 | 0 | – | 72.988 | 5.00 | – | – | 0.2489 | 0.2885 | 0.1152 | 11.835 | 4.98 | – | – | – | 0.2489 | 0.2885 | 0.1152 | ||||||||
| 5.00 | 0.40 | 264 | 193 | 86.400 | 5.00 | 190 | 0.415 | 0.2657 | 8.1520 | 0.8631 | 11.459 | 5.00 | 25 | 6.189 × 1001 | 4.319 × 1003 | 0.2664 | 8.4294 | 0.8733 | ||||||||
| 4.00 | 0.00 | 0 | – | 115.094 | 4.00 | – | – | 0.2489 | 0.2885 | 0.1152 | 21.848 | 3.98 | – | – | – | 0.2489 | 0.2974 | 0.1169 | ||||||||
| 4.00 | 0.40 | 233 | 186 | 137.296 | 4.00 | 183 | 0.417 | 0.2633 | 6.1577 | 0.7842 | 20.427 | 4.00 | 9 | 2.162 × 1002 | 1.649 × 1004 | 0.2638 | 6.3173 | 0.7921 | ||||||||
| 3.00 | 0.00 | 0 | – | 215.821 | 3.00 | – | – | 0.2489 | 0.2885 | 0.1152 | 51.303 | 2.98 | – | – | – | 0.2500 | 0.8770 | 0.2452 | ||||||||
| 3.00 | 0.40 | 240 | 177 | 258.008 | 3.00 | 174 | 0.422 | 0.2611 | 4.2777 | 0.6544 | 42.400 | 2.98 | 6 | 3.303 × 1002 | 2.893 × 1004 | 0.2720 | 7.1652 | 0.8027 | ||||||||
| 2.50 | 0.00 | 0 | – | 329.121 | 2.50 | – | – | 0.2489 | 0.2885 | 0.1152 | 90.633 | 2.48 | – | – | – | 0.2542 | 1.3759 | 0.3119 | ||||||||
| 2.50 | 0.40 | 211 | 172 | 398.525 | 2.50 | 169 | 0.429 | 0.2605 | 3.3981 | 0.5558 | 74.790 | 2.47 | 6 | 2.800 × 1002 | 2.650 × 1004 | 0.2812 | 8.3793 | 0.7865 | ||||||||
| 2.00 | 0.00 | 0 | – | 582.601 | 2.00 | – | – | 0.2489 | 0.2885 | 0.1152 | ||||||||||||||||
| 2.00 | 0.40 | 197 | 170 | 716.745 | 2.00 | 171 | 0.451 | 0.2629 | 2.7703 | 0.4722 | ||||||||||||||||
| 1.70 | 0.00 | 0 | – | 929.506 | 1.70 | – | – | 0.2489 | 0.2885 | 0.1152 | ||||||||||||||||
| 1.70 | 0.40 | 185 | 163 | 1175.367 | 1.70 | 172 | 0.453 | 0.2707 | 2.8011 | 0.4685 | ||||||||||||||||
Notes. Columns 1–4 give the initial mass of the model, the initial ratio between the rotational velocity at the equator and the critical rotational velocity, the initial rotational velocity at the equator, and the time-averaged equatorial surface velocity during the MS phase, respectively. Columns 5–11 show properties of the stellar models at the end of the core H-burning phase: age, actual mass, surface equatorial velocity, ratio of the equatorial surface velocity to the critical velocity, mass fraction of helium at the surface, ratios in mass fraction of the nitrogen to carbon abundances at the surface, and of nitrogen to oxygen at the surface, respectively. Columns 12–19 and 20 to 27 show properties of the models at the end of the core He- and C-burning phases, respectively. The columns labeled M, Veq, Ysurf, N/C and N/O have the same meaning as the corresponding columns for the end of the core hydrogen burning phase. The quantity τHe (τC) corresponds to the duration of the He- (C-) core burning phase, Prot is the spin period of the star at the surface, ΩC/ΩS is the ratio of the angular velocity of the core to that of the surface.
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