Table 3
Models of stars with internal differential rotation.
ZAMS | M = 5 M⊙, Ωcr = 1.92 × 10-4 | ZAMS | M = 15 M⊙, Ωcr = 1.34 × 10-4 | ||||||||||||
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Ωo/Ωcr | ρ c | Rav/R⊙ | Re/R⊙ | Re/Rp | V eq | J/M | K/|W| | Ωo/Ωcr | ρ c | Rav/R⊙ | Re/R⊙ | Re/Rp | V eq | J/M | K/|W| |
× 10-17 | × 10-17 | ||||||||||||||
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β = 2 | β = 2 | ||||||||||||||
1.0 | 19.996 | 2.671 | 2.711 | 1.052 | 117 | 3.326 | 0.0044 | 1.0 | 5.945 | 4.915 | 4.986 | 1.047 | 151 | 9.920 | 0.0064 |
2.0 | 21.593 | 2.821 | 2.967 | 1.269 | 225 | 6.723 | 0.0175 | 2.0 | 6.482 | 5.092 | 5.383 | 1.265 | 294 | 20.091 | 0.0250 |
3.0 | 24.741 | 3.451 | 3.938 | 1.947 | 290 | 10.437 | 0.0389 | 3.0 | 7.580 | 5.828 | 6.666 | 1.878 | 396 | 31.115 | 0.0553 |
3.5 | 27.451 | 4.813 | 5.799 | 3.143 | 255 | 12.898 | 0.0532 | 3.5 | 8.529 | 7.330 | 8.938 | 2.809 | 381 | 38.020 | 0.0752 |
3.9 | 32.121 | 9.933 | 11.652 | 6.998 | 152 | 17.775 | 0.0683 | 4.0 | 10.930 | 16.655 | 20.092 | 7.455 | 216 | 58.322 | 0.1035 |
β = 4 | β = 4 | ||||||||||||||
1.0 | 19.870 | 2.639 | 2.656 | 1.023 | 70 | 2.824 | 0.0033 | 1.0 | 5.899 | 4.875 | 4.915 | 1.025 | 91 | 8.220 | 0.0046 |
2.0 | 21.022 | 2.667 | 2.729 | 1.138 | 139 | 5.642 | 0.0130 | 2.0 | 6.273 | 4.861 | 4.981 | 1.133 | 181 | 16.443 | 0.0179 |
3.0 | 23.095 | 2.731 | 2.867 | 1.353 | 202 | 8.458 | 0.0285 | 4.0 | 8.085 | 4.955 | 5.455 | 1.697 | 341 | 32.810 | 0.0663 |
4.0 | 26.378 | 2.906 | 3.185 | 1.728 | 250 | 11.318 | 0.0489 | 5.5 | 11.219 | 5.774 | 6.887 | 2.843 | 396 | 45.878 | 0.1163 |
5.0 | 31.538 | 3.400 | 3.899 | 2.489 | 269 | 14.450 | 0.0736 | 6.2 | 14.319 | 7.599 | 9.291 | 4.558 | 349 | 56.026 | 0.1457 |
6.2 | 46.905 | 6.692 | 7.790 | 6.456 | 181 | 22.434 | 0.1128 | 6.4 | 16.610 | 9.221 | 11.247 | 5.958 | 304 | 64.434 | 0.1588 |
β = 6 | β = 6 | ||||||||||||||
1.0 | 19.796 | 2.634 | 2.652 | 1.022 | 50 | 2.482 | 0.0027 | 1.0 | 5.874 | 4.856 | 4.889 | 1.010 | 65 | 7.103 | 0.0035 |
2.0 | 21.022 | 2.626 | 2.670 | 1.095 | 100 | 4.946 | 0.0104 | 3.0 | 6.681 | 4.726 | 4.869 | 1.221 | 196 | 21.149 | 0.0303 |
4.0 | 23.095 | 2.631 | 2.768 | 1.426 | 195 | 9.761 | 0.0392 | 5.0 | 8.684 | 4.544 | 4.941 | 1.693 | 324 | 34.451 | 0.0770 |
5.0 | 28.193 | 2.677 | 2.907 | 1.727 | 235 | 12.103 | 0.0586 | 7.0 | 12.871 | 4.618 | 5.417 | 2.664 | 424 | 46.715 | 0.1336 |
7.0 | 40.196 | 3.160 | 3.641 | 2.969 | 275 | 17.048 | 0.1047 | 8.0 | 16.731 | 5.171 | 6.299 | 3.689 | 430 | 53.793 | 0.1648 |
8.35 | 67.403 | 5.514 | 6.446 | 6.938 | 196 | 25.828 | 0.1483 | 8.4 | 19.300 | 5.767 | 7.106 | 4.564 | 408 | 58.318 | 0.1796 |
β = 8 | β = 8 | ||||||||||||||
1.0 | 19.746 | 2.626 | 2.640 | 1.009 | 39 | 2.227 | 0.0022 | 1.0 | 5.857 | 4.857 | 4.884 | 1.011 | 51 | 6.293 | 0.0029 |
3.0 | 21.808 | 2.580 | 2.630 | 1.164 | 118 | 6.610 | 0.0190 | 2.0 | 6.092 | 4.790 | 4.837 | 1.066 | 102 | 12.548 | 0.0112 |
5.0 | 26.464 | 2.519 | 2.669 | 1.495 | 195 | 10.776 | 0.0492 | 4.0 | 7.143 | 4.551 | 4.722 | 1.304 | 209 | 24.704 | 0.0425 |
7.0 | 34.953 | 2.529 | 2.788 | 2.070 | 264 | 14.665 | 0.0878 | 6.0 | 9.316 | 4.229 | 4.610 | 1.733 | 319 | 35.796 | 0.0869 |
9.0 | 50.578 | 2.873 | 3.343 | 3.305 | 292 | 18.741 | 0.1313 | 8.0 | 13.338 | 3.980 | 4.573 | 2.373 | 428 | 45.301 | 0.1363 |
10.0 | 66.836 | 3.572 | 4.219 | 4.962 | 264 | 22.199 | 0.1575 | 9.6 | 18.901 | 4.078 | 4.940 | 3.327 | 484 | 52.380 | 0.1764 |
|
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TAMS | M = 5 M⊙, Ωcr = 4.79 × 10-4 | TAMS | M = 15 M⊙, Ωcr = 2.76 × 10-4 | ||||||||||||
|
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β = 2 | β = 2 | ||||||||||||||
1.0 | 27.626 | 6.639 | 7.708 | 1.051 | 71 | 1.692 | 0.0008 | 1.0 | 9.255 | 13.564 | 13.777 | 1.049 | 86 | 4.119 | 0.0007 |
2.0 | 28.085 | 7.556 | 7.915 | 1.280 | 132 | 3.482 | 0.0031 | 2.0 | 9.357 | 15.546 | 16.370 | 1.285 | 160 | 8.521 | 0.0030 |
3.0 | 29.015 | 12.077 | 13.648 | 2.334 | 137 | 5.633 | 0.0072 | 3.0 | 9.572 | 25.858 | 25.259 | 2.411 | 162 | 14.021 | 0.0073 |
3.5 | 29.954 | 27.310 | 30.655 | 5.467 | 78 | 7.475 | 0.0104 | 3.5 | 9.982 | 66.541 | 73.661 | 6.333 | 81 | 19.758 | 0.0107 |
β = 4 | β = 4 | ||||||||||||||
1.0 | 27.601 | 6.535 | 6.564 | 1.028 | 43 | 1.541 | 0.0006 | 1.0 | 9.249 | 13.363 | 13.483 | 1.026 | 52 | 3.753 | 0.0006 |
3.0 | 28.632 | 7.844 | 8.169 | 1.384 | 110 | 4.829 | 0.0059 | 2.0 | 9.331 | 14.200 | 14.476 | 1.128 | 99 | 7.644 | 0.0025 |
4.0 | 29.723 | 10.200 | 11.025 | 1.984 | 116 | 6.805 | 0.0107 | 3.0 | 9.480 | 16.212 | 16.970 | 1.387 | 133 | 11.882 | 0.0058 |
5.0 | 31.729 | 19.386 | 20.867 | 4.110 | 81 | 9.748 | 0.0177 | 4.0 | 9.732 | 21.574 | 23.300 | 2.021 | 138 | 16.979 | 0.0108 |
5.5 | 34.006 | 42.148 | 44.030 | 9.199 | 43 | 13.124 | 0.0221 | 5.0 | 10.236 | 44.869 | 48.918 | 6.602 | 87 | 25.481 | 0.0183 |
5.7 | 36.217 | 85.056 | 88.533 | 19.108 | 22 | 16.649 | 0.0246 | 5.5 | 11.028 | 129.78 | 136.36 | 9.820 | 35 | 39.665 | 0.0240 |
β = 6 | β = 6 | ||||||||||||||
1.0 | 27.584 | 6.497 | 6.515 | 1.021 | 31 | 1.428 | 0.0006 | 1.0 | 9.246 | 13.246 | 13.307 | 1.013 | 37 | 3.479 | 0.0006 |
3.0 | 28.440 | 7.200 | 7.383 | 1.232 | 83 | 4.396 | 0.0051 | 3.0 | 9.437 | 14.815 | 15.268 | 1.238 | 72 | 10.791 | 0.0050 |
4.0 | 29.275 | 8.086 | 8.447 | 1.494 | 100 | 6.025 | 0.0091 | 4.0 | 9.626 | 16.812 | 17.571 | 1.498 | 121 | 14.905 | 0.0091 |
5.0 | 30.516 | 9.898 | 10.573 | 2.007 | 103 | 7.883 | 0.0145 | 5.0 | 9.914 | 20.975 | 22.325 | 2.043 | 123 | 19.763 | 0.0148 |
6.0 | 32.471 | 14.334 | 15.413 | 3.190 | 88 | 10.297 | 0.0216 | 6.0 | 10.393 | 31.844 | 34.264 | 3.419 | 99 | 26.539 | 0.0223 |
7.0 | 36.522 | 32.588 | 33.300 | 7.737 | 48 | 14.903 | 0.0308 | 7.0 | 11.634 | 91.051 | 95.665 | 10.725 | 42 | 43.227 | 0.0334 |
β = 8 | β = 8 | ||||||||||||||
1.0 | 27.571 | 6.474 | 6.496 | 1.018 | 24 | 1.337 | 0.0005 | 1.0 | 9.243 | 13.239 | 13.327 | 1.006 | 29 | 3.260 | 0.0005 |
3.0 | 28.311 | 6.933 | 7.037 | 1.173 | 67 | 4.082 | 0.0045 | 3.0 | 9.408 | 14.238 | 14.472 | 1.164 | 82 | 10.008 | 0.0049 |
5.0 | 29.992 | 8.280 | 8.640 | 1.610 | 94 | 7.099 | 0.0127 | 5.0 | 9.790 | 17.301 | 18.070 | 1.624 | 113 | 17.656 | 0.0128 |
6.0 | 31.368 | 9.791 | 10.361 | 2.081 | 96 | 8.858 | 0.0185 | 6.0 | 10.112 | 20.816 | 22.169 | 2.148 | 113 | 22.314 | 0.0189 |
8.0 | 36.726 | 20.408 | 21.171 | 5.150 | 65 | 14.213 | 0.0345 | 7.0 | 10.602 | 28.159 | 30.082 | 3.159 | 99 | 28.363 | 0.0267 |
9.0 | 47.921 | 88.304 | 88.136 | 24.993 | 18 | 24.175 | 0.0453 | 8.5 | 12.570 | 86.558 | 90.257 | 11.410 | 41 | 49.916 | 0.0438 |
Notes. ρc is given in g cm-3; Ωcr is given in s-1; Veq is given in km s-1; the units of J/M are cm2s-1; Rav/R⊙ is the radius of a sphere having the same volume as the rotatio-nally deformed object.
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