Constraints on rotational mixing from surface evolution of light elements in massive stars

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Volume 522 (November 2010)

A&A, 522 (2010) A39

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Table 2

Model parameters.

M _ini

J _ini

τ _H

υ _eq

³He

⁴He

¹⁰B

¹¹B

¹²C

¹³C

¹⁴N

[M_⊙]

[10⁵² erg s]

[10⁷ yr]

[km s^-1]

Mass fraction

0.0

0.00

2.538

0 (0)^a

0.720

6.51E-05

0.266

7.79E-10

3.46E-09

2.28E-03

2.77E-05

6.59E-04

0^b

0.720

6.51E-05

0.266

7.79E-10

3.46E-09

2.28E-03

2.77E-05

6.59E-04

0^c

0.703

4.40E-05

0.283

3.84E-11

2.66E-10

1.36E-03

7.01E-05

2.18E-03

0.2

0.35

2.632

88 (115)^a

0.720

6.00E-05

0.266

5.85E-11

5.25E-10

2.13E-03

5.97E-05

8.09E-04

76^b

0.720

4.96E-05

0.266

1.14E-11

1.38E-10

1.76E-03

1.03E-04

1.20E-03

1^c

0.696

3.07E-05

0.290

1.05E-12

1.53E-11

1.05E-03

1.11E-04

2.59E-03

0.4

0.67

2.663

182 (231)^a

0.720

3.37E-05

0.266

2.83E-13

7.42E-12

1.31E-03

1.55E-04

1.67E-03

163^b

0.719

2.63E-05

0.267

1.04E-14

4.68E-13

9.48E-04

1.56E-04

2.15E-03

1^c

0.692

1.97E-05

0.294

9.25E-16

5.09E-14

6.71E-04

1.28E-04

3.03E-03

0.6

0.95

2.692

275 (348)^a

0.719

2.22E-05

0.267

1.50E-15

1.01E-13

8.25E-04

1.53E-04

2.28E-03

256^b

0.717

1.84E-05

0.269

1.07E-17

1.57E-15

5.49E-04

1.28E-04

2.74E-03

2^c

0.687

1.47E-05

0.298

6.87E-19

1.48E-16

4.04E-04

1.01E-04

3.43E-03

0.0

0.00

1.605

0 (0)^a

0.720

6.51E-05

0.266

7.79E-10

3.46E-09

2.28E-03

2.77E-05

6.59E-04

0^b

0.720

6.51E-05

0.266

7.79E-10

3.46E-09

2.28E-03

2.77E-05

6.59E-04

0^c

0.684

3.77E-05

0.302

2.30E-11

2.35E-10

1.33E-03

7.15E-05

2.42E-03

0.1

0.31

1.619

44 (62)^a

0.720

6.51E-05

0.266

3.05E-10

1.89E-09

2.28E-03

2.92E-05

6.60E-04

36^b

0.720

6.09E-05

0.266

9.37E-11

7.25E-10

2.19E-03

5.21E-05

7.43E-04

0^c

0.680

3.25E-05

0.306

7.51E-12

7.06E-11

1.23E-03

9.24E-05

2.57E-03

0.2

0.62

1.638

94 (123)^a

0.720

5.33E-05

0.266

2.37E-11

2.56E-10

2.02E-03

8.10E-05

9.18E-04

79^b

0.720

4.02E-05

0.266

2.94E-12

4.49E-11

1.61E-03

1.26E-04

1.36E-03

1^c

0.678

2.49E-05

0.308

2.57E-13

4.71E-12

1.02E-03

1.17E-04

2.81E-03

0.3

0.91

1.663

144 (184)^a

0.720

3.63E-05

0.266

9.93E-13

1.98E-11

1.56E-03

1.47E-04

1.40E-03

125^b

0.719

2.67E-05

0.267

3.92E-14

1.31E-12

1.19E-03

1.68E-04

1.85E-03

1^c

0.677

1.88E-05

0.309

3.32E-15

1.34E-13

8.39E-04

1.38E-04

2.98E-03

0.4

1.20

1.669

194 (246)^a

0.719

2.55E-05

0.266

2.50E-14

1.03E-12

1.20E-03

1.74E-04

1.80E-03

173^b

0.718

1.95E-05

0.268

2.97E-16

2.43E-14

9.05E-04

1.73E-04

2.23E-03

1^c

0.676

1.47E-05

0.310

2.38E-17

2.38E-15

6.67E-04

1.39E-04

3.19E-03

0.5

1.46

1.676

245 (309)^a

0.719

1.96E-05

0.267

7.29E-16

5.69E-14

9.57E-04

1.76E-04

2.12E-03

224^b

0.716

1.56E-05

0.269

2.42E-18

4.73E-16

6.98E-04

1.60E-04

2.55E-03

1^c

0.676

1.24E-05

0.310

8.87E-20

4.36E-17

5.33E-04

1.29E-04

3.35E-03

0.6

1.68

1.681

295 (371)^a

0.719

1.62E-05

0.267

3.51E-17

4.47E-15

7.85E-04

1.68E-04

2.36E-03

276^b

0.715

1.34E-05

0.271

2.72E-22

1.39E-17

5.51E-04

1.42E-04

2.80E-03

1^c

0.692

1.18E-05

0.293

4.15E-24

1.21E-18

4.65E-04

1.23E-04

3.24E-03

0.7

1.87

1.698

344 (431)^a

0.718

1.41E-05

0.267

3.19E-18

5.71E-16

6.81E-04

1.63E-04

2.50E-03

337^b

0.713

1.20E-05

0.273

7.73E-27

5.07E-20

4.54E-04

1.27E-04

2.98E-03

2^c

0.660

9.22E-06

0.326

8.21E-29

5.38E-22

3.39E-04

9.72E-05

3.79E-03

0.4

1.20

1.667

195 (248)^a^,^d

0.735

1.95E-05

0.258

3.48E-16

3.11E-14

4.17E-04

7.33E-05

1.16E-03

173^b^,^d>

0.733

1.52E-05

0.260

7.39E-19

2.67E-16

2.83E-04

6.38E-05

1.38E-03

1^c^,^d

0.727

1.41E-05

0.266

1.32E-20

2.91E-17

2.47E-04

5.89E-05

1.50E-03

0.0

0.00

1.128

0 (0)^a

0.720

6.51E-05

0.266

7.79E-10

3.46E-09

2.28E-03

2.77E-05

6.59E-04

0^b

0.720

6.51E-05

0.266

7.78E-10

3.46E-09

2.28E-03

2.77E-05

6.59E-04

0^e

0.680

3.14E-05

0.305

2.99E-16

6.92E-11

1.17E-03

6.73E-05

2.70E-03

0.2

0.96

1.197

97 (129)^a

0.720

4.88E-05

0.266

8.58E-12

1.19E-10

1.95E-03

9.93E-05

9.84E-04

80^b

0.719

3.56E-05

0.267

6.82E-13

1.48E-11

1.56E-03

1.45E-04

1.43E-03

0^e

0.661

2.01E-05

0.325

4.68E-14

1.24E-12

9.18E-04

1.19E-04

3.17E-03

0.4

1.85

1.209

203 (257)^a

0.719

2.23E-05

0.267

3.59E-15

2.15E-13

1.22E-03

1.96E-04

1.80E-03

179^b

0.716

1.69E-05

0.270

2.07E-17

2.68E-15

9.54E-04

1.94E-04

2.22E-03

0^e

0.650

1.21E-05

0.336

1.26E-18

2.13E-16

6.78E-04

1.47E-04

3.42E-03

0.6

2.61

1.224

308 (387)^a

0.718

1.42E-05

0.268

1.72E-18

3.86E-16

8.55E-04

1.93E-04

2.29E-03

286^b

0.712

1.14E-05

0.274

6.07E-28

4.13E-20

6.24E-04

1.65E-04

2.76E-03

1^e

0.642

8.30E-06

0.344

4.15E-30

2.82E-22

4.49E-04

1.22E-04

3.79E-03

Notes.

^(a)

The surface velocity and mass fractions when the central hydrogen abundance X_c ≈ 0.36 is given on the first line for each model. The velocity values in brackets are the values at ZAMS.

^(b)

The surface velocity and mass fractions at the end of hydrogen burning (X_c ≈ 10^-5) is given on the second line for each model. The velocity was not taken exactly when the hydrogen was depleted but when it reached its minimum, i.e., a little bit earlier.

^(c)

The third line for the 9 and 12 M_⊙ models corresponds to the surface values during the RGB phase.

^(d)

Model with lower initial metallicity Z = 0.5·Z_⊙.

^(e)

The third line for the 15 M_⊙ models corresponds to the surface values at the end of He-burning.

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