Bibliographical notes

Because the theory of early-type stars has developed quite slowly over the past twenty years, my first book is still a useful reference for these objects. See:

1. Tassoul, J. L., Theory of Rotating Stars, pp. 95-115 and pp. 305-361, Princeton: Princeton University Press, 1978.

The following general references may also be noted:

2. Moss, D., and Smith, R. C., Rep. Prog. Phys, 44, 831, 1981.

3. Smith, R. C., in Physics of Be Stars (Slettebak, A., and Snow, T. P., eds.), p. 123 and p. 486, Cambridge: Cambridge University Press, 1987.

4. Kippenhahn, R., and Weigert, A., Stellar Structure and Evolution, pp. 427-453, Berlin: Springer-Verlag, 1990.

Section 6.2. Almost everything we know about the state of rotation in a con-vective core has been reviewed in:

5. Tayler, R. J.,Mon. Not. R. Astron. Soc., 165, 39, 1973.

The straightforward expansion method is due to Milne (Reference 5 of Chapter 4). The double-approximation technique was first discussed in:

6. Takeda, S., Mem. College Sci. Kyoto Univ., A, 17, 197, 1934. The following key references may also be noted:

7. Ostriker, J. P., and Mark, J. W.-K., Astrophys. J., 151, 1075, 1968.

8. Kippenhahn, R., and Thomas, H. C., in Stellar Rotation (Slettebak, A., ed.), p. 20, New York: Gordon and Breach, 1970.

Other technical papers may be traced to Reference 1 (pp. 112-115). Subsequent contributions are due to:

10. Gingold, R. A., and Monaghan, J. J.,Mon. Not. R. Astron. Soc., 181, 375,1977.

11. Smith, B. L., Astrophys. Space Sci., 47, 61, 1977.

13. Wolfe, R. H., Jr., and Kern, J. W., Astrophys. Space Sci., 64, 443, 1979.

14. Kopal, Z., Astrophys. Space Sci., 93, 149, 1983.

15. Eriguchi, Y., and Müller, E., Astron. Astrophys., 146,260,1985; ibid., 147,161, 1985.

16. Hachisu, I., Astrophys. J. Suppl., 61, 479, 1986; ibid., 62, 461, 1986.

17. Geroyannis, V. S., Astrophys. J., 327, 273, 1988; ibid., 350, 355, 1990.

See also:

18. Smith, R. C., and Collins, G. W., Mon. Not. R. Astron. Soc., 257, 340, 1992.

19. Aksenov, A. G., and Blinnikov, S. I., Astron. Astrophys., 290, 674, 1994.

20. Uryü, K., and Eriguchi, Y.,Mon. Not. R. Astron. Soc., 269, 24,1994; ibid., 277, 1411, 1995.

Related contributions are quoted in Reference 18.

Section 6.2.1. The presentation in the text follows:

21. Sackmann, I. J., Astron. Astrophys., 8, 76, 1970.

22. Bodenheimer, P., Astrophys. J., 167, 153, 1971.

23. Clement, M. J., Astrophys. J., 230, 230, 1979; ibid., 420, 797, 1994.

See also:

24. Shindo, M., Hashimoto, M., Eriguchi, Y., and Müller, E., Astron. Astrophys., 326, 177, 1997.

Section 6.2.2. The analysis in this section is taken from:

25. Maeder, A., and Peytremann, E., Astron. Astrophys., 7,120,1970; ibid., 21,279, 1972.

27. Smith, R. C.,Mon. Not. R. Astron. Soc., 151, 463, 1971.

28. Collins, G. W., and Smith, R. C.,Mon. Not. R. Astron. Soc., 213, 519, 1985.

The effects of rotation on line profiles are considered in:

29. Gray, D. F., Astrophys. J., 211, 198, 1977; ibid., 258, 201, 1982.

30. Stoeckley, T. R., and Buscombe, W.,Mon. Not. R. Astron. Soc., 227, 801, 1987.

31. Collins, G. W., and Truax, R. J., Astrophys. J., 439, 860, 1995.

Section 6.3.1. The following review paper may be noted:

32. Abt, H. A., in Stellar Rotation (Slettebak, A., ed.), p. 193, New York: Gordon and Breach, 1970.

Recent contributions are by:

33. Levato, H., and Garcia, B., Astrophys. Letters, 24, 49, 1984; ibid., p. 161.

34. Glaspey, J. W., Publ. Astron. Soc. Pacific, 99, 1089, 1987.

Section 6.3.2. The reference to McNally is to his paper:

See also Kraft's discussion (Reference 28 of Chapter 1). The presentation in the text follows:

36. Kawaler, S. D., Publ. Astron. Soc. Pacific, 99, 1322, 1987.

The relationship between total angular momentum and mass for a large variety of astronomical objects has been discussed in:

39. Carrasco, L., Roth, M., and Serrano, A., Astron. Astrophys., 106, 89, 1982. Section 6.3.3. See:

40. Wolff, S. C., Edwards, S., and Preston, G. W., Astrophys. J., 252, 322, 1982.

Section 6.3.4. The following review is particularly worth noting:

41. Slettebak, A., Space Sci. Review, 23, 541, 1979. Statistical studies of Be and shell stars have been made by:

42. Chen, H. Q., and Huang, L., Chinese Astron. Astrophys., 11, 10, 1987.

43. Porter, J. M.,Mon. Not. R. Astron. Soc., 280, L31, 1996.

Section 6.3.5. Rotation of the Am and Ap stars is discussed in:

44. Ginestet, N., Jaschek, M., Carquillat, J. M., and Pedoussaut, A., Astron. Astrophys., 107,215, 1982.

45. Abt, H. A., and Morrell, N. I., Astrophys. J. Suppl, 99, 135, 1995.

46. Budaj, J., Astron. Astrophys., 313, 523, 1996; ibid, 326, 655, 1997.

Conflicting results about the braking of Ap stars will be found in:

47. Wolff, S. C., Astrophys. J., 202, 101, 1975; ibid., 244, 221, 1981.

50. North, P., Astron. Astrophys., 141, 328, 1984; ibid, 334, 181, 1998; ibid, 336, 1072,1998.

51. Borra, E. F., Beaulieu, A., Brousseau, D., and Shelton, I., Astron. Astrophys., 149, 266, 1985.

Section 6.4. The following key reference may be noted:

The meridional circulation solutions are those of Tassoul and Tassoul (References 16, 23, and 25 of Chapter 4). The interaction between microscopic diffusion and meridional circulation was originally considered by:

54. Michaud, G., Tarasick, D., Charland, Y., and Pelletier, C., Astrophys. J., 269, 239, 1983.

188 The early-type stars Two-dimensional calculations will be found in:

55. Charbonneau, P., and Michaud, G., Astrophys. J., 327, 809, 1988; ibid., 334, 746, 1988; ibid., 370, 693, 1991.

56. Charbonneau, P., Michaud, G., and Proffitt, C. R., Astrophys. J., 347, 821,1989.

57. Charbonneau, P., Astrophys. J., 405, 720, 1993.

58. Turcotte, S., and Charbonneau, P., Astrophys. J., 413, 376, 1993.

Papers of related interest are:

59. Chaboyer, B., and Zahn, J. P., Astron. Astrophys., 253, 173, 1992.

60. Charbonneau, P., Astron. Astrophys., 259, 134, 1992.

See especially Charbonneau's comprehensive discussion.

Section 6.5. A cutoff in the distribution of rotational velocity for evolved stars was originally noticed by Herbig and Spalding. As they pointed out, if a level of 20 km s-1 is chosen as reference, later than spectral type G0 giants and subgiants with appreciable rotation rates are very rare. See:

61. Herbig, G. H., and Spalding, J. F., Jr., Astrophys. J., 121, 118, 1955.

More accurate determinations of the sudden drop in rotation for these stars have been made by:

62. Gray, D. F.,Astrophys. J., 251,155,1981; ibid., 262,682,1982; ibid., 347,1021, 1989.

63. Gray, D. F., and Nagar, P., Astrophys. J., 298, 756, 1985. Detailed discussions of Gray's mechanism are contained in:

64. de Medeiros, J. R., and Mayor, M., in Angular Momentum Evolution of Young Stars (Catalano, S., and Stauffer, J. R., eds.), p. 201, Dordrecht: Kluwer, 1991.

65. Gray, D. F., in Angular Momentum Evolution of Young Stars (Catalano, S., and Stauffer, J. R., eds.), p. 183, Dordrecht: Kluwer, 1991.

67. Schrijver, C. J., and Pols, O. R., Astron. Astrophys., 278, 51, 1993; ibid., 293, 640, 1995.

Reference is also made to:

68. Simon, T., and Drake, S. A., Astrophys. J., 346, 303, 1989.

Their discussion of Gray's discontinuity for the giant stars should be modified, however, since it has been subsequently recognized that the sudden drop in rotation is located near spectral type G0 III and not at G5 III. (This remark does not affect the contents of their paper.)

Several discussions of post-main-sequence evolution may be traced to Reference 1 (pp. 358-361). Subsequent contributions are due to:

69. Endal, A. S., and Sofia, S., Astrophys. J., 210, 184, 1976; ibid., 220, 279, 1978; ibid., 232, 531, 1979.

See especially their third paper. Among the many recent papers relating to post-main-sequence evolution, reference may be made to:

70. Wiita, P. J., J. Astrophys. Astron., 2, 387, 1981.

71. Sreenivasan, S. R., and Wilson, W. J. F., Astrophys. J., 254, 287, 1982; ibid., 290, 653, 1985; ibid., 292, 506, 1985.

72. Deupree, R. G., Astrophys. J., 357, 175, 1990; ibid., 439, 357, 1995; ibid., 499, 340, 1998.

73. MacGregor, K. B., Friend, D. B., and Gilliland, R. L., Astron. Astrophys., 256, 141, 1992.

74. Maheswaran, M., and Cassinelli, J., Astrophys. J., 421, 718, 1994.

75. Sofia, S., Howard, J. M., and Demarque, P., in Pulsation, Rotation and Mass Loss in Early-Type Stars (Balona, L. A., Henrichs, H. F., and Le Contel, J. M., eds.), I.A.U. Symposium No 162, p. 131, Dordrecht: Kluwer, 1994.

The results presented in Reference 75 are clearly indicative that rotationally induced chemical mixing plays an essential role in the evolution of massive stars. Unfortunately, as was pointed out at the end of Section 3.6, turbulent mixing in stellar radiative zones is difficult to model with any confidence. Other papers dealing with this poorly understood mechanism may be traced to:

76. Langer, N., Astron. Astrophys., 329, 551, 1998. See also my comments in the epilogue.

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