The presentation in Sections 8.2-8.4 largely follows:
1. Tassoul, J. L., and Tassoul, M., Fund. Cosmic Physics, 16, 377, 1996.
This review paper contains many additional references as well as a more detailed comparison between theory and observation. See also:
2. Claret, A., and Gimenez, A., Astron. Astrophys., 296, 180, 1995.
3. Claret, A., Gimenez, A., and Cunha, N. C. S., Astron. Astrophys., 299, 724, 1995.
4. Claret, A., and Cunha, N. C. S., Astron. Astrophys., 318, 187, 1997. Reference 35 is a useful addendum to these four papers.
Section 8.2. The tidal-torque theory was originally considered in:
5. Darwin, G. H., Phil. Trans. Roy. Soc. London, Part II, 170,447,1879 (reprinted in Scientific Papers, II, p. 36, Cambridge: Cambridge University Press, 1908).
Application to stars with an outer convective envelope was first made by:
Tidal evolution in close binary systems for high eccentricities is discussed in:
7. Alexander, M. E., Astrophys. Space Science, 23, 459, 1973.
8. Mignard, F., The Moon and the Planets, 20, 301, 1979; ibid., 23, 185, 1980.
9. Hut, P., Astron. Astrophys., 99, 126, 1981; ibid., 110, 37, 1982.
Other contributions are by:
10. Zahn, J.P., Astron. Astrophys., 57, 383, 1977; ibid., 67, 162, 1978; ibid., 220, 112, 1989.
11. Scharlemann, E. T., Astrophys. J., 246, 292, 1981; ibid., 253, 298, 1982.
12. Goldman, I., and Mazeh, T., Astrophys. J., 376, 260, 1991.
13. Goodman, J., and Oh, S. P., Astrophys. J., 486, 403, 1997.
Detailed comparisons between theory and observation will be found in References 1, 4, and 13. See also:
14. Zahn, J. P., and Bouchet, L., Astron. Astrophys., 223, 112, 1989.
15. Maceroni, C., and van't Veer, F., Astron. Astrophys., 246, 91, 1991.
16. Verbunt, F., and Phinney, E. S., Astron. Astrophys., 296, 709, 1995.
Section 8.3. The classical references on the subject are those of:
17. Cowling, T. G.,Mon. Not. R. Astron. Soc., 101, 367, 1941.
18. Zahn, J. P., Astron. Astrophys., 41, 329, 1975; ibid., 57, 383, 1977.
Additional calculations are due to:
19. Rocca, A., Astron. Astrophys., 111, 252, 1982; ibid., 175, 81, 1987; ibid., 213, 114, 1989.
See especially her third paper. Related discussions are those of:
20. Goldreich, P., and Nicholson, P. D., Astrophys. J., 342, 1079, 1989.
21. Ruymaekers, E., Astron. Astrophys., 259, 349, 1992.
22. Savonije, G. J., and Papaloizou, J. C. B., Mon. Not. R. Astron. Soc., 291, 633, 1997.
Detailed comparisons between theory and observation will be found in References 1 and 4; see also:
23. Pan, K. K., Astron. Astrophys., 321, 202, 1997.
Section 8.4.1. See especially Reference 14 of Chapter 2. The following review paper is particularly worth noting:
24. Benton, E. R., and Clark, A., Jr., Annu. Rev. FluidMech., 6, 257, 1974. The reference to Weidman is to his paper:
Sections 8.4.2-8.4.4. The hydrodynamical mechanism was originally discussed in:
26. Tassoul, J. L., Astrophys. J., 322, 856, 1987; ibid., 358, 196, 1990.
27. Tassoul, J. L., Astrophys. J. Letters, 324, L71, 1988.
28. Tassoul, J. L., and Tassoul, M., Astrophys. J., 359, 155, 1990; ibid., 395, 259, 1992.
29. Tassoul, M., and Tassoul, J. L., Astrophys. J., 395, 604, 1992. See also:
30. van't Veer, F., and Maceroni, C., in Binaries as Tracers of Stellar Formation (Duquennoy, A., and Mayor, M., eds.), p. 237, Cambridge: Cambridge University Press, 1992.
The combined effects of the tidal-torque and hydrodynamical mechanisms are treated in:
32. Keppens, R., Astron. Astrophys., 318, 275, 1997.
Reference 1 (pp. 408-412) presents a detailed comparison between theory and observation; see also References 2 and 3, as well as Budaj's contribution (Reference 46 of Chapter 6).
The hydrodynamical mechanism has been criticized by:
33. Rieutord, M., Astron. Astrophys., 259, 581, 1992.
34. Rieutord, M., and Zahn, J. P., Astrophys. J., 474, 760, 1997.
In Reference 33 the claim is made that Ekman pumping is not efficient enough to reduce the synchronization time, which should remain of the order of the viscous time. For some reason, the same argument was repeated in Reference 34.
To be specific, in both papers they describe the internal motion by means of a series in the powers of the small parameter 8/R, which is the relative thickness of the Ekman layer at the free surface. By making use of this one-parameter expansion in the powers of 8/R, they conclude that the meridional currents described in Section 8.4.2, which are proportional to the product eT(8/R), should not exist. It is a simple matter to show that their analysis of the second-order terms is inadequate because they have failed to prescribe that these terms, which are intricately coupled to the first-order terms, must satisfy the vorticity equation as well as the boundary conditions on the tensions (see Eqs. [8.45] and [8.48]). Their analysis of the meridional flow in a tidally distorted configuration is incomplete, therefore, and so cannot be presented as a proofthat these currents should be of order (8/R)2. (Note also that their one-parameter expansion is quite inadequate to describe tidally driven currents, since it defines meridional motions, of order (8/R)2, that do not vanish in the limiting case eT ^ 0.) Accordingly, there is no reason to claim that tidally driven currents of order eT (8/R) do not exist in a nonsynchronous binary component.
In both papers, the claim is also made that the synchronization time should be equal to the ratio of the available kinetic energy to the power dissipated by friction in the surface boundary layer. This may be true in the case of a laboratory fluid with fixed solid boundaries in the rotating frame. It is certainly incorrect in the double-star problem, however, because the outer surface of a binary component is not perfectly fixed in the corotating frame, so that the tidally distorted body is liable to exchange kinetic energy and angular momentum with the orbital motion. This is another fundamental difference between the well-known problems with solid boundaries and the double-star problem for which the time-dependent torque caused by the small tidal lag plays an essential role.
This and other misapprehensions presented in References 33 and 34 are discussed in:
35. Tassoul, M., and Tassoul, J. L., Astrophys. J, 481, 363, 1997.
In Reference 35 (p. 367) it is also explained why planetary systems, such as Io-Jupiter or recently discovered planet-star systems, do not fulfill the stringent conditions under which the time scale defined in Eq. (8.50) has been obtained.
Sections 8.5 and 8.6. An exhaustive discussion of the binary Roche model, its associated coordinates, and associated harmonics will be found in:
36. Kopal, Z., The Roche Problem, Dordrecht: Kluwer, 1989.
See also Reference 51. The difficulties of constructing contact systems composed of two unequal stellar components were originally noted by:
37. Kuiper, G. P., Astrophys. J., 93, 133, 1941. The following key references are discussed in the text:
39. Osaki, Y., Publ. Astron. Soc. Japan, 17, 97, 1965.
41. Lucy, L. B., Astrophys. J., 151, 1123, 1968; ibid., 205, 208, 1976.
42. Shu, F. H., Lubow, S. H., and Anderson, L., Astrophys. J., 209, 536,1976; ibid., 229, 223, 1979; ibid., 239, 937, 1980.
43. Lubow, S. H., and Shu, F. H., Astrophys. J., 216, 517, 1977; ibid., 229, 657, 1979.
Good critical reviews of these and other theoretical contributions have been given by:
44. Shu, F. H., in Close Binary Stars: Observations and Interpretation (Plavec, M. J., Popper, D. M., and Ulrich, R. K., eds.), p. 477, Dordrecht: Reidel, 1980.
45. Smith, R. C., Quart. J. R. Astron. Soc., 25, 405, 1984.
46. Rucinski, S. M., in Interacting Binary Stars (Pringle, J. E., and Wade, R. A., eds.), p. 113, Cambridge: Cambridge University Press, 1985.
The difficulties of modeling large-scale thermally driven currents in Roche geometry are well illustrated in the following papers:
49. Smith, R. C., and Smith, D. H.,Mon. Not. R. Astron. Soc., 194, 583, 1981.
50. Zhou, D. Q., and Leung, K. C., Astrophys. J., 355, 271, 1990.
Application of the astrostrophic balance to contact binaries was first explicitly made in:
51. Tassoul, J. L., Astrophys. J., 389, 375, 1992. See also Reference 7 (pp. 45-56) of Chapter 2.
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