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So, if we neglect the Coriolis term, the only difference between the potential including uniform asynchronous rotation and the original one in (3.1.65) is that the centrifugal term is multiplied by F2. But note that for asynchronous rotation there are separate potential systems for the two stars. The dynamical extension of the Roche models including asynchronous rotation not only complies with more realistic physical conditions but also allows us to model spectral line broadening, as discussed in Sect. 3.6.

Common envelope evolution is thought to lead to cataclysmic variables [see, for instance, Warner (1995)] which contain white dwarf stars and erupt as classical novae, recurrent novae, dwarf novae, and the novae-like variables (sometimes called UX UMa stars). If one component of a binary undergoes evolutionary expansion the binary's outer envelope may begin to engulf the companion. If synchronism cannot be maintained, the orbit decays in a tight spiral as the orbital motion becomes faster than the rotation, which cannot keep up through the usual tidal locking mechanism [see the review articles by Webbink (1992, 2008), Taam & Bodenheimer (1992), Iben & Livio (1994) for references to original work in this field].

3.1.5.3 Eccentric Orbits and Asynchronous Rotation

At each phase 0 in the eccentric two-body problem the position and separation d = d(0) of the components follow from Kepler's equation (3.1.28). The force field on any third object is time dependent and therefore nonconservative. This precludes the existence of a static potential field and a relation such as (3.1.58). If, however, a binary component can readjust to equilibrium on a timescale short compared to that on which forces vary (orbital period P), Wilson (1979) has shown that it is possible to define the effective potential

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