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Astron. Astrophys. 363, 555-567 (2000)

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Appendix: the angular momentum conservation model of wind accretion for barium stars: equations

For the binary system, the two components (an intrinsic AGB star with mass [FORMULA], the present white dwarf, and a main sequence star with mass [FORMULA], the present barium star) rotating around the mass core C, so the total angular momentum is conservative in the mass core reference frame. If the two components exchange material through wind accretion, the angular momentum conservation of total system is showed by:

[EQUATION]

where µ is reduced mass, and r is the distance from [FORMULA] to [FORMULA]. [FORMULA] and [FORMULA] are the distances from [FORMULA], [FORMULA] to the mass core C respectively. [FORMULA] (=2[FORMULA]) is angular velocity, where [FORMULA] is the orbital period (Huang 1956). v is an additional effective velocity defined through the angular momentum variation in the direction of orbital motion of component 2. The first term on the right side of the equal-sign is the angular momentum lost by the escaping material and the second term is the additional angular momentum lost by the escaping material.

For the binary system, according to Huang (1956), the changes of orbital elements, the orbital semi-major axis A and eccentricity e, are

[EQUATION]

[EQUATION]

where

[EQUATION]

According to the angular momentum conservation model, the [FORMULA] term can be obtained from the following equation:

[EQUATION]

thus

[EQUATION]

then, we can obtain

[EQUATION]

Thus

[EQUATION]

The [FORMULA] term is:

[EQUATION]

Combining Eqs. (9), (10), (15) and (16), we can obtain the changes of orbital semi-major axis A and eccentricity e:

[EQUATION]

[EQUATION]

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
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