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Astron. Astrophys. 326, 1001-1012 (1997)

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Appendix A: species conservation

A.1. Mass fraction

Consider a species i whose mass fraction in the accreted matter and in the star at shell j are [FORMULA] and [FORMULA], respectively. The total mass of element i after accretion is given by [FORMULA] and represent a summation over the n shells of the model:

[EQUATION]

So, we have

[EQUATION]

and finally we obtain

[EQUATION]

A.2. Rescaled abundances

The new fractional mass [FORMULA] derived alone refers to the old mesh point. However, modifications of the mass profile can result in changes in the mesh points. If k is the shell number such that [FORMULA] where subscript j refers to the old mesh points and k to the current ones, the interpolated composition at mass [FORMULA] is then

[EQUATION]

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© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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