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Astron. Astrophys. 323, L9-L12 (1997)

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2. Solar modeling and data

The calibrated solar models discussed in this paper include the pre-main sequence evolution. The calibration consists in the adjustment of, i) the ratio of the mixing-length to the pressure scale height, ii) the initial mass fraction [FORMULA] of hydrogen and, iii) the initial protosolar mass fraction of heavy elements to hydrogen, in order that the models have at present solar age, the observed luminosity, radius (Guenter et al. 1992) and mass fraction of heavy elements to hydrogen (Grevesse & Noels 1993). The models have been computed using the code CESAM (Morel 1997). The relevant features are: the changes due to nuclear reactions, microscopic diffusion and convective mixing are explicitly computed for [FORMULA], 2 H , 3 He , 4 He , 7 Li, 7 Be, 12 C, 13 C, 14 N, 15 N, 16 O and 17 O which enter into the most important nuclear reactions of the PP+CNO cycles; the protosolar abundance of each heavy element is derived from [FORMULA] according to the nuclide abundances of Anders & Grevesse (1989); [FORMULA] is taken equal to [FORMULA] [FORMULA] as measured by the Galileo probe into Jupiter; the microscopic diffusion coefficients of Michaud & Proffitt (1993) are used, all species, but [FORMULA] and [FORMULA], are trace elements. [FORMULA] is taken as a parameter and constrained to fit [FORMULA].

As pointed out by G93, 3 He could be somewhat favored over 4 He in the solar wind acceleration process (Burgi & Geiss 1986). However, the first results of the SWICS instrument aboard the Ulysses spacecraft (Bodmer et al. 1995) do not provide evidence that such a fractionation could exceed the uncertainties on the measurements of the helium isotopic ratio. Moreover, the chromospheric process is not expected to result in a significant mass fractionation (G93). Therefore we assume that [FORMULA] is equal, within uncertainties, to [FORMULA].

The values of [FORMULA] obtained by three experiments on three different space missions are:

  1. Apollo [FORMULA] [FORMULA] (Geiss et al. 1972),
  2. ISSEE-3 [FORMULA] [FORMULA] (Coplan et al. 1984, Bochsler 1984),
  3. Ulysses [FORMULA] [FORMULA] (Bodmer et al. 1995).
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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998