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

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3. Results and Discussion

For models initialized for various values of [FORMULA], the [FORMULA] profiles are plotted Fig. 1 for [FORMULA] and compared to the three observed [FORMULA] values. According to these models, [FORMULA] can be fitted by the quadratic polynomial:

[EQUATION]

here [FORMULA], [FORMULA] profiles within [FORMULA] are plotted Fig. 2 at various ages of a solar model computed with [FORMULA] = [FORMULA]. During the pre-main sequence 2 H is converted to 3 He and, due to mixing, [FORMULA] increases through the model. At time [FORMULA] Myr the convection zone has receded almost to its present days location, at center, the temperature is not high enough to convert 3 He into 4 He via He3 (He3,2p)4 He, then [FORMULA] is maximum there. At [FORMULA] Myr i.e., zero age main sequence, the flat profile of [FORMULA] for radius [FORMULA], is due to the mixing in the convective core resulting form the conversion of 12 C into 14 N; then the nuclear reactions reach their equilibrium. Around the center the increase of 4 He depresses [FORMULA] and its maximum progressively reaches its present days location around [FORMULA] ; the gravitational settling being more efficient for 4 He than for 3 He, at surface [FORMULA] slowly increases until present days. As seen in Fig. 3, along the evolution, [FORMULA] varies from [FORMULA] to [FORMULA] and [FORMULA] from 0.0966 to 0.0830.

[FIGURE] Fig. 1. Profiles of [FORMULA] in envelopes of solar models computed with [FORMULA]: [FORMULA] (thick), [FORMULA] (medium) and [FORMULA] (thin). The observed [FORMULA] from APOLLO (1), ISEEE-3 (2) and Ulysses (3) are plotted with their error bars.
[FIGURE] Fig. 2. [FORMULA] profiles for [FORMULA], in a solar model initialized with [FORMULA] [FORMULA] for various ages: 0 Myr (dash-dot-dot-dot), 0.138 Myr (dashed), 20 Myr (dash-dot-dash), 49.1 Myr (thin full), 200 Myr (dotted) and 4550 Myr (thick full).
[FIGURE] Fig. 3. Changes of [FORMULA] (thick) and [FORMULA] (thin) ratios (with different scaling) at surface with respect to time for the solar model of Fig. 2. The dashed heavy line (49 Myr) separates the pre-main sequence (PMS) from the main sequence (MS).

Using Eq. 1 the three observed [FORMULA] values allow to infer:

  1. [FORMULA] [FORMULA],
  2. [FORMULA] [FORMULA],
  3. [FORMULA] [FORMULA].

Assuming no systematic errors, the weighted mean of these determinations results in:

[EQUATION]

Niemann et al. (1996) have derived a similar value but using our [FORMULA] [FORMULA] value, they would have found [FORMULA] [FORMULA].

Our new estimate of [FORMULA] overlaps within the domain of uncertainty the Galileo result. At this point, we can thus consider that it is consistent with Galileo. However, it rules out Jovian values higher than [FORMULA] [FORMULA] if we assume that Jupiter is representative of the isotopic composition of the nebula. As mentioned in Sect. 1, [FORMULA] results from a mixing of hydrogen originating from the nebula - and thus in protosolar abundance - with ices more or less enriched in deuterium. Assuming that the two reservoirs equilibrated at high temperature at the time of the formation of the planet, the present hydrogen in Jupiter may have been somewhat enhanced in deuterium if the amount of ices was large enough. This question deserves to be reexamined in the light of the most recent models of interiors of Jupiter. Following Hubbard & MacFarlane (1980), the deuterium enhancement is a function of the mass [FORMULA] of the ices embedded in Jupiter and of their deuterium enrichment f with respect to the protosolar value. According to Guillot et al. (1997), the amount of ices should not exceed 32 Earth masses in the extreme case. The value of the enrichment f depends on the origin of Jovian protoices. They may have been formed in the solar nebula, which implies that f not to exceed 2.5. In such a case, the deuterium enhancement in Jupiter is negligible. Alternatively, ices may have originated directly from the protosolar cloud following the scenario discussed by Lunine et al. (1991) and would have then kept their interstellar isotopic signature. The recent determinations of [FORMULA] in water in P/Halley (Eberhardt et al. 1995) and in Hyakutake comet (Gautier et al. 1996) suggest f of the order of 10. This maximum scenario then results in a deuterium enhancement of 20%. Accordingly, [FORMULA] should then be equal to [FORMULA] [FORMULA], entirely within the error bars of the Galileo value.

Ground based remote sensing determinations of [FORMULA] conclude to values less than [FORMULA] (Lecluse et al. 1996), in conflict with the maximum enrichment scenario. The preliminary analysis of observations from ISO suggest similar results (Encrenaz et al. 1996). In contrast, the reanalysis of the Voyager infrared observations by Carlson et al. (1993) results in [FORMULA] between [FORMULA] and [FORMULA] (Lecluse et al. 1996), a value compatible with the maximum enrichment scenario. Preliminary results of HST observations of the Lyman [FORMULA] emission of Jupiter (Ben Jaffel et al. 1996) give [FORMULA] = [FORMULA], a value much higher than the upper limit of the maximum enrichment case.

In summary, we cannot yet decide whether the abundance of deuterium in Jupiter is representative of the protosolar value or if it has been somewhat enhanced during the planetary formation.

The lower limit of our revised protosolar [FORMULA] value, namely [FORMULA] [FORMULA], is higher than the upper limit of the ISM determination of Linsky et al. (1993), by a factor 1.6. This is consistent with the evolution in 4.55 Gyr of the deuterium abundance in the solar neighborhood, estimated from models of chemical evolution of the Galaxy with infall of primordial composition (Prantzos 1996). Obtaining higher depletion factors requires different models which invoke galactic winds in the Galaxy (Vangioni-Flam & Casse 1995).

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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