Mass fractions primordial

Fig. 4. A summary of the time evolution of primordial 4He abundance determinations (mass fraction Yp) from observations of metal-poor, extragalactic Hu regions (see the text for references). The solid horizontal line is the SBBN-predicted 4He abundance expected for the WMAP (and/or D) inferred baryon density. The two dashed lines show the la uncertainty in this prediction.

The final outcome of these reactions, as a function of rj or equivalently Slboh2, is shown in Fig. 4.3. The primordial helium mass fraction TP, shown on a large scale, is not very sensitive to r), since this parameter only affects the time for neutron decay before nucleosynthesis sets in, and it can be fitted by the relation FP = 0.226 + 0.025log 0 + 0.0075(g - 10.75) + 0.014(r1/2( ) - 10.3 min). 

Table 4.3. Estimates of primordial helium mass fraction...

Fig. A1.3. Comparison between observed abundances and abundances predicted by the theory of primordial nucleosynthesis. The horizontal axis shows the ratio r between the number of baryons and the number of photons. The vertical axis shows the mass fraction of helium and the numerical ratios D/H, He/H and li/H. Observational data are represented by boxes with height equal to the error bar. In the case of helium and lithium, there are two boxes, indicating the divergence between different observers. Deuterium holds the key to the mystery, but it is difficult to measure. The region of agreement is shown as a shaded vertical ribbon (after Buries Tytler 1997). A higher level of deuterium would lead to a lower baryonic density, of the order of 2%. This would agree better with the lithium data, which have been remarkably finely established. This idea is supported by E. Vangioni-Flam and shared by myself. (From Tytler 1997.)...

FIGURE 1. The SBBN-predicted primordial abundances of D, 3He, 7 Li (by number with respect to hydrogen), and the 4He mass fraction Y as a function of the nucleon abundance r/w- The widths of the bands reflect the theoretical uncertainties. 

In contrast to the other light nuclides, the primordial abundance of 4He (mass fraction Y) is relatively insensitive to the baryon density, but since virtually all neutrons available at BBN are incorporated in 4He, it does depend on the competition between the weak interaction rate (largely fixed by the accurately measured neutron lifetime) and the universal expansion rate (which depends on geff)- The higher the nucleon density, the earlier can the D-bottleneck be breached. At early times there are more neutrons and, therefore, more 4He will be synthesized. This latter effect is responsible for the very slow (logarithmic) increase in Y with rj. Given the standard model relation between time and temperature and the nuclear and weak cross sections and decay rates measured in the laboratory, the evolution of the light nuclide abundances may be calculated and the frozen-out relic abundances predicted as a function of the one free parameter, the nucleon density or rj. These are shown in Fig. 1. 

Figure 2. The BBN-predicted primordial 4He mass fraction Y as a function of the BBN-predicted primordial Deuterium abundance (by number relative to Hydrogen) for three choices of N . The width of the bands represents the theoretical uncertainty, largely due to that of the neutron lifetime rn.

Figure 13. The diagonal band is the SBBN-predicted helium-4 mass fraction versus the SBBN-predicted deuterium abundance (by number relative to hydrogen). The width of the band accounts for the theoretical uncertainties in the SBBN predictions. Also shown by the filled circle and error bars are the primordial 4He and D abundance estimates adopted here.

Helium, the second most abundant element, has significance for cosmology and stellar structure. Most 4He was produced in the Big Bang, and the primordial mass fraction Yp is a constraint on the photon/baryon ratio and thus on the cosmological model. The He mass fraction also affects stellar structure, but He is difficult to measure in stars and so must be inferred from other measurements. On the other hand, He I recombination lines are relatively easy to measure in H II regions, and so a large amount of data is available on He/H in ionized nebulae. 

When nucleosynthesis begins, nearly all the surviving neutrons end up bound in the most stable light element " He. Heavier nuclei do not form in any significant quantity both because of the absence of stable nuclei with mass number 5 or 8 (which impedes nucleosynthesis via " He + n, " He + p or " He + " He reactions) and the large Coulomb barriers for reactions such as the T + " He 7 + Li and He + " He 7 + Be reactions listed above. Hence the primordial mass fraction of " He, conventionally referred to as Yp, can be estimated by the simple counting argument... 

Figure 4. The predictions of standard BBN [22], with thermonuclear rates based on the NACRE compilation [24]. (a) Primordial abundances as a function of the baryon-to-photon ratio tj. Abundances are quantified as ratios to hydrogen, except for He which is given in baryonic mass fraction Yp = Ph/Pb-The lines give the mean values, and the surrounding bands give the la uncertainties, (b) The la abundance uncertainties, expressed as a fraction of the mean value p for each q.

A suitable initial composition for the atmosphere has been deduced from meteorites. Multi-dimensional isotopic correlations of chondrite data have been used to constrain a range of compositions that, when mass-fractionated, yields the light-isotope ratios of terrestrial Xe. In order to match the terrestrial heavy Xe isotope ratios, addition of radiogenic I and a heavy Xe isotope component is required. Constraining the composition of the heavy isotope component to known fission spectra then defines the U-Xe composition and identifies " Tu-derived fissiogenic Xe as the heavy isotope component (see Primordial Xe section). This is compatible with meteorite data that... 

SNC-based geochemical model of Mars bulk composition which calls for a -40% mass fraction of volatile-rich, oxidized Cl-like material in the planet. However subsequent expansion and recalculation of Xe data from the SNC meteorites now suggest that solar-wind Xe is a viable alternative to Cl-Xe as the principal atmospheric constituent on early Mars (see Primordial Xenon section below), raising the challenging question of how Mars could have acquired a large solar Xe component while Earth apparently did not. 

This kind of model has not been applied in any detail to Mars. A problem that confronts it on that planet is the observation that Xe on Mars and Earth, while displaying comparable light-isotope ratios, is compositionally different at the heaviest isotopes in ways that cannot be explained by variable additions of or fission Xe to either or both atmospheres. As discussed below, it appears that Xe compositions on the two planets reflect mass fractionation of two isotopically distinct primordial starting compositions, in conflict with the hypothesis of a common planetesimal source. Venus is the key. Even a moderately accurate isotopic analysis of Venusian Xe, where no data presently exist and where the nonradiogenic Xe compositions predicted by the two models—Earth-like if supplied by porous planetesimals, and solar-like if unfractionated by hydrodynamic escape—are very different, should rule definitively between them—or create problems for both. 

However, the contribution of fissiogenic heavy isotopes are more difficult to calculate fractionated chondritic and solar Xe have greater proportions of " Xe and Xe than is actually seen in the atmosphere and so cannot serve as the primordial terrestrial composition (see Pepin 2000). While no other suitable common solar system compositions have been found that provide the nonradiogenic heavy isotope composition, multi-dimensional isotopic correlations of chondrite data have been used to define a composition, U-Xe, that when mass-fractionated yields the light-isotope ratios of terrestrial Xe and differs from atmospheric Xe by a heavy isotope component that has the composition of " " Pu-derived fission Xe (Pepin 2000). The fractionated U-Xe ratios of Xe/ °Xe = 6.053 and Xe/ °Xe = 2.075 are the present best estimates of the isotopic composition of nonradiogenic terrestrial Xe (see further discussion in Pepin and Porcelli... 

Figure 4.4. The comparison (Sadat Blanchard, 2001) of the theoretical baryon fraction, as derived from numerical simulations, for two primordial gas fraction, fg =0.11 and fg = 0.09 (dotted lines), with the observed gas fraction at different density contrasts and using two different mass estimators inferred from numerical simulations filled symbols are values obtained with Bryan and Norman (1998) mass estimator, open symbols are obtained using Evrard et al (1996). Stars are derived from the data of Vikhlinin et al. (1999), corrected for the clumping factor (Mathiesen et al. (1999)).

In the first evolutionary epoch, note that the extent of xenon fractionation from primordial to present composition is similar on both Earth and Mars despite the much smaller mass of Mars, the apparent differences (U-Xe versus SW-Xe) in their precursor xenon, the much greater overall depletion of martian noble gases, and the possibility that escape episodes were powered by... 

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