Theoretical Solar Models

Our sun is classified as a dwarf G-type main sequence star which is generating energy primarily by the fusion of hydrogen into helium. The overall hydrogen fusion process can be represented  

TABLE II The Proton-Proton Chain and Carbon-Nitrogen Cycle 

All of the reactions shown in Table II are used in solar model calculations and are the only reactions considered. 

The nuclear reactions in Table II have been studied extensively in the laboratory. It has been established that these are the only reactions that are important in the hydrogen fusion processes. However, the primary reaction that initiates the proton-proton chain, 

To determine the rates of these reactions in the sun, detailed calculations must be made of the temperatures, particle densities, and chemical composition of the different regions of the solar interior. Knowing the rates of the neutrino-producing reactions, one can calculate the energy spectrum and fluxes of the neutrinos emitted by the sun. 

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The theoretical solar conversion efficiency of a regenerative photovoltaic cell with a semiconductor photoelectrode therefore depends on the model used to describe the thermodynamic and kinetic energy losses. The CE values, which consider all the mentioned losses can generally only be estimated the full line in Fig. 5.65 represents such an approximation. Unfortunately, the materials possessing nearly the optimum absorption properties (Si, InP, and GaAs) are handicapped by their photocorrosion sensitivity and high price. 

The absolute value of the cross section for this key reaction is known relatively poorly both experimentally and theoretically. However, the agreement between the standard solar model and solar neutrino data thus provides additional constraints on variations in this cross section. Using the standard solar model of Bahcall [75], and recent solar neutrino data [76], one can exclude systematic variations of the magnitude needed to resolve the BBN Li problem at the > 95% confidence level [74]. Thus the nuclear fix to the Li BBN problem is unlikely. 

Solar model Theoretical calculation of the internal structure of the sun that follows the changes in structure, temperature, and composition as the sun ages. 

The theoretical forecasts of the neutrino fluxes used to compare with experimental observations are those from the so-called standard solar model (SSM). This model relies on the values of the solar mass, radius, luminosity, and age (4.7 billion years) and on the best-considered values of the nuclear reaction cross sections. In addition, there are some special assumptions. It is presumed that the sun is not rotating, or differentially rotating, rapidly enough in its interior to affect its internal structure or dynamics. Processes that could mix the solar interior, such as diffusion or periodic hydrodynamic oscillation, are not taken into... 

Our data indicate that the stars become fainter as metallicity increases, until a plateau or turnover point is reached at about solar metallicity. Our data are incompatible with both no dependence of th PL relation on iron abundance and with the linearly decreasing behaviour often found in the literature (e.g. [5], [8]). On the other hand, non-linear theoretical models of [2] provide a fairly good description of the data. For an in-depth discussion see [7]. 

An interesting aside to this discussion concerns the composition mix assumed in the theoretical models. Recent measurements have suggested that the solar O abundance might be 0.2 dex lower than previously believed [1]. A change of this size in the model compositions could lead to significantly less PMS Li depletion among solar-type stars, reducing the discrepancy between the Li depletion predicted by solar-tuned convective models and the ZAMS cluster data. 

The chemical analysis has revealed that rather low C/O ratios are found in metal-poor extragalactic carbon stars, as found for galactic carbon stars of the solar vicinity. Furthermore, the three analyzed stars show similar s-elements enhancements [ls/Fe]=0.8-1.3 and [hs/Fe]=l.l-1.7. This leads to new constraints for evolutionary models. For instance, the derived C/O and 13C/12C ratios are lower than model predictions at low metallicity. On the contrary, theoretical predictions of neutrons exposures for the production of the s-elements are compatible with observations (see Fig. 1). Finally, from their known distances, we have estimated the luminosities and masses of the three stars. It results that SMC-B30 and Sgr-C3 are most probably intrinsic carbon stars while Sgr-Cl could be extrinsic. 

Fig. 6.6. Correlation of heavy (Ba, Nd etc.) and light (Y, Zr) s-process enhancements in AGB stars, with theoretical curves based on the old exponential-exposure model, to = 0.3 corresponds approximately to the main s-process distribution in the Solar System. After Busso, Gallino and Wasserburg (1999). Reprinted with kind permission of Annual Reviews, Inc. Courtesy Maurizio Busso.

Almost all of the elements heavier than He are synthesized in the interiors of stars. The work of Burbidge et al. (1957) gives the theoretical framework for the synthesis of the elements. The experimental evidence of active nucleosynthesis came from the discovery of the unstable nuclei of technetium in the spectra of red giants (Merrill 1952). The solar elemental and isotopic abundances which are taken from the primitive carbonaceous chondrites constitute the guidelines for testing such models (Anders and Grevesse 1989). A minimum of eight basic processes are required to reproduce the observed compositions. Nucleosynthetic... 

As a concluding remark of this section, the theoretical models of nucleosynthesis within stars show that the isotopic compositions of the elements are highly variable depending on star size, metallicity, companion s presence. From the isotopic data obtained in diverse solar system materials it turns out that most of this material was highly homogenized in the interstellar medium or by the formation of the solar system. The presence of isotopic anomalies preserved in some primitive materials are the last witnesses of the initial diversity of the materials constituting our planetary system. 

We also know that processes that eject solar wind fractionate elements based on their first ionization potential, the energy necessary to ionize the element. Over time, ejection of solar wind that is fractionated relative to the bulk Sun changes the surface composition of the Sun, the part that we measure spectroscopically. There are theoretical models to account for this effect, but it introduces uncertainties into the inferred composition of the bulk Sun. 

Theoretical modeling provides strong evidence that most presolar silicon carbide grains come from 1.5 to 3 M stars. As discussed in Chapter 3, stellar modeling of the evolution of the CNO isotopes in the envelopes of these stars makes clear predictions about the 12C/13C, 14N/15N, 170/160,180/160 ratios as a star evolves. For example, in the envelopes of low- to intermediate-mass stars of solar composition, the 12C/13C ratio drops to 40 (from a starting value of 89), and 14N/15N increases by a factor of six as carbon and nitrogen processed by... 

Condensation under the conditions obtained in the solar nebula is not really amenable to direct experiment. However, experiments have provided thermodynamic data with which the condensation process can be modeled theoretically. 

The value of the decay constant (1) must have remained constant over the age of the solar system and the galaxy, and it must be accurately known. As we discussed in Chapter 2, this third assumption is well founded for conditions relevant to cosmochemistry. The concordance of dates given by systems using a variety of decay paths and astronomical observations of decay rates of newly synthesized elements over billions of years provides strong evidence that the decay rates have remained constant. In addition, detailed experiments and theoretical models have identified the extreme conditions (e.g. centers of stars) under which this assumption breaks down for certain isotopes, thereby identifying the exceptions that prove the rule. (4) It must be possible to assign a realistic value to the initial abundance of the... 

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