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[ Chiwriter 3.x, Grapher, in Russian (66KB) ]
Given the chemical composition (hydrogen abundance mainly), the mass and internal physics, the structure of the star is determined uniquely. The commonly used method for the choice of the hydrogen abundance profile in the model of the present Sun is evolutionary calculations. But the existing uncertainties in physics and evolution give us an idea to consider a more extended set of possible solar models. We consider models with solar values of radius, luminosity and mass, but with an arbitrary profiles of hydrogen abundance in the core. Of course, to get up to solar values, profile X(m/M) must satisfy some (nonstrict) restrictions, which are determined by fitting.
In this poster we propose a hypothesis that within fixed assumptions about internal physics (opacity, thermodynamics, nuclear reactions) a strict relation between the surface helium abundance and the entropy of the adiabatic part of the convective zone exists for all solar models. This hypothesis is verified with models under simplified physics (Christensen-Dalsgaard 1988) and with six evolutionary models computed by Christensen-Dalsgaard (1992). Such relation mainly depends on the functions of the opacities in radiative zone between the lower boundary of convection and the region of nuclear reactions. The possibilities of the agreement between such relation and helioseismic determination of surface helium abundance and entropy is discussed.
[ LaTeX, Figure 1 | Postscript (37KB) ]
[ Postscript, in Russian, no figures (140KB) ]
We propose to use the surface helium abundance Y and the specific plasma entropy Scnv in the adiabatic part of the convective zone for the solar model comparison. The influence of the opacity and the hydrogen abundance profile modifications on the model position on the (Y,Scnv) plane is discussed. It is revealed that such variations (when localized in the energy-generating core) shift the solar model along a straight line. Opacity increasing in the radiative zone results in this line shift to higher Y.
[ ASCII (866) | ASCII (KOI8) | Figure 1 | Postscript, in Russian (620KB) ]
Standard solar models with five different opacity tables are computed. Replacing the Los Alamos opacities with the Livermore ones results in the increase of the convection zone depth by 0.015Rsun and surface helium abundance (by mass) by 1.5% up to approximately 28% (Grevesse mixture).
[ ASCII (866) | ASCII (KOI8) | Figure 1 | Postcript, in Russian (275KB) ]
A variety of solar models (namely, models of stars having solar values of mass, radius, luminosity) is a subject of our study. The hydrogen profile in the star's interior is usually determined by course of the evolution, but we also consider models with arbitrary hydrogen profiles or diffusion profiles also. Applying additional restrictions on the model which follow from recent helioseismic results we consider the question of existence of the models. These restrictions are: 1) calibration of the surface helium abundance and the specific entropy in the convection zone (Vorontsov et al. 1991; Baturin, Vorontsov 1994; there are few results on the helium calibration but we used cited ones because they contain simultaneous determination of the helium and the entropy); 2) estimation of the convection zone depth (Christensen-Dalsgaard et al., 1991); 3) sound speed profile inferred from oscillation frequencies (Vorontsov, Shibahashi 1992). These results are basically independent of a specific solar model. Hereafter we roughly divide a regular solar model into three zones: 1) the outer convection zone (the envelope); the chemical composition and specific entropy are constant there; 2) the radiative zone; the chemical composition is constant there when diffusion isn't taken into account; the structure of this area depends mainly on the opacity; 3) the energy-generating core where the thermonuclear reactions are significant; there is definitely variable hydrogen/helium profile. Commonly speaking we study the possibility of fitting some cores and convection zones while the fit conditions are determined by the radiative zone...
[ Postscript, long preliminary version (38KB) | Postscript, final version (210KB) ]
[ ChiWriter 3.x (ouch!), in Russian ]
Given the chemical composition profile and mass the internal structure of the star is determined by Vogt-Russell theorem. It gives that this model will have definite radius and luminosity (and they will not be equal to solar ones). So we need two parameters to adjust when computing static solar model. While computing the standard model these two parameters are initial chemical composition and convection theory parameter controlling te temperature gradient in the outermost layers. This choice is rather arbitrary and done due to lack of knowledge about these values. In the other words, these values were transformed from the parameters to the results (e.g., the solar evolution modelling gives the best estimate of the presolar helium abundance). The other results are neutrino fluxes, convection zone depth, oscillation spectrum etc. The input data (nuclear reactions, opacity, equation of state and description of convection) may contain significant errors, especially opacity. And there is a question: how can these error alter our results?
In this work we try to investigate some aspects of this problem. First, we replace the convection theory parameter with the entropy of the adiabatic part of the convection zone. Second, we study the influence of the opacity tables on the solar models. Third, we analyze the connections between the model parameters and the hydrogen profile and the opacities in the nonstandard models.
[ Postscript (620KB) ]
We present the results of high-precision computing of standard solar models with different opacity tables. A comparative analysis of models is done utilizing two key parameters--helium abundance and specific entropy in the convection zone. The influence of stellar opacity on these two parameters is studied. Comparison of standard models with different opacities shows that the increase of the opacity in the radiative zone causes decrease of entropy whereas the increase of the opacity in the energy-generating core leads to higher helium abundance. Investigation of nonstandard static models points out that the common relation between the specific entropy and opacity in the radiative zone of the Sun (outside of nuclear reactions region).
[ Postscript, in Russian, no figures (850KB) | LaTeX plus figures (KB) | Postscript, in English, with figures (KB) ]
Published in: Bull. Astr. Soc. India, 1996, 24, 329.
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This poster was not presented actually. I wish I were there....
The problem of computation of the model of the present Sun with given sound speed profile in the solar radiative zone is considered. It is shown that the chemical composition is still a free parameter but the entropy of the adiabatic part of the convection zone is determined by this procedure. Parameters of the models are compared with the helioseismic calibration of solar envelope and the disagreement is revealed. A study of the seismic properties of the models' cores indicates that the best model is the one closest to the standard solar model.
[ Postscript, in Russian, no figures (1680KB) | LaTeX plus figures (87KB) | Postscript, in English, with figures (145KB) ]
Three alternative approaches in evaluating of the entropy of the adiabatic part of the solar convection zone are compared.
[ Postscript (60KB) ]
[ Postscript, 126 pages, in Russian (999KB) ]