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Sternberg Astronomical Institute, Universitetsky pr., 13, Moscow, Russia
E-mail: asv@sai.msu.su
Sternberg Astronomical Institute . Moscow
S. V. Ajukov
THE SOLAR ENVELOPE
PARAMETERS
AND RADIATIVE OPACITIES
IN THE MODELS
OF THE PRESENT SUN

Comparison of the different opacity tables at the solar core conditions.
The decimal logarithm of the difference between the opacity table k and analytic
approximation k 0 from Christensen-Dalsgaard J., 1988, Computational Procedures for
GONG Solar Model Project is plotted. The points (T, r, X) were taken from the standard
OPAL solar model. The type of the opacity table is shown near the each line.
CS70 -- Cox A.N., Stewart J.N. 1970, Astrophys. J. Suppl., 19, 243.
CT76 -- Cox A.N., Tabor J. E. 1976, Astrophys. J. Suppl., 31, 271.
BU88 -- Bahcall J.N., Ulrich R. K., 1988, Rev. Mod. Phys., 60, 297.
WKM -- Weiss A., Keady J.J., Magee N.M. Jr., 1990, Atomic Data and Nuclear Data
Tables, 45, 209.
IR91 -- Iglesias C. A., Rogers F. J., 1991, Astrophys. J. 371, 408.

The convection zone depth versus the envelope entropy for the three opacity tables.
1) M--CS70 ® A -- illustrates the change in H bcz with increasing of helium;
2) A ® B -- change in H bcz due to change of entropy;
3) B ® M--LAOL -- due to increasing of opacity from CS70 to LAOL;
4) M--LAOL ® C -- difference between the opacity tables LAOL and OPAL;
5) C ® M--OPAL -- increasing of the entropy.

Solar models on the (Y, S) plane.
Five asterisks indicate standard solar models. The abbreviations are:
CS70 -- Cox A.N., Stewart J.N. 1970, Astrophys. J. Suppl., 19, 243.
CT76 -- Cox A.N., Tabor J. E. 1976, Astrophys. J. Suppl., 31, 271.
BU88 -- Bahcall J.N., Ulrich R. K., 1988, Rev. Mod. Phys., 60, 297.
WKM -- Weiss A., Keady J.J., Magee N.M. Jr., 1990, Atomic Data and Nuclear Data
Tables, 45, 209.
IR91 -- Iglesias C. A., Rogers F. J., 1991, Astrophys. J. 371, 408.
¤ -- Y and S obtained in Baturin V.A., Vorontsov S.V., 1994, Proceedings of GONG'94
Annual Meeting.
Two vectors K core and K rad indicate directions in which the standard model moves when
decreasing opacity in the core and radiative zone, respectively. K X respresents the vector
of model change with varying hydrogen profile in the core.
R g is the gas constant.

Introduction
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.
Convective envelope entropy as a solar model parameter
The standard solar model has two ``calibration'' parameters allowing to get the right values
of the radius and luminosity at the given age---the initial chemical composition and the
convection theory parameter. The second governs the temperature gradient in the
superadiabatic layers of the convection zone. These two values allow to compute evotionary
track; the choice was caused mainly by the historical reasons. The value of hydrogen
abundance on the solar outer layers has its own meaning as an important cosmological and
cosmogonical parameter but the information contained in the convection theory parameter
is rarely used. Meantime this parameter is very important. It defines the adiabate of the
convective envelope; any adiabate has T®0 and r®0 at the Sun's surface and we need
some additional value to distinguish one adiabate from another. The most natural value
parameterizing the adiabate is its entropy (S cnv ). Convection theory parameter is the most
convenient parameter to vary in the model but not the most meaningful as it also depends
on the convection theory internals and the atmosphere structure details (e.g., opacity).
Comparison of the evolutionary models based on the convection parameter is nonadequate
due to fact that this parameter determines the structure of the atmospheric layers while
the evolutionary model can't distinguish between the different atmospheres: the atmosphere
details are irrelevant in the problem of computing the evolutionary model of the Sun. The
theory of Sun's evolution can't answerthe questions about the atmosphere and superadiabatic
layers of convection zone; it can only give the thickness of these layers, their mass (very
roughly) and the entropy of the convective envelope. These are the reasons why we
choosed the convection zone entropy S cnv as a model parameter to use together with
surface chemical composition (helium abundance Y).

The influence of opacity
on the standard solar model parameters
Increasing opacities from CS70 up to LAOL (WKM) (both in the core and the radiative
zone) raises helium content by 4--5%. Changing from WKM to OPAL (IR91) doesn't
change Y at all as versions of LAOL and OPAL tables used by us have nearly the same
opacity values in the core of the Sun, so corresponding models have nearly the same Y.
On the other side, the transition from CS70 to LAOL decreased the convection zone
depth, mainly due to increased helium content. This effect supersedes both the increasing
of the opacity near the convection zone boundary and the decreasing of the entropy of the
convection zone (they both lead to increasing of H bcz ). Substitution of OPAL instead of
LAOL raised H bcz due to increasing of the opacities and decreasing of the entropy.
The estimates of the neutrino fluxes for standard models are close to common values
and significantly larger than Davis'. The attractive looking chlorine flux of CS70 model is
due to low core opacities (and low central temperature).
Hence the average modern standard solar model (with LAOL or OPAL opacities) must
have Y approximately equal to 0.28. Any opacity decrease in the core (e.g., due to
WIMPs) or ``collective effects'' will lead to decrease of Y by 1% per each 3% in opacity.
The opacity lowering also adjusts the chlorine neutrino flux but it depends mainly on the
very central values whereas Y is sensitive to the opacities in the whole energy-generating
core. So the dependence between the neutrino flux and Y isn't so straightforward.
Solar models with modified opacities
. The opacity variations in the energy-generating core are very similar to
changes in the hydrogen profile in the core: they can compensate each other in
terms of model parameters;
. Changing of opacity near the bottom of the convection zone does not
affect model parameters; it only affects convection zone depth;
. Opacity in the core determines the model's surface helium abundance
while opacity in the radiative zone changes mainly the entropy of the adiabatic
part of the convection zone;
. The current helioseismological estimates of helium abundance and convection
zone entropy are in disagreement with the standard solar models: the core
opacities have to be lowered significantly.