We have evolved 10,000 solar models using 21 input parameters that are
randomly drawn for each model from separate probability distributions for every
parameter. We use the results of these models to determine the theoretical
uncertainties in the predicted surface helium abundance, the profile of the
sound speed versus radius, the profile of the density versus radius, the depth
of the solar convective zone, the eight principal solar neutrino fluxes, and
the fractions of nuclear reactions that occur in the CNO cycle or in the three
branches of the p-p chains. We also determine the correlation coefficients of
the neutrino fluxes for use in analysis of solar neutrino oscillations. Our
calculations include the most accurate available input parameters, including
radiative opacity, equation of state, and nuclear cross sections. We
incorporate both the recently determined heavy element abundances recommended
by Asplund, Grevesse & Sauval (2005) and the older (higher) heavy element
abundances recommended by Grevesse & Sauval (1998). We present best-estimates
of many characteristics of the standard solar model for both sets of
recommended heavy element compositions.Comment: ** John N. Bahcall passed away on August 17, 2005. Manuscript has 60
pages including 10 figure