Recent solar neutrino results together with the assumption of a stationary Sun imply severe constraints on the individual components of the total neutrino flux : $Phi_{Be} leq 0.7 cdot 10^{9} cm^{-2} s^{-1}, Phi_{CNO} leq 0.6 cdot 10^{9} cm^{-2} s^{-1}$ and $64 cdot 10^{9} cm^{-2} s^{-1} leq Phi_{pp+pep} leq 65 cdot 10^{9} cm^{-2} s^{-1}$ (at 1$ sigma$ level), the constraint on $ u_{Be}$ being in strong disagreement with $Phi_{Be}^{SSM} = 5 cdot 10^{9} cm^{-2} s^{-1}$. We study a large variety of non-standard solar models with low inner temperatures, finding that the temperature profiles T(m) follow the homology relationship: T(m)=k$T(m)^{SSM}$, so that they are specified just by the central temperature $T_{c}$. There is no value of $T_{c}$ which can account for all the available experimental results and also if we restrict to consider just Gallium and Kamiokande results the fit is poor. Finally we discuss what can be learned from new generation experiments, planned for the detection of monochromatic solar neutrinos, about the properties of neutrinos and of the Sun.
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