For standard neutrinos , recent solar neutrino results together with the assumption of a nuclearly powered Sun imply severe constraints on the individual components of the total neutrino flux : \Phi _ { \text { Be } } \leq 0.7 \times 10 ^ { 9 } \text { cm } ^ { -2 } \text { s } ^ { -1 } , \Phi _ { \text { CNO } } \leq 0.6 \times 10 ^ { 9 } \text { cm } ^ { -2 } \text { s } ^ { -1 } , and 64 \times 10 ^ { 9 } \text { cm } ^ { -2 } \text { s } ^ { -1 } \leq \Phi _ { pp + pep } \leq 65 \times 10 ^ { 9 % } \text { cm } ^ { -2 } \text { s } ^ { -1 } ( at 1 \sigma level ) .
The bound on \Phi _ { \text { Be } } is in strong disagreement with the standard solar model ( SSM ) prediction \Phi _ { \text { Be } } ^ { \text { SSM } } \approx 5 \times 10 ^ { 9 } \text { cm } ^ { -2 } \text { s } ^ { -1 } .
We study a large variety of non-standard solar models with low inner temperature , finding that the temperature profiles T ( m ) follow the homology relationship : T ( m ) = kT ^ { \text { SSM } } ( m ) , 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 .
Even if we only consider the Gallium and Kamiokande results , they remain incompatible .
Lowering the cross section p + { } ^ { 7 } \text { Be } \to \gamma + { } ^ { 8 } \text { B } is not a remedy .
The shift of the nuclear fusion chain towards the pp -I termination could be induced by a hypothetical low energy resonance in the ^ { 3 } \text { He } + { } ^ { 3 } \text { He } reaction .
This mechanism gives a somehow better , but still bad fit to the combined experimental data .
We also discuss what can be learnt from new generation experiments , planned for the detection of monochromatic solar neutrinos , about the properties of neutrinos and of the Sun .