Implications of combined solar-neutrino observations and their theoretical uncertainties

Constraints on the core temperature ($T_c$) of the Sun and on neutrino-oscillation parameters are obtained from the existing solar neutrino data, including the recent GALLEX, SAGE, and Kamiokande III results. (1) A purely astrophysical solution to the solar-neutrino problem is strongly disfavored by the data: the Homestake and Kamiokande data together are incompatible with any temperature in the Sun; the central values of both the SAGE and GALLEX results require a large reduction of $T_c$ when they are fit to a cooler Sun. (2) Assuming the standard solar model (SSM) and matter-enhanced neutrino oscillations, the Mikheyev-Smirnov-Wolfenstein (MSW) parameters are constrained to two small regions: nonadiabatic oscillations with $\Delta m^2=(0.3-1.2)\mathrm{}\times {10}^{-5\mathrm{}}$ e${\mathrm{V}}^2$, ${sin}^{2}2\theta =(0.4-1.5)\mathrm{}\times {10}^{-2\mathrm{}}$, or large mixing-angle oscillations with $\Delta m^2=(0.3-3)\mathrm{}\times {10}^{-5\mathrm{}}$ e${\mathrm{V}}^2$, ${sin}^{2}2\theta =0.6-0.9\mathrm{}$. The nonadiabatic solution gives a considerably better fit. For ${\nu }_e$ oscillations into sterile neutrinos, the allowed region (90% C.L.) is constrained to nonadiabatic oscillations. As long as the SSM is assumed, the neutrino mixing angles are at least four times larger, or considerably smaller, than the corresponding quark mixing angles. (3) Allowing both MSW oscillations and a nonstandard core temperature, (a) the experiments determine the core temperature at the 5% level, $T_c={1.02}_{-0.05\mathrm{}}^{+0.03\mathrm{}}$ (90% C.L.) relative to the SSM, and (b) when $T_c$ is used as a free parameter, the allowed MSW region is broadened: a 2% cooler Sun allows $\Delta m^2$, ${sin}^{2}2\theta$ implied by the supersymmetric SO(10) grand unified theory (GUT), while a 3-4% warmer Sun extends the allowed parameter space into values suggested by intermediate-scale SO(10) GUT's, for which the ${\nu }_{\tau }$ may be cosmologically relevant. Superstring-inspired models are consistent with all solutions. (4) From the narrowed parameter space, we predict the neutrino spectral shape which should be observed in the Sudbury Neutrino Observatory (SNO). Expected rates for SNO, SuperKamiokande, and BOREXINO are also discussed. Throughout the calculation we use the Bahcall-Pinsonneault SSM (1992) with helium diffusion, and include nuclear and astrophysical uncertainties in a simplified, but physically transparent way.