The Temperature Dependence of Solar Neutrino Fluxes

By comparing neutrino fluxes and central temperatures calculated from 1000 detailed numerical solar models, we derive improved scaling laws which show how each of the neutrino fluxes depends upon the central temperature (flux $\propto T^m$); we also estimate uncertainties for the temperature exponents. With the aid of a one-zone model of the sun, we derive expressions for the temperature exponents of the neutrino fluxes. For the most important neutrino fluxes, the exponents calculated with the one-zone model agree to within 20\% or better with the exponents extracted from the detailed numerical models. The one-zone model provides a physical understanding of the temperature dependence of the neutrino fluxes. For the $pp$ neutrino flux, the one-zone model explains the (initially-surprising) dependence of the flux upon a negative power of the temperature and suggests a new functional dependence. This new function makes explicit the strong anti-correlation between the $^7$Be and $pp$ neutrino fluxes. The one-zone model also predicts successfully the average linear relations between neutrino fluxes, but cannot predict the appreciable scatter in a $\Delta \phi_i/\phi_i$ versus $\Delta \phi_j/\phi_j$ diagram.