Projections for Measuring the Size of the Solar Core with Neutrino-Electron Scattering

We quantify the amount of data needed in order to measure the size and position of the ^{8}B neutrino production region within the solar core, for experiments looking at elastic scattering between electrons and solar neutrinos. The directions of the electrons immediately after scattering are strongly correlated with the incident directions of the neutrinos; however, this is degraded significantly by the subsequent scattering of these electrons in the detector medium. We generate distributions of such electrons for different neutrino production profiles, and use a maximum likelihood analysis to make projections for future experimental sensitivity. We find that with approximately 20 years worth of data the Super Kamiokande experiment could constrain the central radius of the shell in which ^{8}B neutrinos are produced to be less than 0.22 of the total solar radius at 95% confidence.