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 ${}^8\mathrm{B}$ 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 ${}^8\mathrm{B}$ neutrinos are produced to be less than 0.22 of the total solar radius at 95% confidence.

Figure 1

Distribution in a neutrino detector of the angles of travel of electrons (integrated over all recoil energies above 5 MeV) with respect to the center of the Sun, which have been liberated from their atoms due to scattering with solar neutrinos, for different values of the mean position of ${}^8\mathrm{B}$ neutrino production in the solar core $R_{8\mathrm{B}}$. We take an exposure of 2000 kt yr and assume a fixed value of ${\delta }_{8\mathrm{B}}=0.05R_{\text{Sun}}$.

Figure 2

95% confidence regions to measure the central position $R_{8\mathrm{B}}$ and width ${\delta }_{8\mathrm{B}}$ of the region in which ${}^8\mathrm{B}$ neutrinos are produced in the Sun with neutrino-electron scattering, as a fraction of the total solar radius $R_{\text{Sun}}$. We have generated simulated data with $R_{8\mathrm{B}}=0.05R_{\text{Sun}}$ and ${\delta }_{8\mathrm{B}}=0.05R_{\text{Sun}}$, in line with expectations from solar modeling [5, 6, 9], and have used a maximum likelihood method to quantify how well different distributions of electrons in a neutrino detector fit to this data.