Be7solar neutrino line: A reflection of the central temperature distribution of the Sun

Abstract

A precise test of the theory of stellar evolution can be performed by measuring the average difference in energy between the neutrino line produced by ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ electron capture in the solar interior and the corresponding neutrino line produced in a terrestrial laboratory. This energy shift is calculated to be 1.29 keV (to an accuracy of a few percent) for the dominant ground-state to ground-state transition. The energy shift is approximately equal to the average temperature of the solar core, computed by integrating the temperature over the solar interior with a weighting factor equal to the locally produced ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ neutrino emission. Therefore, a measurement of the energy shift is a measurement of the central temperature distribution of the Sun. The energy profile of the ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ line is derived analytically and is evaluated numerically. The line shape is asymmetric: on the low-energy side, the line shape is Gaussian with a half-width at half-maximum of 0.6 keV and, on the high-energy side, the line shape is exponential with a half-width at half-maximum of 1.1 keV. The effective temperature of the high-energy exponential tail is 15 × ${10}^6$ K. The energy profile of the ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ neutrino line should be taken into account in calculations of vacuum neutrino oscillations and of the absorption cross section for ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ solar neutrinos incident on ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ nuclei. The characteristic modulation of the ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ line shape that would be caused by either vacuum neutrino oscillations or by matter-enhanced (MSW) neutrino oscillations is shown to be small. Other frequently discussed weak interaction solutions to the solar neutrino problem are also not expected to change significantly the line profile.