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A precise test of the theory of stellar evolution can be performed bymeasuring the average difference in energy between the neutrino line producedby ${\rm ^7Be}$ electron capture in the solar interior and the correspondingneutrino line produced in a terrestrial laboratory. This energy shift iscalculated to be 1.29~keV (to an accuracy of a few percent) for the dominantground-state to ground-state transition. The energy shift is approximatelyequal to the average temperature of the solar core, computed by integrating thetemperature over the solar interior with a weighting factor equal to thelocally-produced $^7$Be neutrino emission. The characteristic modulation of the${\rm ^7Be}$ line shape that would be caused by either vacuum neutrinooscillations or by matter-enhanced (MSW) neutrino oscillations is shown to besmall. Other frequently-discussed weak interaction solutions to the solarneutrino problem are also not expected to change significantly the lineprofile. Therefore, a measurement of the energy shift is a measurement of thecentral temperature distribution of the sun.Comment: 58 pages, REVTEX file. For hardcopy of figures contact  BEST@SNS.IAS.EDU. Institute for Advanced Study number AST 93/4

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Be</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>7</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>solar neutrino line: A reflection of the central temperature distribution of the Sun

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