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We investigate the sensitivity of solar neutrino data to mixing of sterileneutrinos with masses $\gtrsim$ eV. For current data, we perform aFeldman-Cousins analysis to derive a robust limit on the sterile neutrinomixing. The solar neutrino limit excludes significant regions of the parameterspace relevant to hints from reactor and radioactive gallium sourceexperiments. We then study the sensitivity of upcoming solar neutrino data,most notably elastic neutrino-electron scattering in the DARWIN and DUNEexperiments as well as coherent neutrino-nucleus scattering in DARWIN. Thesehigh precision measurements will increase the sensitivity to sterile neutrinomixing by about a factor of 4.5 compared to present limits. As a by-product, weintroduce a simplified solar neutrino analysis using only four data points: thelow- and high-energy $\nu_e$ survival and transition probabilities. We showthat this simplified analysis is in excellent agreement with a full solarneutrino analysis; it is very easy to handle numerically and can be applied toany new physics model in which the energy dependence of the $\nu_e$ transitionprobabilities is not significantly modified.

Testing sterile neutrino mixing with present and future solar neutrino data