Aims. We analyze the non-standard mixing history of the solar twins HIP55459, HIP79672, HIP56948, HIP73815, and HIP100963, to determine as precisely as possible their mass and age. Methods. We computed a grid of evolutionary models with non-standard mixing at several metallicities with the Toulouse-Geneva code for a range of stellar masses assuming an error bar of 50K in .We choose the evolutionary model that reproduces accurately the observed low lithium abundances observed in the solar twins. Results. Our best-fit model for each solar twin provides a mass and age solution constrained by their Li content and determination. HIP56948 is the most likely solar-twin candidate at the present time and our analysis infers a mass of and an age of Gyr. Conclusions. Non-standard mixing is required to explain the low Li abundances observed in solar twins. Li depletion due to additional mixing in solar twins is strongly mass dependent. An accurate lithium abundance measurement and non-standard models provide more precise information about the age and mass more robustly than determined by classical methods alone. Key words: stars: fundamental parameters - stars: horizontal-branch - stars: abundances - stars:evolution - stars: interiors - Sun: fundamental parameters
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