Young nearby runaway stars are suitable to search for their place of origin and possibly associated objects, for example neutron stars. Tetzlaff, Neuhauser & Hohle (2011) selected young ($le 50$ Myr) runaway star candidates from Hipparcos, for which they had estimated the ages from the location in the Hertzsprung-Russell diagram and evolutionary models. Here, we redetermine or constrain their young ages more precisely not only by using the new Gaia DR2 data, but also by measuring lithium, which is a youth indicator. For 308 stars, we took spectra to search for the strong resonance doublet of the lithium-7 isotope at 6708 $unicode{xC5}$. The spectra were taken with the Echelle spectrograph FLECHAS at the University Observatory Jena between February 2015 and June 2018 and with TRES between April 2011 and June 2017 at the Fred L. Whipple Observatory. We found 208 stars with significant occurrence of lithium in their spectra, and five possess a possible age younger or about 50 Myr. Three of these targets are even closer than GJ 182, the nearest known runaway star at about 24 pc. Theses stars are young runaway stars suitable for further investigation of their origin from either a dynamical or supernova ejection.
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