  Runaway stars can result from core-collapse supernovae in multiple stellar
systems. If the supernova disrupts the system, the companion gets ejected with
its former orbital velocity. A clear identification of a runaway star can yield
the time and place of the explosion as well as orbital parameters of the
pre-supernova binary system. Previous searches have mostly considered O- and
B-type stars as runaway stars because they are always young in absolute terms
(not much older than the lifetime of the progenitor) and can be detected up to
larger distances. We present here a search for runaway stars of all spectral
types. For late-type stars, a young age can be inferred from the lithium test.
We used Gaia data to identify and characterise runaway star candidates in
nearby supernova remnants, obtained spectra of 39 stars with UVES at the VLT
and HDS at the Subaru telescope and found a significant amount of lithium in
the spectra of six dwarf stars. We present the spectral analysis, including
measurements of radial velocities, atmospheric parameters and lithium
abundances. Then we estimate the ages of our targets from the
Hertzsprung-Russell diagram and with the lithium test, present a selection of
promising runaway star candidates and draw constraints on the number of ejected
runaway stars compared to model expectations.
