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Published online by Cambridge University Press: 14 August 2015
Using a version of the Toomre-criterion (Toomre, 1964) for a mixture of stellar populations, limits are derived for the kinematical properties of the newly discovered population of low-velocity M-dwarfs (Weistrop, 1972; Murray and Sanduleak, 1972); these stars are claimed to be a large mass-fraction (≳ 0.5) of all stars in the solar neighbourhood and to have only 10 km s−1 velocity dispersion. They could make up for the locally missing mass (Oort, 1965; Schmidt, 1974). It is found that a configuration of stellar populations with the M-dwarfs included (having such properties) is not stable in the sense of the Toomre-criterion. The limiting stability properties are given.