  We present a strategy to identify several thousand stars that are
astrometrically stable at the micro-arcsecond level for use in the SIM (Space
Interferometry Mission) astrometric grid. The requirements on the grid stars
make this a rather challenging task. Taking a variety of considerations into
account we argue for K giants as the best type of stars for the grid, mainly
because they can be located at much larger distances than any other type of
star due to their intrinsic brightness. We show that it is possible to identify
suitable candidate grid K giants from existing astrometric catalogs. However,
double stars have to be eliminated from these candidate grid samples, since
they generally produce much larger astrometric jitter than tolerable for the
grid. The most efficient way to achieve this is probably by means of a radial
velocity survey. To demonstrate the feasibility of this approach, we repeatedly
measured the radial velocities for a pre-selected sample of 86 nearby Hipparcos
K giants with precisions of 5-8 m/s. The distribution of the intrinsic radial
velocity variations for the bona-fide single K giants shows a maximum around 20
m/s, which is small enough not to severely affect the identification of stellar
companions around other K giants. We use the results of our observations as
input parameters for Monte-Carlo simulations on the possible design of a radial
velocity survey of all grid stars. Our favored scenario would result in a grid
which consists to 68% of true single stars and to 32% of double or multiple
stars with periods mostly larger than 200 years, but only 3.6% of all grid
stars would display astrometric jitter larger than 1 microarcsecond. This
contamination level is probably tolerable.
