Statistical constraints for astrometric binaries with nonlinear motion

Useful constraints on the orbits and mass ratios of astrometric binaries in the Hipparcos catalog are derived from the measured proper motion differences of Hipparcos and Tycho-2 (Delta mu), accelerations of proper motions ((mu)over dot), and second derivatives of proper motions (<(mu)double over dot>). It is shown how, in some cases, statistical bounds can be estimated for the masses of the secondary components. Two catalogs of astrometric binaries are generated, one of binaries with significant proper motion differences and the other of binaries with significant accelerations of their proper motions. Mathematical relations between the astrometric observables Delta mu, (mu)over dot, and <(mu)double over dot> and the orbital elements are derived in the appendices. We find a remarkable difference between the distribution of spectral types of stars with large accelerations but small proper motion differences and that of stars with large proper motion differences but insignificant accelerations. The spectral type distribution for the former sample of binaries is the same as the general distribution of all stars in the Hipparcos catalog, whereas the latter sample is clearly dominated by solar-type stars, with an obvious dearth of blue stars. We point out that the latter set includes mostly binaries with long periods (longer than about 6 yr).