Unconstrained astrometric orbits for Hipparcos stars with stochastic solutions

A considerable number of astrometric binaries whose positions on the sky do not obey the standard model of mean position, parallax, and linear proper motion were observed by the Hipparcos satellite. Some of them remain undiscovered, and their observational data have not been properly processed with the more adequate astrometric model that includes nonlinear orbital motion. We develop an automated algorithm, based on "genetic optimization,'' to solve the orbital fitting problem in the most difficult setup, when no prior information about the orbital elements is available ( from, e. g., spectroscopic data or radial velocity monitoring). We also offer a technique to accurately compute the probability that an orbital fit is bogus, that is, that an orbital solution is obtained for a single star, and to estimate the probability distributions for the fitting orbital parameters. We test this method on Hipparcos stars with known orbital solutions in the catalog and further apply it to 1561 stars with stochastic solutions, which may be unresolved binaries. At a confidence level of 99%, orbital fits are obtained for 65 stars, most of which have not been known as binary. It is found that reliable astrometric fits can be obtained even if the period is somewhat longer than the time span of the Hipparcos mission, that is, if the orbit is not closed. A few of the new probable binaries with A-type primaries with periods 444-2015 days are chemically peculiar stars, including Ap and lambda Bootis types. The anomalous spectra of these stars are explained by admixtures of light from the unresolved, sufficiently bright and massive companions. We estimate the apparent orbits of four stars that have been identified as members of the approximate to 300 Myr old Ursa Major kinematic group. Another four new nearby binaries may include low-mass M-type or brown dwarf companions. Follow-up spectroscopic observations in conjunction with more accurate inclination estimates will lead to better estimates of the secondary mass. Similar astrometric models and algorithms can be used for binary stars and planet hosts observed by SIM and Gaia.