Galaxy Distances via Rotational Parallaxes

Astrometry is one of the foundations of astrophysics. Accurate distances to stars and galaxies allow for significant tests of stellar evolution, galaxy formation and evolution and cosmology. NASA’s Space Interferometry Mission (SIM) will obtain extraordinary precision astrometry [1-10 μas positional accuracy] for ten to twenty thousand objects brighter than V=20 mag. In this paper we discuss a method to determine the distance of nearby spiral galaxies using the technique of rotational parallaxes. We show that it is possible to achieve distance errors of only a few percent using this method. With such distances at hand, it becomes possible to determine an accurate zero-point for the Tully-Fisher relation, one of the tools to measure distances throughout the universe. Precision cosmology will become possible once the Hubble constant has been accurately determined from a SIM-based calibration of the Tully-Fisher relation. The rotational parallax method employs the common motions of a number of stars to determine the distance to the group as a whole. If we assume that a given target star in an external galaxy is on a circular orbit around the center of that galaxy, three observables –the two proper motions and the radial velocity– suffice to determine the three unknowns: the inclination of the orbit, the rotational velocity and the distance. Several factors complicate the application of this simple technique to real galaxies: 1) the target galaxy may have substantial space-motion, 2) stars in real galaxies are not on circular orbits (e.g. due to spiral-arm streaming motions or induced by random motions), 3) stars in the galaxy are at significantly different distances from the Sun (the near side of M 31 is ∼5% closer than the far side), 4) target stars might have large z-heights or velocities (“run-away” stars). In this paper we show how one-percent distances can be obtaind for the nearest spirals, even in the presence of the complications mentioned above.