Sagittarius A* “Visual Binaries”: A Direct Measurement of the Galactocentric Distance

Abstract

We present a new geometrical method for measuring the distance to the Galactic center (R_0) by solving for the Keplerian orbit of individual stars bound to the black hole associated with Sgr A* from radial velocity and proper-motion measurements. We identify three stars to which the method may be applied, and show that two of them individually could produce 1%-5% accuracy of R_0 after 15 years of observing, and 0.5%-2% after 30 years of observing, depending on what the orbital parameters of these stars turn out to be. Further, we show that combining the measurements of the three stars, together with the constraints that they must orbit a common center having a common mass, produces considerable improvement in the R_0 determination over simple averaging of the three determinations. Using a power-law stellar density model, we find the probability distribution over allowed orbital parameter space. Then we perform a Monte Carlo simulation to pick orbits and find the corresponding R_0 uncertainty. We find that there is a 40% chance of getting a 5% measurement of R_0 as early as the year 2003. Seven years later, 3% precision is almost guaranteed, while there is a 30% chance of obtaining 1% precision. All these estimates assume that annual position measurements will continue to be made with the sigma_rho=2 mas precision recently reported by Ghez and coworkers. The precision of the distance measurement is relatively insensitive to the radial velocity errors, provided that the latter are less than 50 km s^-1. Another useful result that would come along with R_0 is the heliocentric radial velocity of Sgr A*. Besides giving an estimate of R_0 that is better than any currently in use, a great advantage of this method is that it is free from the kind of systematic errors that affect other methods currently in use. Moreover, a sustained observing campaign will produce predictable improvements in the measurement of R_0 whether the quality of the position and velocity measurements improves or not.