Tidal Streams as Probes of the Galactic Potential

We explore the use of tidal streams from Galactic satellites to recover thepotential of the Milky Way. Our study is motivated both by the discovery of thefirst lengthy stellar stream in the halo (\cite{it98}) and by the prospect ofmeasuring proper motions of stars brighter than 20th magnitude in such a streamwith an accuracy of $\sim 4\mu as/$yr, as will be possible with the SpaceInterferometry Mission (SIM). We assume that the heliocentric radial velocitiesof these stars can be determined from supporting ground-based spectroscopicsurveys, and that the mass and phase-space coordinates of the Galacticsatellite with which they are associated will also be known to SIM accuracy.Using results from numerical simulations as trial data sets, we find that, ifwe assume the correct form for the Galactic potential, we can predict thedistances to the stars as a consequence of the narrow distribution of energyexpected along the streams. We develop an algorithm to evaluate the accuracy ofany adopted potential by requiring that the satellite and stars recombinewithin a Galactic lifetime when their current phase-space coordinates areintegrated backwards. When applied to a four-dimensional grid of triaxiallogarithmic potentials, with varying circular velocities, axis ratios andorientation of the major-axis in the disk plane, the algorithm can recover theparameters used for the Milky Way in a simulated data set to within a fewpercent using only 100 stars in a tidal stream.Comment: Revised version - original algorithm generalised to be applicable to any potential shape. LaTeX, 12 pages including 3 figures. To be published in ApJ Letter