Fitting orbits to tidal streams

Abstract

Recent years have seen the discovery of many tidal streams through the Galaxy. Relatively straightforward observations of a stream allow one to deduce three phase-space coordinates of an orbit. An algorithm is presented that reconstructs the missing phase-space coordinates from these data. The reconstruction starts from assumed values of the Galactic potential and a distance to one point on the orbit, but with noise-free data the condition that energy be conserved on the orbit enables one to reject incorrect assumptions. The performance of the algorithm is investigated when errors are added to the input data that are comparable to those in published data for the streams of Pal 5. It is found that the algorithm returns distances and proper motions that are accurate to of order one percent, and enables one to reject quite reasonable but incorrect trial potentials. In practical applications it will be important to minimize errors in the input data, and there is considerable scope for doing this.