Locating the orbits delineated by tidal streams

ABSTRACT

We describe a technique that finds orbits through the Galaxy that are consistent with measurements of a tidal stream, taking into account the extent that tidal streams do not precisely delineate orbits. We show that if accurate line-of-sight velocities are measured along a well-defined stream, the technique recovers the underlying orbit through the Galaxy and predicts the distances and proper motions along the stream to high precision. As the error bars on the location and velocities of the stream grow, the technique is able to find more and more orbits that are consistent with the data and the uncertainties in the predicted distances and proper motions increase. With radial velocity data along a stream ∼40° long and ≲0.3° wide on the sky accurate to ∼1 km s⁻¹, the precisions of the distances and tangential velocities along the stream are 4 per cent and 5 km s⁻¹, respectively. The technique can be used to diagnose the Galactic potential: if circular speed curve is actually flat, both a Keplerian potential and Φ(r) ∝r are readily excluded. Given the correct radial density profile for the dark halo, the halo's mass can be determined to a precision of 5 per cent.