Stream–orbit misalignment – II. A new algorithm to constrain the Galactic potential

Abstract

In the first of these two papers we demonstrated that assuming streams delineate orbits can lead to order one errors in potential parameters for realistic Galactic potentials. Motivated by the need for an improvement on orbit-fitting, we now present an algorithm for constraining the Galactic potential using tidal streams without assuming that streams delineate orbits. This approach is independent of the progenitor mass so is valid for all observed tidal streams. The method makes heavy use of angle-action variables and seeks the potential which recovers the expected correlations in angle space. We demonstrate that the method can correctly recover the parameters of a simple two-parameter logarithmic potential by analysing an N-body simulation of a stream. We investigate the magnitude of the errors in observational data for which the method can still recover the correct potential and compare this to current and future errors in data. The errors in the observables of individual stars for current and near future data are shown to be too large for the direct use of this method, but when the data are averaged in bins on the sky, the resulting averaged data are accurate enough to constrain correctly the potential parameters for achievable observational errors. From pseudo-data with errors comparable to those that will be furnished in the era of Gaia (20 per cent distance errors, 1.2 mas/yr proper motion errors, and 10 km/s line-of-sight velocity errors) we recover the circular velocity, V_c=220 km/s, and the flattening of the potential, q=0.9, to be V_c=223+/-10km/s and q=0.91+/-0.09.