Connecting the Milky Way potential profile to the orbital time-scales and spatial structure of the Sagittarius Stream

Recent maps of the halo using RR Lyrae from Pan-STARRS1 depict the spatial structure of the Sagittarius stream, showing the leading and trailing stream apocentres differ in Galactocentric radius by a factor of 2, and also resolving substructure in the stream at these apocentres. Here we present dynamical models that reproduce these features of the stream in simple Galactic potentials. We find that debris at the apocentres must be dynamically young, being stripped off in pericentric passages either one or two orbital periods ago. The ratio of the leading and trailing apocentres is sensitive to both dynamical friction and the outer slope of the Galactic rotation curve. These dependencies can be understood with simple regularities connecting the apocentric radii, circular velocities, and orbital period of the progenitor. The effect of dynamical friction can be constrained using substructure within the leading apocentre. Our models are far from final; the errors allowed when sampling parameter space are deliberately generous, not every stream feature is reproduced, and we explore a limited set of potentials. Still, it is interesting that we consistently find the mass within 100 kpc to be ∼ 7 × 10^{11} M_{⊙}, with a nearly flat rotation curve between 50 and 100 kpc. This points to a more extended Galactic halo than assumed in some current models. We show one example model in various observational dimensions. A plot of velocity versus distance separates younger from older debris, and suggests that the young trailing debris will serve as an especially useful probe of the outer Galactic potential.