Connecting the Milky Way potential profile to the orbital timescales and spatial structure of the Sagittarius Stream

Recent maps of the halo using RR Lyrae from Pan-STARRS1 have clearly depicted the spatial structure of the Sagittarius stream. These maps show the leading and trailing stream apocenters differ in galactocentric radius by a factor of two, and also resolve substructure in the stream at these apocenters. Here we present dynamical models that reproduce these features of the stream in simple Galactic potentials. We find that debris at the apocenters must be dynamically young, in the sense of being stripped off in the last two pericentric passages, while the Sagittarius dwarf is currently experiencing a third passage. The ratio of apocenters is sensitive to both dynamical friction and the outer slope of the Galactic rotation curve. These dependences can be understood with simple regularities connecting the apocentric radii, circular velocities, and orbital period of the progenitor. The effect of dynamical friction on the stream can be constrained using substructure within the leading apocenter. Our ensembles of models are not intended as statistically proper fits to the stream. Nevertheless, out of the range of models we consider, we consistently find the mass within 100 kpc to be $\sim 7 \times 10^{11} \, M_{\odot}$, 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. As in previous work, we find prolate or triaxial halos ease agreement with the track of the leading stream. We display the behavior of our models in various observational spaces and characterize the substructure expected within the stream. In particular, the young trailing stream visible near trailing apocenter should exhibit a tight trend of velocity with distance separate from the older debris, and we suggest that this will serve as an especially useful probe of the outer Galactic potential.