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Recent maps of the halo using RR Lyrae from Pan-STARRS1 have clearly depictedthe spatial structure of the Sagittarius stream. These maps show the leadingand trailing stream apocenters differ in galactocentric radius by a factor oftwo, and also resolve substructure in the stream at these apocenters. Here wepresent dynamical models that reproduce these features of the stream in simpleGalactic potentials. We find that debris at the apocenters must be dynamicallyyoung, in the sense of being stripped off in the last two pericentric passages,while the Sagittarius dwarf is currently experiencing a third passage. Theratio of apocenters is sensitive to both dynamical friction and the outer slopeof the Galactic rotation curve. These dependences can be understood with simpleregularities connecting the apocentric radii, circular velocities, and orbitalperiod of the progenitor. The effect of dynamical friction on the stream can beconstrained using substructure within the leading apocenter. Our ensembles ofmodels are not intended as statistically proper fits to the stream.Nevertheless, out of the range of models we consider, we consistently find themass within 100 kpc to be $\sim 7 \times 10^{11} \, M_{\odot}$, with a nearlyflat rotation curve between 50 and 100 kpc. This points to a more extendedGalactic halo than assumed in some current models. As in previous work, we findprolate or triaxial halos ease agreement with the track of the leading stream.We display the behavior of our models in various observational spaces andcharacterize the substructure expected within the stream. In particular, theyoung trailing stream visible near trailing apocenter should exhibit a tighttrend of velocity with distance separate from the older debris, and we suggestthat this will serve as an especially useful probe of the outer Galacticpotential.

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