$S^5$: Probing the Milky Way and Magellanic Clouds potentials with the 6-D map of the Orphan-Chenab stream

We present a 6-D map of the Orphan-Chenab (OC) stream by combining the data from Southern Stellar Stream Spectroscopic Survey ($S^5$) and {\it Gaia}. We reconstruct the proper motion, radial velocity, distance, on-sky track and stellar density along the stream with spline models. The stream has a total luminosity of $M_V=-8.2$ and metallicity of $\mathrm{[Fe/H]}=-1.9$, similar to classical Milky Way (MW) satellites like Draco. The stream shows drastic changes in its physical width varying from 200 pc to 1 kpc, but a constant line of sight velocity dispersion of 5 km/ss. Despite the large apparent variation in the stellar number density along the stream, the flow rate of stars along the stream is remarkably constant. We model the 6-D stream track by a Lagrange-point stripping method with a flexible MW potential in the presence of a moving extended Large Magellanic Cloud (LMC). This allows us to constrain the mass profile of the MW within the distance range 15.6 < r < 55.5 kpc, with the best measured enclosed mass of $(2.85\pm 0.1)\times 10^{11}\,M_\odot$ within 32.4 kpc. Our stream measurements are highly sensitive to the LMC mass profile with the most precise measurement of its enclosed mass made at 32.8 kpc, $(7.02\pm 0.9)\times10^{10}\, {\rm M}_\odot$. We also detect that the LMC dark matter halo extends to at least 53 kpc. The fitting of the OC stream allows us to constrain the past LMC trajectory and the degree of dynamical friction it experienced. We demonstrate that the stars in the OC stream show large energy and angular momentum spreads caused by LMC perturbation.