The radio afterglow of Swift J1644+57 reveals a powerful jet with fast core and slow sheath

We model the non-thermal transient Swift J1644+57 as resulting from a relativistic jet powered by the accretion of a tidally-disrupted star onto a super-massive black hole. Accompanying synchrotron radio emission is produced by the shock interaction between the jet and the dense circumnuclear medium, similar to a gamma-ray burst afterglow. An open mystery, however, is the origin of the late-time radio rebrightening, which occurred well after the peak of the jetted X-ray emission. Here, we systematically explore several proposed explanations for this behavior by means of multi-dimensional hydrodynamic simulations coupled to a self-consistent radiative transfer calculation of the synchrotron emission. Our main conclusion is that the radio afterglow of Swift J1644+57 is not naturally explained by a jet with a one-dimensional top-hat angular structure. However, a more complex angular structure comprised of an ultra-relativistic core (Lorentz factor $\Gamma \sim 10$) surrounded by a slower ($\Gamma \sim $ 2) sheath provides a reasonable fit to the data. Such a geometry could result from the radial structure of the super-Eddington accretion flow or as the result of jet precession. The total kinetic energy of the ejecta that we infer of $\sim$ few $10^{53}\,$erg requires a highly efficient jet launching mechanism. Our jet model providing the best fit to the light curve of the on-axis event Swift J1644+57 is used to predict the radio light curves for off-axis viewing angles. Implications for the presence of relativistic jets from TDEs detected via their thermal disk emission, as well as the prospects for detecting orphan TDE afterglows with upcoming wide-field radio surveys and resolving the jet structure with long baseline interferometry, are discussed.