Afterglow Imaging and Polarization of Misaligned Structured GRB Jets and Cocoons: Breaking the Degeneracy in GRB 170817A

Abstract

The X-ray to radio afterglow emission of GRB 170817A/GW 170817 so far scales as $F_ν\proptoν^{-0.6}t^{0.8}$ with observed frequency and time, consistent with a single power-law segment of the synchrotron spectrum from the external shock going into the ambient medium. This requires the effective isotropic equivalent afterglow shock energy in the visible region to increase as $\sim t^{1.7}$. The two main channels for such an energy increase are (i) \emph{radial}: more energy carried by slower material (in the visible region) gradually catches up with the afterglow shock and energizes it, and (ii) \emph{angular}: more energy in relativistic outflow moving at different angles to our line of sight, whose radiation is initially beamed away from us but its beaming cone gradually reaches our line of sight as it decelerates. One cannot distinguish between these explanations (or combinations of them) using only the X-ray to radio $F_ν(t)$. Here we demonstrate that the most promising way to break this degeneracy is through afterglow imaging and polarization, by calculating the predicted evolution of the afterglow image (its size, shape and flux centroid) and linear polarization $Π(t)$ for different angular and/or radial outflow structures that fit $F_ν(t)$. We consider two angular profiles -- a Gaussian and a narrow core with power-law wings in energy per solid angle, as well as a (cocoon motivated) (quasi-) spherical flow with radial velocity profile. For a jet viewed off-axis (and a magnetic field produced in the afterglow shock) $Π(t)$ peaks when the jet's core becomes visible, at $\approx2t_p$ where the lightcurve peaks at $t_p$, and the image can be elongated with aspect ratios$\;\gtrsim2$. A quasi-spherical flow has an almost circular image and a much lower $Π(t)$ (peaking at $\approx t_p$) and flux centroid displacement.