On re-brightening afterglows of XRFs, Soft GRBs and GRB081028
  It has been claimed recently that Swift has captured for the first time a
late-time afterglow re-brightening of clear nonflaring origin after the steep
decay of the prompt emission in a long gamma-ray burst (GRB), which may have
been produced by a narrow jet viewed far off-axis. However, this interpretation
of the observed re-brightening of the X-ray afterglow (AG) of GRB081028 is
unlikely in view of its large equivalent isotropic gamma-ray energy. Moreover,
we show that the late-time re-brightening of the AG of GRB081028 is well
explained by the cannonball (CB) model of GRBs as a synchrotron flare emitted
when the jet that produced the GRB in a star formation region (SFR) in the host
galaxy crossed the SFR boundary into the interstellar medium or the halo of the
host galaxy. We also show that all the other observed properties of GRB081028
and its afterglow are well reproduced by the CB model. On the other hand, we
demonstrate that far-off axis GRBs, which in the CB model are `soft' GRBs and
XRFs and consequently have much smaller isotropic equivalent gamma-ray
energies, have slowly rising afterglows with a late-time power-law decay
identical to that of ordinary GRBs, in good agreement with the CB model
predictions.
