The late jet in gamma-ray bursts and its interactions with a supernova ejecta and a cocoon

Late X-ray flares observed in X-ray afterglows of gamma-ray bursts (GRBs) suggest late central engine activities at a few minuets to hours after the burst. A few unambiguously confirmed cases of supernova associations with nearby long GRBs imply that an accompanying supernova-like component might be a common feature in all long GRB events. These motivate us to study the interactions of a late jet, responsible for a x-ray flare, with various components in a stellar explosion, responsible for a GRB. These components include a supernova shell-like ejecta, and a cocoon that was produced when the main jet producing the GRB itself was propagating through the progenitor star. We find that the interaction between the late jet and the supernova ejecta may produce a luminous (up to 10^49 erg s^-1) thermal X-ray transient lasting for ~ 10 s. The interaction between the late jet and the cocoon produces synchrotron self-absorbed non-thermal emission, with the observed peak X-ray flux density from 0.001 micro Jy to 1 mJy at 1 keV and a peak optical flux density from 0.01 micro Jy to 0.1 Jy (for a redshift z= 2). The light curve due to the late jet - cocoon interaction has very small pulse-width-to-time ratio, \Delta t / t \approx 0.01 - 0.5, where t is the pulse peak time since the burst trigger. Identifying these features in current and future observations would open a new frontier in the study of GRB progenitor stars.