Jet propagations, breakouts, and photospheric emissions in collapsing massive progenitors of long-duration gamma-ray bursts

We investigate the following by two-dimensional axisymmetric relativistic hydrodynamical simulations: (1) jet propagations through an envelope of a rapidly rotating and collapsing massive star, which is supposed to be a progenitor of long-duration gamma-ray bursts (GRBs); (2) breakouts and subsequent expansions into stellar winds; and (3) the accompanying photospheric emissions. We find that if the envelope rotates uniformly almost at the mass shedding limit, its outer part eventually stops contracting when the centrifugal force becomes large enough. Then another shock wave is formed, propagates outward, and breaks out of the envelope into the stellar wind. Whether the jet or the centrifugal bounce-induced shock breaks out earlier depends on the timing of jet injection. If the shock breakout occurs earlier, owing to a later injection, the jet propagation and subsequent photospheric emissions are affected substantially. We pay particular attention to observational consequences of the difference in the timing of jet injection. We calculate optical depths to find the location of photospheres, extracting densities, and temperatures at appropriate retarded times from the hydrodynamical data. We show that the luminosity and observed temperature of the photospheric emissions are both much lower than those reported in previous studies. Although luminosities are still high enough for GRBs, the observed temperatures are lower than the energy at the spectral peak expected by the Yonetoku relation. This may imply that energy exchanges between photons and matter are terminated deeper inside or that some non-thermal processes are operating to boost photon energies.