Study of prompt emission of short gamma ray bursts using multi-color blackbody: a clue to the viewing angle

The prompt emission of short gamma ray bursts (sGRBs) with known redshifts are analyzed using the model of multi-color blackbody which is interpreted as the emission from a non-dissipative photosphere taking into account a power law jet structure and the viewing geometry of the jet. We find nearly $69\%$ and $26\%$ of the sample are consistent with multi-color blackbody and a pure blackbody model, respectively. Using this interpretation, we infer that nearly $57\% \, (18\%)$ of the sGRBs in our sample are observed within (or along the edge of) the jet core. The sGRB jets are deduced to possess a narrow core with a median $\theta_c \sim 3^{\circ}$. This suggests the rate of sGRBs that would be viewed within the jet core to be $1.8 - 26 \, \rm Gpc^{-3} \, yr^{-1}$. The power law index of the decreasing Lorentz factor profile of the jet structure is deduced to be $1.3 - 2.2$. The intrinsic luminosity is found to range between $10^{48} - 10^{53}\, \rm erg/s$. The average values of Lorentz factor and nozzle radius of the sGRB jets are inferred to be $210\, (85)$ and $10^{7.7} \, (10^{9.6}) \, \rm cm$ for the cases when the photosphere forms in the coasting (accelerating) phase respectively. The viability of the inferred values of the different parameters of the GRB outflow and viewing geometry within this physical interpretation enhances the prospect of the photospheric emission model to explain the observed GRB spectrum.