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GRB 110721A: photosphere "death line" and the physical origin of the GRB "Band" function

The prompt emission spectra of gamma-ray bursts (GRBs) usually have a dominant component that is well described by a phenomenological "Band" function. The physical origin of this spectral component is debated. Although the traditional interpretation is synchrotron radiation of non-thermal electrons accelerated in internal shocks or magnetic dissipation regions, a growing trend in the community is to interpret this component as modified thermal emission from a dissipative photosphere of a GRB fireball. We analyze the time dependent spectrum of GRB 110721A detected by {\em Fermi} GBM and LAT, and pay special attention to the rapid evolution of the peak energy $E_p$. We define a "death line" of thermally-dominated dissipative photospheric emission in the $E_p - L$ plane, and show that $E_p$ of GRB 110721A at the earliest epoch has a very high $E_p \sim 15$ MeV that is beyond the "death line". Together with the finding that an additional "shoulder" component exists in this burst that is consistent with a photospheric origin, we suggest that at least for some bursts, the "Band" component is not from a dissipative photosphere, but must invoke a non-thermal origin (e.g. synchrotron or inverse Compton) in the optically thin region of a GRB outflow. We also suggest that the rapid "hard-to-soft" spectral evolution is consistent with the quick discharge of magnetic energy in a magnetically-dominated outflow in the optically thin region.