A large fraction of gamma-ray burst ( GRB ) spectra are very hard below the peak .
Indeed , the observed distribution of sub-peak power-law indices , \alpha , has been used as an argument for a photospheric origin of GRB spectra .
Here , we investigate what fraction of GRBs have spectra that are consistent with emission from a photopshere in a non-dissipative outflow .
This is the simplest possible photospheric emission scenario .
We create synthetic spectra , with a range of peak energies , by folding the theoretical predictions through the detector response of the FERMI /GBM detector .
These simulated spectral data are fit with typically employed empirical models .
We find that the low-energy photon indices obtain values ranging -0.4 < \alpha < 0.0 , peaking at around -0.1 , thus covering a non-negligible fraction of observed values .
These values are significantly softer than the asymptotic value of the theoretical spectrum of \alpha \sim 0.4 .
The reason for the \alpha -values to be much softer than expected , is the limitation of the empirical functions to capture the true curvature of the theoretical spectrum .
We conclude that more than a 1 / 4 of the bursts in the GBM catalogue have at least one time-resolved spectrum , whose \alpha -values are consistent with a non-dissipative outflow , releasing its thermal energy at the photosphere .
The fraction of spectra consistent with emission from the photosphere will increase even more if dissipation of kinetic energy in the flow occurs below the photosphere .