We study the spectral evolution of 13 short duration Gamma Ray Bursts (GRBs) detected by the Gamma Burst Monitor (GBM) on board Fermi. We study spectra resolved in time at the level of 2-512 ms in the 8 keV-35 MeV energy range. We find a strong correlation between the observed peak energy Ep and the flux P within individual short GRBs. The slope of the Ep P^s correlation for individual bursts ranges between ~0.4 and ~1. There is no correlation between the low energy spectral index and the peak energy or the flux. Our results show that in our 13 short GRBs Ep evolves in time tracking the flux. This behavior is similar to what found in the population of long GRBs and it is in agreement with the evidence that long GRBs and (the still few) short GRBs with measured redshifts follow the same rest frame Ep-Liso correlation. Its origin is most likely to be found in the radiative mechanism that has to be the same in both classes of GRBs.
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