The giant flare observed on Dec. 27th 2004 from SGR 1806-20 has revived the idea that a fraction of short (<2 s) Gamma Ray Bursts (GRBs) is due to giant flares from Soft Gamma Ray Repeaters located in nearby galaxies. One of the distinguishing characteristics of these events is the thermal (black body) spectrum with temperatures ranging from ~50 to ~180 keV, with the highest temperature observed for the initial 0.2 s spike of the Dec. 27th 2004 event. We analyzed the spectra of a complete sample of short GRBs with peak fluxes greater than 4 photon s^(-1) cm^(-2) detected by BATSE. Of the 115 short GRBs so selected only 76 had sufficient signal to noise to allow the spectral analysis. We find only 3 short GRBs with a spectrum well fitted by a black body, with 60<kT<90 keV, albeit with a considerably longer duration (i.e. >1 sec) and a more complex light curve than the Dec. 27th 2004 event. This implies a stringent limit on the rate of extragalactic SGR giant flares with spectral properties analogous to the Dec. 27th flare. We conclude that up to 4 per cent of the short GRBs could be associated to giant flares (2 sigma confidence). This implies that either the distance to SGR 1806-20 is smaller than 15 kpc or the rate of Galactic giant flares is lower than the estimated 0.033 per year.
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