We report on time-resolved spectroscopy of the 63 brightest bursts of SGR J1550-5418, detected with Fermi/Gamma-ray Burst Monitor during its 2008-2009 intense bursting episode. We performed spectral analysis down to 4 ms time-scales, to characterize the spectral evolution of the bursts. Using a Comptonized model, we find that the peak energy, E_peak, anti-correlates with flux, while the low-energy photon index remains constant at -0.8 up to a flux limit F~10^-5 erg s-1 cm-2. Above this flux value the E_peak-flux correlation changes sign, and the index positively correlates with flux reaching 1 at the highest fluxes. Using a two black-body model, we find that the areas and fluxes of the two emitting regions correlate positively. Further, we study here for the first time, the evolution of the temperatures and areas as a function of flux. We find that the area-kT relation follows lines of constant luminosity at the lowest fluxes, R^2 propto kT^-4, with a break at higher fluxes ($F>10^-5.5 erg s-1 cm-2). The area of the high-kT component increases with flux while its temperature decreases, which we interpret as due to an adiabatic cooling process. The area of the low-kT component, on the other hand, appears to saturate at the highest fluxes, towards R_max~30 km. Assuming that crust quakes are responsible for SGR bursts and considering R_max as the maximum radius of the emitting photon-pair plasma fireball, we relate this saturation radius to a minimum excitation radius of the magnetosphere, and put a lower limit on the internal magnetic field of SGR J1550-5418, B_int>~4.5x10^15 G.
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