Synchrotron cooling in energetic gamma-ray bursts observed by the Fermi Gamma-Ray Burst Monitor

Context. We study the time-resolved spectral properties of energetic gamma-ray bursts (GRBs) with good high-energy photon statistics observed by the Gamma-Ray Burst Monitor (GBM) onboard the Fermi Gamma-Ray Space Telescope. Aims. We aim to constrain in detail the spectral properties of GRB prompt emission on a time-resolved basis and to discuss the theoretical implications of the fitting results in the context of various prompt emission models. Methods. Our sample comprises eight GRBs observed by the Fermi GBM in its first five years of mission, with 1 keV–1 MeV fluence f> 1.0 × 10-4 erg cm-2 and a signal-to-noise ratio level of S/N ≥ 10.0 above 900 keV. We performed a time-resolved spectral analysis using a variable temporal binning technique according to optimal S/N criteria, resulting in a total of 299 time-resolved spectra. We performed Band function fits to all spectra and obtained the distributions for the low-energy power-law index α, the high-energy power-law index β, the peak energy in the observed νFν spectrum Ep, and the difference between the low- and high-energy power-law indices Δs = α − β. We also applied a physically motivated synchrotron model, which is a triple power-law with constrained power-law indices and a blackbody component, to test the prompt emission for consistency with a synchrotron origin and obtain the distributions for the two break energies Eb,1 and Eb,2, the middle segment power-law index β, and the Planck function temperature kT. Results. The Band function parameter distributions are α = -0.73+0.16-0.21, β =ي-2.13+0.28-0.56, Ep = 374.4+307.3-187.7 , , keV (log10Ep = 2.57+0.26-0.30), and Δs = 1.38+0.54-0.31 , with average errors σα ~ 0.1, σβ ~ 0.2, and σEp ~ 0.1Ep. Using the distributions of Δs and β, the electron population index p is found to be consistent with the “moderately fast” scenario, in which fast- and slow-cooling scenarios cannot be distinguished. The physically motivated synchrotron-fitting function parameter distributions are Eb,1 = 129.6+132.2-32.4 keV, Eb,2 = 631.4+582.6-309.6 keV, β = -1.72+0.48-0.25 , and kT = 10.4+4.9-3.7 keV, with average errors σβ ~ 0.2, σEb,1 ~ 0.1Eb,1, σEb,2 ~ 0.4Eb,2, and σkT ~ 0.1kT. This synchrotron function requires the synchrotron injection and cooling break (i.e., Emin and Ecool) to be close to each other within a factor of ten, often in addition to a Planck function. Conclusions. A synchrotron model is found that is consistent with most of the time-resolved spectra for eight energetic Fermi GBM bursts with good high-energy photon statistics as long as both the cooling and injection break are included and the leftmost spectral slope is lifted either by including a thermal component or when an evolving magnetic field is accounted for.