Reconciling observed gamma-ray burst prompt spectra with synchrotron radiation?

International audienceContext. Gamma-ray burst emission in the prompt phase is often interpreted as synchrotron radiation from high-energy electrons accelerated in internal shocks. Fast synchrotron cooling of a power-law distribution of electrons leads to the prediction that the slope below the spectral peak has a photon index α = -3/2 (N(E) ∝ Eα). However, this differs significantly from the observed median value α ≈ -1. This discrepancy has been used to argue against this scenario. Aims: We quantify the influence of inverse Compton (IC) and adiabatic cooling on the low energy slope to understand whether these processes can reconcile the observed slopes with a synchrotron origin. Methods: We use a time-dependent code developed to calculate the GRB prompt emission within the internal shock model. The code follows both the shock dynamics and electron energy losses and can be used to generate lightcurves and spectra. We investigate the dependence of the low-energy slope on the parameters of the model and identify parameter regions that lead to values α > -3/2. Results: Values of α between -3/2 and -1 are reached when electrons suffer IC losses in the Klein-Nishina regime. This does not necessarily imply a strong IC component in the Fermi/LAT range (GeV) because scatterings are only moderately efficient. Steep slopes require that a large fraction (10-30%) of the dissipated energy is given to a small fraction (⪉1%) of the electrons and that the magnetic field energy density fraction remains low (⪉ 0.1%). Values of α up to -2/3 can be obtained with relatively high radiative efficiencies (>50%) when adiabatic cooling is comparable with radiative cooling (marginally fast cooling). This requires collisions at small radii and/or with low magnetic fields. Conclusions: Amending the standard fast cooling scenario to account for IC cooling naturally leads to values α up to -1. Marginally fast cooling may also account for values of α up to -2/3, although the conditions required are more difficult to reach. About 20% of GRBs show spectra with slopes α > -2/3. Other effects, not investigated here, such as a thermal component in the electron distribution or pair production by high-energy gamma-ray photons may further affect α. Still, the majority of observed GRB prompt spectra can be reconciled with a synchrotron origin, constraining the microphysics of mildly relativistic internal shocks