2022ApJ...938..132P

This work is a continuation of a previous effort (Panaitescu) to study the cooling of relativistic electrons through radiation (synchrotron and self-Compton) emission and adiabatic losses, with application to the spectra and light curves of the synchrotron gamma-ray burst (GRB) produced by such cooling electrons. Here, we derive the low-energy slope β_LE of a GRB pulse-integrated spectrum and quantify the implications of the measured distribution of β_LE. Radiative processes that produce soft integrated spectra can accommodate the harder slopes measured by CGRO/BATSE and Fermi/GBM only if the magnetic field lifetime t_B is shorter than the time during which the typical GRB electrons cool to radiate below 1-10 keV, which is less than (at most) 10 radiative cooling timescales t_rad of the typical GRB electron. In this case, there is a one-to-one correspondence between t_B and β_LE. To account for low-energy slopes β_LE > -3/4, the adiabatic electron-cooling requires a similar restriction on t_B. In this case, the diversity of slopes arises mostly from how the electron-injection rate varies with time (temporal power-law injection rates yield power-law low-energy GRB spectra) and not from the magnetic field timescale.