Nonthermal afterglow of the binary neutron star merger GW170817: a more natural modeling of electron energy distribution leads to a qualitatively different new solution

The observed nonthermal afterglow spectrum of the binary neutron star (BNS) merger GW170817 from radio to X-ray are consistent with synchrotron radiation by shock-accelerated electrons. However, previous afterglow modeling studies were based on a simplified assumption that the acceleration efficiency is extremely high, i.e. all electrons in the shock are accelerated as a nonthermal population. This affects the estimate of the minimum electron energy and hence $\nu_m$, the peak frequency of the afterglow spectrum. Here we present Bayesian fitting to the observed data with a more natural electron energy distribution, in which the acceleration efficiency is a free parameter. Interestingly, the maximum likelihood solutions are found with radio flux below $\nu_m$ in the early phase, in contrast to previous studies that found the radio frequency always above $\nu_m$. Therefore the $\nu_m$ passage through the radio band could have been clearly detected for GW170817, if sufficient low-frequency radio data had been taken in early time. In the new solutions, the lowest energy of electrons is found close to equipartition with the post shock protons, but only a small fraction ($<$10\%) of electrons are accelerated as nonthermal particles. The jet energy and interstellar medium density are increased by 1--2 orders of magnitude from the conventional modeling, though these are still consistent with other constraints. We encourage to take densely sampled low-frequency radio data in the early phase for future BNS merger events, which would potentially detect $\nu_m$ passage and give a strong constraint on electron energy distribution and particle acceleration efficiency.