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.