The Low-Frequency Absorption Turnover in Fast Radio Burst Spectra

This paper computes free-free absorption turnover frequencies for fast radio bursts across the range of emission measures expected in host and near-source environments, derives the bound that detection at 400 megahertz places on a burst's near-source emission measure, and shows how absorption and dispersion together localise the gas around burst sources. The headline results are as follows. Turnover frequency for an emission measure of ten to the fourth: 0.0656 GHz; Turnover frequency for an emission measure of ten to the sixth: 0.588 GHz; Turnover frequency for an emission measure of ten to the seventh: 1.76 GHz; Optical depth at 400 MHz for an emission measure of ten to the fifth: 0.225; Emission measure at which the turnover reaches 400 MHz: 4.45e+05 pc cm-6; Attenuation factor at 400 MHz for an emission measure of ten to the sixth: 0.106. All values are computed from the stated assumptions and published inputs; the study is simulated and computed, not measured.