We present a Monte Carlo-based population synthesis study of fast radio burst (FRB) dispersion and scattering focusing on the first catalog of sources detected with the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst (CHIME/FRB) project. We simulate intrinsic properties and propagation effects for a variety of FRB population models and compare the simulated distributions of dispersion measures (DMs) and scattering timescales with the corresponding distributions from the CHIME/FRB catalog. Our simulations confirm the results of previous population studies, which suggested that the interstellar medium of the host galaxy alone cannot explain the observed scattering timescales of FRBs. We therefore consider additional sources of scattering, namely, the circumgalactic medium (CGM) of intervening galaxies and the circumburst medium whose properties are modeled based on typical Galactic plane environments. We find that a population of FRBs with scattering contributed by these media is marginally consistent with the CHIME/FRB catalog. In this scenario, our simulations favor a population of FRBs offset from their galaxy centers over a population which is distributed along the spiral arms. However, if the models proposing the CGM as a source of intense scattering are incorrect, then we conclude that FRBs must inhabit environments with more extreme properties than those inferred for pulsars in the Milky Way.
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