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With the rapid increase of fast radio burst (FRB) detections within the pastfew years, there is now a catalogue being developed for all-sky extragalacticdispersion measure (DM) observations in addition to the existing collection ofall-sky extragalactic Faraday rotation measurements (RMs) of radio galaxies. Wepresent a method of reconstructing all-sky information of the Galactic magneticfield component parallel to the line of sight, $B_{\parallel}$, using simulatedobservations of the RM and DM along lines of sight to radio galaxies and FRBpopulations, respectively. This technique is capable of distinguishing betweendifferent input Galactic magnetic field and thermal electron density models.Significant extragalactic contributions to the DM are the predominantimpediment in accurately reconstructing the Galactic DM and$\left<B_{\parallel}\right>$ skies. We look at ways to improve thereconstruction by applying a filtering algorithm on the simulated DM lines ofsight and we derive generalized corrections for DM observations at $|b|$ > 10deg that help to disentangle Galactic and extragalactic DM contributions.Overall, we are able to reconstruct both large-scale Galactic structure andlocal features in the Milky Way's magnetic field from the assumed models. Wediscuss the application of this technique to future FRB observations andaddress possible differences between our simulated model and observed data,namely: adjusting the priors of the inference model, an unevenly distributedpopulation of FRBs on the sky, and localized extragalactic DM structures.

A method for reconstructing the Galactic magnetic field using dispersion of fast radio bursts and Faraday rotation of radio galaxies