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Recent studies of fast radio bursts (FRBs) have led to many theoriesassociating them with young neutron stars. If this is the case, then thepresence of supernova ejecta and stellar winds provide a changing dispersionmeasure (DM) and rotation measure (RM) that can potentially be probes of theenvironments of FRB progenitors. Here we summarize the scalings for the DM andRM in the cases of a constant density ambient medium and of a progenitorstellar wind. Since the amount of ionized material is controlled by thedynamics of the reverse shock, we find the DM changes more slowly than inprevious simpler work, which simply assumed a constant ionization fraction.Furthermore, the DM can be constant or even increasing as the supernova remnantsweeps up material, arguing that a young neutron star hypothesis for FRBs isnot ruled out if the DM is not decreasing over repeated bursts. The combined DMand RM measurements for the repeating FRB 121102 are consistent with supernovaejecta with an age of $\sim10^2-10^3\,{\rm yrs}$ expanding into a high density($\sim100\,{\rm cm^{-3}}$) interstellar medium. This naturally explains itsrelatively constant DM over many years as well. Other FRBs with much lower RMsmay indicate that they are especially young supernovae in wind environments orthat their DMs are largely from the intergalactic medium. We therefore cautionabout inferring magnetic fields from simply by dividing an RM by DM, becausethese quantities could originate from distinct regions along the path an FRBpropagates.

Dispersion and Rotation Measure of Supernova Remnants and Magnetized Stellar Winds: Application to Fast Radio Bursts