Probing the Dispersion and Rotation Measure Contributions from Supernova Remnants in Fast Radio Burst Source Environments with 1D SNR Simulation
Fast radio bursts (FRBs) provide a sensitive probe of ionized baryons through their dispersion measure (DM). In addition to slowly evolving cosmological terms, at least two repeaters now show clear secular DM-decrease episodes: FRB~20190520B and FRB~20121102 , supporting a dense, dynamically evolving local environment. We adopt a \emph{forward-modeling} approach and use time-dependent 1D SNR simulations for a young magnetar embedded in SN ejecta, combining single-star and binary-stripped progenitors with HD+NEI calculations to follow shock structure, ionization, and electron density. The shocked region contributes only limited DM ($\lesssim10\,{\rm pc\,cm^{-3}}$), while the dominant time-varying component is the unshocked ejecta, whose early behavior follows ${\rm DM}\propto t^{-\alpha}$ with $\alpha\simeq1.8$--$1.9$. Although shocked-region DM is small, shock-amplified magnetic fields can still generate substantial RM; in our shock-only RM framework, only the $11\,M_\odot$ SS model reproduces the FRB~20121102 RM evolution. Binary-stripped progenitors generally yield smaller DM than single-star models at fixed $M_{\rm ZAMS}$, with composition-dependent mean molecular weights introducing non-monotonic mass trends. Matching the observed ${\rm dDM}/{\rm d}t$ of FRB~20190520B (and the late-stage slope of FRB~20121102), we infer local SNR DM contributions of tens to hundreds ${\rm pc\,cm^{-3}}$. We also find GHz escape is allowed in most models, with $\tau_{\rm ff}=1$ typically reached by $t_{\rm esc}\lesssim70$ yr; for weakly ionized ejecta, the source can be nearly transparent from very early times. These results support a young CCSN/SNR origin for a substantial fraction of ${\rm DM}_{\rm source}$ and highlight that physically consistent local-environment modeling is essential for robust FRB cosmological DM inferences.