Cosmological Parameter Estimate from Persistent Radio Sources of Fast Radio Bursts

We introduce a novel method to constrain the Hubble constant ($H_0$) by combining fast radio bursts (FRBs) and their persistent radio sources (PRSs) through the observationally validated Yang relation, $L_{\nu }\propto \mathrm{\mid }\mathrm{R}\mathrm{M}\mathrm{\mid }$, which links PRS luminosity to the rotation measure (RM) of the associated FRB. Using a mock sample of PRSs, we demonstrate that the Yang relation can help to unravel the degeneracies among $H_0$, baryon density parameter ${\mathrm{\Omega }}_b$, and baryon fraction in the intergalactic medium $f_{\mathrm{I}\mathrm{G}\mathrm{M}}$ in the traditional approach of using dispersion measure only to perform cosmological analyses. Our method employs a two-stage Markov Chain Monte Carlo (MCMC) analysis to constrain $H_0$. Using the available data of six observed PRS systems, we obtain a preliminary constraint of $H_0=75\pm 30\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$. We briefly discuss possible refinements of the method by reducing residual degeneracies and systematic uncertainties using future data and physical modeling. Our results indicate that the Yang relation can potentially become a new probe for performing FRB cosmology.