Scatter in the Relation between Persistent Radio Source Luminosity and Fast Radio Burst Rotation Measure: A Window into Circum-burst Environments

TL;DR

This paper introduces a new method using the scatter in the relation between radio source luminosity and rotation measure to probe the evolution and environment of nebulae around repeating fast radio bursts, providing insights into their physical nature.

Contribution

It develops a diagnostic framework linking luminosity and rotation measure residuals to nebula evolution, constraining the dynamics of circum-burst environments in FRBs.

Findings

The nebula's evolutionary index is constrained to $oxed{ ext{1.5} ext{ ± } ext{0.7}}$.

The results favor forward shock models over SNR Sedov-Taylor or PWN decaying wind scenarios.

Active repeaters are likely powered by young, rapidly expanding nebulae.

Abstract

The association of persistent radio sources (PRSs) with repeating fast radio bursts (FRBs) offers unique insights into their circum-burst environments. Building upon the physical link between PRS luminosity ($L_\nu$) and FRB rotation measure (RM), we introduce a novel diagnostic framework utilizing the intrinsic scatter of the $L_\nu - |{\rm RM}|$ relation as a physical probe of nebula dynamics. We demonstrate that this scatter encodes critical information regarding the temporal evolution of the nebula radius ($R \propto t^\alpha$). By deriving a generic scaling $L_\nu \propto R^\epsilon |\mathrm{RM}|$ and analyzing the residuals of the five confirmed FRB-PRS systems, we constrain the nebula's evolutionary index to $\alpha|\epsilon| = 1.5 \pm 0.7$ (1$\sigma$ uncertainty). This measurement provides a powerful diagnostic tool for distinguishing among different astrophysical scenarios. Its value deviates from the expectations for supernova remnants (SNRs) in the Sedov-Taylor phase ($\alpha|\epsilon| \sim 0.2-0.4$), reverse shocks during the free-expansion phase of SNR/interstellar medium (ISM) interactions ($\alpha|\epsilon| \gtrsim 3.5$), and pulsar wind nebulae (PWNe) powered by a decaying wind ($\alpha|\epsilon| \sim 0-0.15$). Instead, it is more consistent with forward shocks in the free-expansion phase of both SNR/ISM and PWN/SNR systems ($\alpha|\epsilon| \sim 2.0-2.8$), and young PWNe driven by a nearly constant wind ($\alpha|\epsilon| \sim 1$). These findings suggest that active repeaters are powered by dynamically young, rapidly expanding nebulae. While currently limited by the small sample size, this framework establishes a robust methodology for future population studies to constrain the physical origin of PRSs.