The rare association of three persistent radio sources (confirmed PRS1 and PRS2, candidate PRS3) with repeating fast radio bursts (FRB 20121102A, 20190520B, 20201124A) offers a unique probe into their magneto-ionic environments. PRSs are attributed to synchrotron emission from relativistic charged particles of magnetar wind nebula (MWN) powered by spin-down magnetohydrodynamic wind or internal magnetic field decay. Using a multizone hydrodynamic model, we track MWN evolution to constrain magnetar progenitor properties. For PRS1 and PRS2, we find an equipartition radius Rₑq 0. 1 pc that is consistent with the radio scintillation estimates (> 0. 03 pc) and radio imaging limits (20 years require an internal field (Bᵢnt 10^16-10^16. 5\;G) with a decay timescale td 10-10^2. 5 yr. The slowest field decay (td, max 500 yr) favors sub-energetic supernovae (ESN 10^50 erg) with massive ejecta (M 10\; M_) and low ionization fraction (3\%). For the sub-energetic scenario for the confirmed PRSs, we predict a cooling break at 100-150 gigahertz at 20-40 \; μJy and self-absorption near 200 megahertz at 180\; μJy. For PRS3, a rotation-powered MWN is viable only if t 10 yr; an inverted spectrum beyond 150 gigahertz would rule out this scenario.
Rahaman et al. (Tue,) studied this question.