Persistent Radio Sources Associated with Fast Radio Bursts: Implications from Magnetar Progenitors

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 a 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 R_eq ∼ 0.1 pc that is consistent with the radio scintillation estimates (>0.03 pc) and radio imaging limits (<0.7 pc). This compact size favors low expansion speeds and large initial spin periods, P_i ≳ 10 ms, ruling out millisecond magnetar progenitors. Given P_i ≳ 10 ms, a current size of ∼0.1 pc, a supernova kinetic energy E SN ∼ 1 0 50 - 1 0 51 erg, and an ejecta mass M ∼ 3-10 M_⊙, the PRS age is t ∼ 10-10² yr. PRSs with t > 20 yr require an internal field (B_int ∼ 10¹⁶-10^16.5 G) with a decay timescale t_d ∼ 10-10^2.5 yr. The slowest field decay ( t d , max ∼ 500 yr) favors subenergetic supernovae ( E SN ∼ 1 0 50 erg) with massive ejecta (M ≳ 10 M_⊙) and a low-ionization fraction (∼3%). For the subenergetic scenario, for the confirmed PRSs, we predict a cooling break at 100-150 GHz at 20-40 μJy and self-absorption near 200 MHz at 180 μJy. For PRS3, a rotation-powered MWN is viable only if t ∼ 10 yr; an inverted spectrum beyond 150 GHz would rule out this scenario.