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 ∼ 10–10 2 yr. PRSs with t > 20 yr require an internal field ( B int ∼ 10 16 –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 μ Jy and self-absorption near 200 MHz at 180 μ Jy. For PRS3, a rotation-powered MWN is viable only if t ∼ 10 yr; an inverted spectrum beyond 150 GHz would rule out this scenario.