Quasi-steady emission from repeating fast radio bursts can be explained by magnetar wind nebulae

Among more than 1000 known fast radio bursts (FRBs), only five sources - FRBs 20121102A, 20190520B, 20201124A, 20240114A and 20190417A - have confirmed associations with persistent radio sources (PRS). The observed quasi-steady emission is consistent with synchrotron radiation from a composite of magnetar wind nebula (MWN) and supernova (SN) ejecta. Using a phenomenological model that incorporates simplified treatments of the nebular dynamics and particle acceleration, we compute the synchrotron flux by solving kinetic equations for energized electrons, accounting for electromagnetic cascades of electron-positron pairs interacting with nebular photons. Within the framework of our model, the rotation-powered scenario requires a young neutron star (NS) with age $t_{\rm age}\approx 20\,{\rm yr}$, dipolar magnetic field $B_{\rm dip}\approx (3-5)\times10^{12}\,{\rm G}$ and initial spin period $P_i\approx 1.5-3\,{\rm ms}$ in an ultra-stripped SN progenitor to account for emissions from FRBs 20121102A and 20190520B. In contrast, FRB 20201124A requires $t_{\rm age}\approx 10\,{\rm yr}$, $B_{\rm dip}\approx 5.5\times10^{13}\,{\rm G}$ and $P_i\approx 10\,{\rm ms}$ in a conventional core-collapse SN progenitor. For the magnetar-flare-powered model, NS aged $t_{\rm age} \approx 25\,/40\,{\rm yr}$ in a USSN progenitor and $t_{\rm age} \approx 12.5\,{\rm yr}$ in a CCSN progenitor explains the observed flux for FRB 20121102A/20190520B and FRB 20201124A, respectively. Finally, we estimate a minimum NS age $t_{\rm age,min} \sim 1-3\,{\rm yr}$ based on the near-source plasma contribution to observed DM, and $t_{\rm age,min} \sim 6.5-10\,{\rm yr}$ from the absence of radio signal attenuation.